Average Error: 0.1 → 0.1
Time: 1.7s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \frac{1}{\frac{1}{x \cdot \mathsf{fma}\left(0.12, x, 0.253\right)}}\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \frac{1}{\frac{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 - (1.0 / (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. Using strategy rm

  3. Applied flip-+0.1

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

  4. Applied associate-*r/7.4

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

  5. Simplified7.3

    \[\leadsto 1 - \frac{\color{blue}{\left(x \cdot \mathsf{fma}\left(0.12, x, 0.253\right)\right) \cdot \left(0.253 - x \cdot 0.12\right)}}{0.253 - x \cdot 0.12}\]
  6. Using strategy rm

  7. Applied clear-num7.4

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020071 +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)))))