Average Error: 2.7 → 0.1
Time: 3.1s
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 r239102 = x;
        double r239103 = y;
        double r239104 = 1.1283791670955126;
        double r239105 = z;
        double r239106 = exp(r239105);
        double r239107 = r239104 * r239106;
        double r239108 = r239102 * r239103;
        double r239109 = r239107 - r239108;
        double r239110 = r239103 / r239109;
        double r239111 = r239102 + r239110;
        return r239111;
}
↓
double f(double x, double y, double z) {
        double r239112 = x;
        double r239113 = 1.0;
        double r239114 = cbrt(r239113);
        double r239115 = r239114 * r239114;
        double r239116 = 1.1283791670955126;
        double r239117 = z;
        double r239118 = exp(r239117);
        double r239119 = y;
        double r239120 = r239118 / r239119;
        double r239121 = r239116 * r239120;
        double r239122 = r239121 - r239112;
        double r239123 = r239115 / r239122;
        double r239124 = r239112 + r239123;
        return r239124;
}

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

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. Simplified0.1

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

  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 2020046 
(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)))))