Average Error: 2.8 → 0.0
Time: 9.0s
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 r453659 = x;
        double r453660 = y;
        double r453661 = 1.1283791670955126;
        double r453662 = z;
        double r453663 = exp(r453662);
        double r453664 = r453661 * r453663;
        double r453665 = r453659 * r453660;
        double r453666 = r453664 - r453665;
        double r453667 = r453660 / r453666;
        double r453668 = r453659 + r453667;
        return r453668;
}
↓
double f(double x, double y, double z) {
        double r453669 = x;
        double r453670 = 1.0;
        double r453671 = z;
        double r453672 = exp(r453671);
        double r453673 = 1.1283791670955126;
        double r453674 = y;
        double r453675 = r453673 / r453674;
        double r453676 = r453672 * r453675;
        double r453677 = r453676 - r453669;
        double r453678 = r453670 / r453677;
        double r453679 = r453669 + r453678;
        return r453679;
}

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-num2.9

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

  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 2019350 
(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)))))