Average Error: 0.1 → 0.1
Time: 1.5s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - x \cdot \mathsf{fma}\left(0.12, x, 0.253\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot \mathsf{fma}\left(0.12, x, 0.253\right)
double code(double x) {
	return (1.0 - (x * (0.253 + (x * 0.12))));
}
↓
double code(double x) {
	return (1.0 - (x * fma(0.12, x, 0.253)));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]

  2. Taylor expanded around 0 0.2

    \[\leadsto 1 - \color{blue}{\left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)}\]

  3. Simplified0.1

    \[\leadsto 1 - \color{blue}{x \cdot \mathsf{fma}\left(0.12, x, 0.253\right)}\]

  4. Final simplification0.1

    \[\leadsto 1 - x \cdot \mathsf{fma}\left(0.12, x, 0.253\right)\]

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))