Average Error: 2.8 → 0.0
Time: 15.9s
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 r273757 = x;
        double r273758 = y;
        double r273759 = 1.1283791670955126;
        double r273760 = z;
        double r273761 = exp(r273760);
        double r273762 = r273759 * r273761;
        double r273763 = r273757 * r273758;
        double r273764 = r273762 - r273763;
        double r273765 = r273758 / r273764;
        double r273766 = r273757 + r273765;
        return r273766;
}
↓
double f(double x, double y, double z) {
        double r273767 = x;
        double r273768 = 1.0;
        double r273769 = 1.1283791670955126;
        double r273770 = z;
        double r273771 = exp(r273770);
        double r273772 = y;
        double r273773 = r273771 / r273772;
        double r273774 = r273769 * r273773;
        double r273775 = r273774 - r273767;
        double r273776 = r273768 / r273775;
        double r273777 = r273767 + r273776;
        return r273777;
}

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

Original2.8
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

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

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