Average Error: 2.7 → 0.1
Time: 9.8s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r330764 = x;
        double r330765 = y;
        double r330766 = 1.1283791670955126;
        double r330767 = z;
        double r330768 = exp(r330767);
        double r330769 = r330766 * r330768;
        double r330770 = r330764 * r330765;
        double r330771 = r330769 - r330770;
        double r330772 = r330765 / r330771;
        double r330773 = r330764 + r330772;
        return r330773;
}
↓
double f(double x, double y, double z) {
        double r330774 = x;
        double r330775 = 1.0;
        double r330776 = 1.1283791670955126;
        double r330777 = z;
        double r330778 = exp(r330777);
        double r330779 = y;
        double r330780 = r330778 / r330779;
        double r330781 = r330776 * r330780;
        double r330782 = r330781 - r330774;
        double r330783 = r330775 / r330782;
        double r330784 = r330774 + r330783;
        return r330784;
}

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

Derivation

  1. Initial program 2.7

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

  3. Applied clear-num2.7

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.12837916709551256 y) (exp z)) x)))

  (+ x (/ y (- (* 1.12837916709551256 (exp z)) (* x y)))))