Average Error: 3.1 → 0.0
Time: 17.9s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}
double f(double x, double y, double z) {
        double r350264 = x;
        double r350265 = y;
        double r350266 = 1.1283791670955126;
        double r350267 = z;
        double r350268 = exp(r350267);
        double r350269 = r350266 * r350268;
        double r350270 = r350264 * r350265;
        double r350271 = r350269 - r350270;
        double r350272 = r350265 / r350271;
        double r350273 = r350264 + r350272;
        return r350273;
}
↓
double f(double x, double y, double z) {
        double r350274 = x;
        double r350275 = 1.0;
        double r350276 = 1.1283791670955126;
        double r350277 = y;
        double r350278 = r350276 / r350277;
        double r350279 = z;
        double r350280 = exp(r350279);
        double r350281 = r350278 * r350280;
        double r350282 = r350281 - r350274;
        double r350283 = r350275 / r350282;
        double r350284 = r350274 + r350283;
        return r350284;
}

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

Original3.1
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.1

    \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num3.1

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied div-sub3.1

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.12837916709551256 \cdot e^{z}}{y} - \frac{x \cdot y}{y}}}\]

  6. Simplified3.1

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.12837916709551256}{y} \cdot e^{z}} - \frac{x \cdot y}{y}}\]

  7. Simplified0.0

    \[\leadsto x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - \color{blue}{x}}\]

  8. Final simplification0.0

    \[\leadsto x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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