Average Error: 2.7 → 0.0
Time: 11.9s
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 r18720872 = x;
        double r18720873 = y;
        double r18720874 = 1.1283791670955126;
        double r18720875 = z;
        double r18720876 = exp(r18720875);
        double r18720877 = r18720874 * r18720876;
        double r18720878 = r18720872 * r18720873;
        double r18720879 = r18720877 - r18720878;
        double r18720880 = r18720873 / r18720879;
        double r18720881 = r18720872 + r18720880;
        return r18720881;
}
↓
double f(double x, double y, double z) {
        double r18720882 = x;
        double r18720883 = 1.0;
        double r18720884 = z;
        double r18720885 = exp(r18720884);
        double r18720886 = y;
        double r18720887 = 1.1283791670955126;
        double r18720888 = r18720886 / r18720887;
        double r18720889 = r18720885 / r18720888;
        double r18720890 = r18720889 - r18720882;
        double r18720891 = r18720883 / r18720890;
        double r18720892 = r18720882 + r18720891;
        return r18720892;
}

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. Using strategy rm

  5. Applied clear-num2.7

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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)))))