Average Error: 0.1 → 0.2
Time: 7.7s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)
double f(double x) {
        double r67863 = 1.0;
        double r67864 = x;
        double r67865 = 0.253;
        double r67866 = 0.12;
        double r67867 = r67864 * r67866;
        double r67868 = r67865 + r67867;
        double r67869 = r67864 * r67868;
        double r67870 = r67863 - r67869;
        return r67870;
}
↓
double f(double x) {
        double r67871 = 1.0;
        double r67872 = 0.12;
        double r67873 = x;
        double r67874 = 2.0;
        double r67875 = pow(r67873, r67874);
        double r67876 = r67872 * r67875;
        double r67877 = 0.253;
        double r67878 = r67877 * r67873;
        double r67879 = r67876 + r67878;
        double r67880 = r67871 - r67879;
        return r67880;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto 1 - x \cdot \color{blue}{\left(\left(\sqrt[3]{0.253 + x \cdot 0.12} \cdot \sqrt[3]{0.253 + x \cdot 0.12}\right) \cdot \sqrt[3]{0.253 + x \cdot 0.12}\right)}\]

  4. Applied associate-*r*0.4

    \[\leadsto 1 - \color{blue}{\left(x \cdot \left(\sqrt[3]{0.253 + x \cdot 0.12} \cdot \sqrt[3]{0.253 + x \cdot 0.12}\right)\right) \cdot \sqrt[3]{0.253 + x \cdot 0.12}}\]

  5. Taylor expanded around 0 0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))