Average Error: 0.1 → 0.1
Time: 2.5s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - x \cdot {\left(0.253 + x \cdot 0.12\right)}^{1}\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - x \cdot {\left(0.253 + x \cdot 0.12\right)}^{1}
double f(double x) {
        double r111105 = 1.0;
        double r111106 = x;
        double r111107 = 0.253;
        double r111108 = 0.12;
        double r111109 = r111106 * r111108;
        double r111110 = r111107 + r111109;
        double r111111 = r111106 * r111110;
        double r111112 = r111105 - r111111;
        return r111112;
}
↓
double f(double x) {
        double r111113 = 1.0;
        double r111114 = x;
        double r111115 = 0.253;
        double r111116 = 0.12;
        double r111117 = r111114 * r111116;
        double r111118 = r111115 + r111117;
        double r111119 = 1.0;
        double r111120 = pow(r111118, r111119);
        double r111121 = r111114 * r111120;
        double r111122 = r111113 - r111121;
        return r111122;
}

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 pow10.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))