Average Error: 2.7 → 0.0
Time: 2.6s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r501657 = x;
        double r501658 = y;
        double r501659 = 1.1283791670955126;
        double r501660 = z;
        double r501661 = exp(r501660);
        double r501662 = r501659 * r501661;
        double r501663 = r501657 * r501658;
        double r501664 = r501662 - r501663;
        double r501665 = r501658 / r501664;
        double r501666 = r501657 + r501665;
        return r501666;
}
↓
double f(double x, double y, double z) {
        double r501667 = x;
        double r501668 = 1.0;
        double r501669 = cbrt(r501668);
        double r501670 = r501669 * r501669;
        double r501671 = 1.1283791670955126;
        double r501672 = z;
        double r501673 = exp(r501672);
        double r501674 = y;
        double r501675 = r501673 / r501674;
        double r501676 = r501671 * r501675;
        double r501677 = r501676 - r501667;
        double r501678 = r501670 / r501677;
        double r501679 = r501667 + r501678;
        return r501679;
}

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

Original2.7
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

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

  3. Applied clear-num2.7

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

  5. Applied add-cube-cbrt2.7

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

  6. Applied associate-/l*2.7

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(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)))))