Average Error: 2.9 → 0.0
Time: 14.9s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z}}{\frac{y}{1.128379167095512558560699289955664426088}} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z}}{\frac{y}{1.128379167095512558560699289955664426088}} - x}
double f(double x, double y, double z) {
        double r17203021 = x;
        double r17203022 = y;
        double r17203023 = 1.1283791670955126;
        double r17203024 = z;
        double r17203025 = exp(r17203024);
        double r17203026 = r17203023 * r17203025;
        double r17203027 = r17203021 * r17203022;
        double r17203028 = r17203026 - r17203027;
        double r17203029 = r17203022 / r17203028;
        double r17203030 = r17203021 + r17203029;
        return r17203030;
}
↓
double f(double x, double y, double z) {
        double r17203031 = x;
        double r17203032 = 1.0;
        double r17203033 = z;
        double r17203034 = exp(r17203033);
        double r17203035 = y;
        double r17203036 = 1.1283791670955126;
        double r17203037 = r17203035 / r17203036;
        double r17203038 = r17203034 / r17203037;
        double r17203039 = r17203038 - r17203031;
        double r17203040 = r17203032 / r17203039;
        double r17203041 = r17203031 + r17203040;
        return r17203041;
}

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

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

    \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}{1}}}\]

  6. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}}\]
  7. Using strategy rm

  8. Applied clear-num0.0

    \[\leadsto x + \color{blue}{\frac{1}{\frac{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}{1}}}\]

  9. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{e^{z}}{\frac{y}{1.128379167095512558560699289955664426088}} - x}}\]

  10. Final simplification0.0

    \[\leadsto x + \frac{1}{\frac{e^{z}}{\frac{y}{1.128379167095512558560699289955664426088}} - x}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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