Average Error: 2.7 → 0.0
Time: 15.0s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{e^{z} \cdot \frac{1.128379167095512558560699289955664426088}{y} - x}
double f(double x, double y, double z) {
        double r297035 = x;
        double r297036 = y;
        double r297037 = 1.1283791670955126;
        double r297038 = z;
        double r297039 = exp(r297038);
        double r297040 = r297037 * r297039;
        double r297041 = r297035 * r297036;
        double r297042 = r297040 - r297041;
        double r297043 = r297036 / r297042;
        double r297044 = r297035 + r297043;
        return r297044;
}
↓
double f(double x, double y, double z) {
        double r297045 = x;
        double r297046 = 1.0;
        double r297047 = z;
        double r297048 = exp(r297047);
        double r297049 = 1.1283791670955126;
        double r297050 = y;
        double r297051 = r297049 / r297050;
        double r297052 = r297048 * r297051;
        double r297053 = r297052 - r297045;
        double r297054 = r297046 / r297053;
        double r297055 = r297045 + r297054;
        return r297055;
}

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

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 
(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)))))