Average Error: 2.8 → 0.0
Time: 3.6s
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 r464648 = x;
        double r464649 = y;
        double r464650 = 1.1283791670955126;
        double r464651 = z;
        double r464652 = exp(r464651);
        double r464653 = r464650 * r464652;
        double r464654 = r464648 * r464649;
        double r464655 = r464653 - r464654;
        double r464656 = r464649 / r464655;
        double r464657 = r464648 + r464656;
        return r464657;
}
↓
double f(double x, double y, double z) {
        double r464658 = x;
        double r464659 = 1.0;
        double r464660 = cbrt(r464659);
        double r464661 = r464660 * r464660;
        double r464662 = 1.1283791670955126;
        double r464663 = z;
        double r464664 = exp(r464663);
        double r464665 = y;
        double r464666 = r464664 / r464665;
        double r464667 = r464662 * r464666;
        double r464668 = r464667 - r464658;
        double r464669 = r464661 / r464668;
        double r464670 = r464658 + r464669;
        return r464670;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original2.8
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

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

  5. Applied add-cube-cbrt2.8

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

  6. Applied associate-/l*2.8

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

  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 2020047 
(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)))))