Average Error: 2.9 → 0.0
Time: 14.6s
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 r14970696 = x;
        double r14970697 = y;
        double r14970698 = 1.1283791670955126;
        double r14970699 = z;
        double r14970700 = exp(r14970699);
        double r14970701 = r14970698 * r14970700;
        double r14970702 = r14970696 * r14970697;
        double r14970703 = r14970701 - r14970702;
        double r14970704 = r14970697 / r14970703;
        double r14970705 = r14970696 + r14970704;
        return r14970705;
}
↓
double f(double x, double y, double z) {
        double r14970706 = x;
        double r14970707 = 1.0;
        double r14970708 = z;
        double r14970709 = exp(r14970708);
        double r14970710 = y;
        double r14970711 = 1.1283791670955126;
        double r14970712 = r14970710 / r14970711;
        double r14970713 = r14970709 / r14970712;
        double r14970714 = r14970713 - r14970706;
        double r14970715 = r14970707 / r14970714;
        double r14970716 = r14970706 + r14970715;
        return r14970716;
}

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)))))