Average Error: 3.0 → 0.0
Time: 5.0s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x} + x\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x} + x
double f(double x, double y, double z) {
        double r276810 = x;
        double r276811 = y;
        double r276812 = 1.1283791670955126;
        double r276813 = z;
        double r276814 = exp(r276813);
        double r276815 = r276812 * r276814;
        double r276816 = r276810 * r276811;
        double r276817 = r276815 - r276816;
        double r276818 = r276811 / r276817;
        double r276819 = r276810 + r276818;
        return r276819;
}
↓
double f(double x, double y, double z) {
        double r276820 = 1.0;
        double r276821 = 1.1283791670955126;
        double r276822 = z;
        double r276823 = exp(r276822);
        double r276824 = r276821 * r276823;
        double r276825 = y;
        double r276826 = r276824 / r276825;
        double r276827 = x;
        double r276828 = r276826 - r276827;
        double r276829 = r276820 / r276828;
        double r276830 = r276829 + r276827;
        return r276830;
}

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

Derivation

  1. Initial program 3.0

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

  3. Applied div-inv3.2

    \[\leadsto x + \color{blue}{y \cdot \frac{1}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity3.2

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

  6. Applied associate-*l*3.2

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

  7. Simplified3.0

    \[\leadsto x + 1 \cdot \color{blue}{\frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}}\]
  8. Using strategy rm

  9. Applied clear-num3.1

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.12837916709551256 y) (exp z)) x)))

  (+ x (/ y (- (* 1.12837916709551256 (exp z)) (* x y)))))