Average Error: 2.8 → 0.0
Time: 15.6s
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 r292790 = x;
        double r292791 = y;
        double r292792 = 1.1283791670955126;
        double r292793 = z;
        double r292794 = exp(r292793);
        double r292795 = r292792 * r292794;
        double r292796 = r292790 * r292791;
        double r292797 = r292795 - r292796;
        double r292798 = r292791 / r292797;
        double r292799 = r292790 + r292798;
        return r292799;
}
↓
double f(double x, double y, double z) {
        double r292800 = x;
        double r292801 = 1.0;
        double r292802 = 1.1283791670955126;
        double r292803 = z;
        double r292804 = exp(r292803);
        double r292805 = y;
        double r292806 = r292804 / r292805;
        double r292807 = r292802 * r292806;
        double r292808 = r292807 - r292800;
        double r292809 = r292801 / r292808;
        double r292810 = r292800 + r292809;
        return r292810;
}

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)))))