Average Error: 2.8 → 0.0
Time: 9.8s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r424688 = x;
        double r424689 = y;
        double r424690 = 1.1283791670955126;
        double r424691 = z;
        double r424692 = exp(r424691);
        double r424693 = r424690 * r424692;
        double r424694 = r424688 * r424689;
        double r424695 = r424693 - r424694;
        double r424696 = r424689 / r424695;
        double r424697 = r424688 + r424696;
        return r424697;
}
↓
double f(double x, double y, double z) {
        double r424698 = x;
        double r424699 = 1.0;
        double r424700 = 1.1283791670955126;
        double r424701 = z;
        double r424702 = exp(r424701);
        double r424703 = r424700 * r424702;
        double r424704 = y;
        double r424705 = r424703 / r424704;
        double r424706 = r424705 - r424698;
        double r424707 = r424699 / r424706;
        double r424708 = r424698 + r424707;
        return r424708;
}

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

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +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)))))