Average Error: 2.9 → 0.0
Time: 3.4s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r434870 = x;
        double r434871 = y;
        double r434872 = 1.1283791670955126;
        double r434873 = z;
        double r434874 = exp(r434873);
        double r434875 = r434872 * r434874;
        double r434876 = r434870 * r434871;
        double r434877 = r434875 - r434876;
        double r434878 = r434871 / r434877;
        double r434879 = r434870 + r434878;
        return r434879;
}
↓
double f(double x, double y, double z) {
        double r434880 = x;
        double r434881 = 1.0;
        double r434882 = cbrt(r434881);
        double r434883 = r434882 * r434882;
        double r434884 = 1.1283791670955126;
        double r434885 = z;
        double r434886 = exp(r434885);
        double r434887 = r434884 * r434886;
        double r434888 = y;
        double r434889 = r434887 / r434888;
        double r434890 = r434889 - r434880;
        double r434891 = r434883 / r434890;
        double r434892 = r434880 + r434891;
        return r434892;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

    \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.9

    \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}\]

  6. Applied associate-/l*2.9

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}{\sqrt[3]{1}}}}\]

  7. Simplified0.1

    \[\leadsto x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\color{blue}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}}\]
  8. Using strategy rm

  9. Applied associate-*r/0.0

    \[\leadsto x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\color{blue}{\frac{1.12837916709551256 \cdot e^{z}}{y}} - x}\]

  10. Final simplification0.0

    \[\leadsto x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))