Average Error: 3.0 → 0.1
Time: 6.9s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z}}{y} \cdot 1.128379167095512558560699289955664426088 - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z}}{y} \cdot 1.128379167095512558560699289955664426088 - x}
double f(double x, double y, double z) {
        double r341675 = x;
        double r341676 = y;
        double r341677 = 1.1283791670955126;
        double r341678 = z;
        double r341679 = exp(r341678);
        double r341680 = r341677 * r341679;
        double r341681 = r341675 * r341676;
        double r341682 = r341680 - r341681;
        double r341683 = r341676 / r341682;
        double r341684 = r341675 + r341683;
        return r341684;
}
↓
double f(double x, double y, double z) {
        double r341685 = x;
        double r341686 = 1.0;
        double r341687 = z;
        double r341688 = exp(r341687);
        double r341689 = y;
        double r341690 = r341688 / r341689;
        double r341691 = 1.1283791670955126;
        double r341692 = r341690 * r341691;
        double r341693 = r341692 - r341685;
        double r341694 = r341686 / r341693;
        double r341695 = r341685 + r341694;
        return r341695;
}

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

Original3.0
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.0

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

  3. Applied clear-num3.0

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(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)))))