Average Error: 2.9 → 0.0
Time: 13.6s
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 r10208173 = x;
        double r10208174 = y;
        double r10208175 = 1.1283791670955126;
        double r10208176 = z;
        double r10208177 = exp(r10208176);
        double r10208178 = r10208175 * r10208177;
        double r10208179 = r10208173 * r10208174;
        double r10208180 = r10208178 - r10208179;
        double r10208181 = r10208174 / r10208180;
        double r10208182 = r10208173 + r10208181;
        return r10208182;
}
↓
double f(double x, double y, double z) {
        double r10208183 = x;
        double r10208184 = 1.0;
        double r10208185 = z;
        double r10208186 = exp(r10208185);
        double r10208187 = 1.1283791670955126;
        double r10208188 = y;
        double r10208189 = r10208187 / r10208188;
        double r10208190 = r10208186 * r10208189;
        double r10208191 = r10208190 - r10208183;
        double r10208192 = r10208184 / r10208191;
        double r10208193 = r10208183 + r10208192;
        return r10208193;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

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

  3. Applied clear-num2.9

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

  4. Simplified0.0

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

  6. Applied div-inv0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(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)))))