Average Error: 0.1 → 0.2
Time: 1.7s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[\left(1 - 0.253 \cdot x\right) - {x}^{2} \cdot 0.12\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
\left(1 - 0.253 \cdot x\right) - {x}^{2} \cdot 0.12
double code(double x) {
	return ((double) (1.0 - ((double) (x * ((double) (0.253 + ((double) (x * 0.12))))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) (0.253 * x)))) - ((double) (((double) pow(x, 2.0)) * 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 distribute-lft-in0.1

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

  4. Applied associate--r+0.1

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

  5. Simplified0.1

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

  7. Applied associate-*r*0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020130 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))