Average Error: 0.1 → 0.1
Time: 3.3s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
double code(double x) {
	return (1.0 - (x * (0.253 + (x * 0.12))));
}
↓
double code(double x) {
	return (1.0 - (x * (0.253 + (x * 0.12))));
}

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. Simplified0.1

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

  6. Applied flip--0.1

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

  7. Applied associate-/r/0.1

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

  8. Applied associate-*r*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020075 +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)))))