Average Error: 2.8 → 0.0
Time: 6.4s
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 r502812 = x;
        double r502813 = y;
        double r502814 = 1.1283791670955126;
        double r502815 = z;
        double r502816 = exp(r502815);
        double r502817 = r502814 * r502816;
        double r502818 = r502812 * r502813;
        double r502819 = r502817 - r502818;
        double r502820 = r502813 / r502819;
        double r502821 = r502812 + r502820;
        return r502821;
}
↓
double f(double x, double y, double z) {
        double r502822 = x;
        double r502823 = 1.0;
        double r502824 = 1.1283791670955126;
        double r502825 = z;
        double r502826 = exp(r502825);
        double r502827 = r502824 * r502826;
        double r502828 = y;
        double r502829 = r502827 / r502828;
        double r502830 = r502829 - r502822;
        double r502831 = r502823 / r502830;
        double r502832 = r502822 + r502831;
        return r502832;
}

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 
(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)))))