Average Error: 2.7 → 0.0
Time: 12.1s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}
double f(double x, double y, double z) {
        double r19640881 = x;
        double r19640882 = y;
        double r19640883 = 1.1283791670955126;
        double r19640884 = z;
        double r19640885 = exp(r19640884);
        double r19640886 = r19640883 * r19640885;
        double r19640887 = r19640881 * r19640882;
        double r19640888 = r19640886 - r19640887;
        double r19640889 = r19640882 / r19640888;
        double r19640890 = r19640881 + r19640889;
        return r19640890;
}
↓
double f(double x, double y, double z) {
        double r19640891 = x;
        double r19640892 = 1.0;
        double r19640893 = z;
        double r19640894 = exp(r19640893);
        double r19640895 = 1.1283791670955126;
        double r19640896 = y;
        double r19640897 = r19640895 / r19640896;
        double r19640898 = r19640894 * r19640897;
        double r19640899 = r19640898 - r19640891;
        double r19640900 = r19640892 / r19640899;
        double r19640901 = r19640891 + r19640900;
        return r19640901;
}

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
Herbie0.0
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.7

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied clear-num2.7

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}{1}}}\]

  6. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}}\]

  7. Final simplification0.0

    \[\leadsto x + \frac{1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))