Average Error: 2.7 → 0.1
Time: 7.9s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}
double f(double x, double y, double z) {
        double r8494667 = x;
        double r8494668 = y;
        double r8494669 = 1.1283791670955126;
        double r8494670 = z;
        double r8494671 = exp(r8494670);
        double r8494672 = r8494669 * r8494671;
        double r8494673 = r8494667 * r8494668;
        double r8494674 = r8494672 - r8494673;
        double r8494675 = r8494668 / r8494674;
        double r8494676 = r8494667 + r8494675;
        return r8494676;
}
↓
double f(double x, double y, double z) {
        double r8494677 = x;
        double r8494678 = 1.0;
        double r8494679 = z;
        double r8494680 = exp(r8494679);
        double r8494681 = 1.1283791670955126;
        double r8494682 = r8494680 * r8494681;
        double r8494683 = y;
        double r8494684 = r8494682 / r8494683;
        double r8494685 = r8494684 - r8494677;
        double r8494686 = r8494678 / r8494685;
        double r8494687 = r8494677 + r8494686;
        return r8494687;
}

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
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.7

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied div-sub2.7

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \frac{x \cdot y}{y}}}\]

  6. Simplified0.1

    \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{y} - \color{blue}{\frac{x}{1}}}\]

  7. Final simplification0.1

    \[\leadsto x + \frac{1}{\frac{e^{z} \cdot 1.1283791670955126}{y} - x}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

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

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