Average Error: 2.8 → 0.1
Time: 9.6s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1.128379167095512558560699289955664426088 \cdot \frac{e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r204671 = x;
        double r204672 = y;
        double r204673 = 1.1283791670955126;
        double r204674 = z;
        double r204675 = exp(r204674);
        double r204676 = r204673 * r204675;
        double r204677 = r204671 * r204672;
        double r204678 = r204676 - r204677;
        double r204679 = r204672 / r204678;
        double r204680 = r204671 + r204679;
        return r204680;
}
↓
double f(double x, double y, double z) {
        double r204681 = x;
        double r204682 = 1.0;
        double r204683 = 1.1283791670955126;
        double r204684 = z;
        double r204685 = exp(r204684);
        double r204686 = y;
        double r204687 = r204685 / r204686;
        double r204688 = r204683 * r204687;
        double r204689 = r204688 - r204681;
        double r204690 = r204682 / r204689;
        double r204691 = r204681 + r204690;
        return r204691;
}

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

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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)))))