Average Error: 2.8 → 0.0
Time: 16.8s
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 r316749 = x;
        double r316750 = y;
        double r316751 = 1.1283791670955126;
        double r316752 = z;
        double r316753 = exp(r316752);
        double r316754 = r316751 * r316753;
        double r316755 = r316749 * r316750;
        double r316756 = r316754 - r316755;
        double r316757 = r316750 / r316756;
        double r316758 = r316749 + r316757;
        return r316758;
}
↓
double f(double x, double y, double z) {
        double r316759 = x;
        double r316760 = 1.0;
        double r316761 = 1.1283791670955126;
        double r316762 = z;
        double r316763 = exp(r316762);
        double r316764 = y;
        double r316765 = r316763 / r316764;
        double r316766 = r316761 * r316765;
        double r316767 = r316766 - r316759;
        double r316768 = r316760 / r316767;
        double r316769 = r316759 + r316768;
        return r316769;
}

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-num2.8

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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)))))