ERFC.PRECISE Function (LibreOffice Calc)

• Computes the complementary error function
• Provides higher precision than ERFC
• Used in Gaussian tail probability, diffusion modeling, and engineering
• Handles any real input

ERFC.PRECISE(x)

Arguments

• x:
  The value at which to evaluate the complementary error function.

[ \text{ERFC}(x) = 1 - \text{ERF}(x) ]

[ \text{ERFC}(x) = \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2} , dt ]

ERFC.PRECISE uses a more stable numerical algorithm.

Standard complementary error function

=ERFC.PRECISE(1)
→ 0.157299207050285

Negative input

=ERFC.PRECISE(-1)
→ 1.842700792949715

Zero input

=ERFC.PRECISE(0)
→ 1

Large positive input

=ERFC.PRECISE(6)
→ extremely small number (close to 0)

Convert to normal distribution tail probability

=0.5 * ERFC.PRECISE(x / SQRT(2))

Probability between two z‑scores

=0.5 * (ERFC.PRECISE(a / SQRT(2)) - ERFC.PRECISE(b / SQRT(2)))

Diffusion/heat‑transfer modeling

=ERFC.PRECISE(x / (2 * SQRT(D * t)))

Smooth activation function

=0.5 * ERFC.PRECISE((threshold - A1) / width)

Survival probability in Gaussian models

=ERFC.PRECISE(z / SQRT(2)) / 2

ERFC.PRECISE returns a number between 0 and 2

Behavior details

• ERFC.PRECISE(∞) → 0
• ERFC.PRECISE(–∞) → 2
• More stable for large |x| than ERFC
• Guaranteed consistent results across platforms
• Accepts any real number

Invalid input → Err:502

• Use ERFC.PRECISE when accuracy matters, especially for large |x|
• Use ERF.PRECISE for the complementary central function
• Convert to normal CDF/tail using standard transformations
• Use in engineering models requiring stable numerical behavior
• Document scaling and units in physical models

• ERFC — standard complementary error function
• ERF.PRECISE — high‑precision ERF
• NORMDIST / NORMSDIST — normal distribution functions
• EXP / SQRT / PI — supporting math
• Custom integrals — advanced modeling

By mastering ERFC.PRECISE, you can build robust, high‑precision statistical and engineering models in LibreOffice Calc.