Average Error: 2.8 → 0.1
Time: 3.4s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x}\]
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 r422120 = x;
        double r422121 = y;
        double r422122 = 1.1283791670955126;
        double r422123 = z;
        double r422124 = exp(r422123);
        double r422125 = r422122 * r422124;
        double r422126 = r422120 * r422121;
        double r422127 = r422125 - r422126;
        double r422128 = r422121 / r422127;
        double r422129 = r422120 + r422128;
        return r422129;
}
↓
double f(double x, double y, double z) {
        double r422130 = x;
        double r422131 = 1.0;
        double r422132 = cbrt(r422131);
        double r422133 = r422132 * r422132;
        double r422134 = 1.1283791670955126;
        double r422135 = z;
        double r422136 = exp(r422135);
        double r422137 = y;
        double r422138 = r422136 / r422137;
        double r422139 = r422134 * r422138;
        double r422140 = r422139 - r422130;
        double r422141 = r422133 / r422140;
        double r422142 = r422130 + r422141;
        return r422142;
}

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

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

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. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 +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)))))