Average Error: 2.8 → 0.0
Time: 11.5s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z}}{y} - x}
double f(double x, double y, double z) {
        double r407309 = x;
        double r407310 = y;
        double r407311 = 1.1283791670955126;
        double r407312 = z;
        double r407313 = exp(r407312);
        double r407314 = r407311 * r407313;
        double r407315 = r407309 * r407310;
        double r407316 = r407314 - r407315;
        double r407317 = r407310 / r407316;
        double r407318 = r407309 + r407317;
        return r407318;
}
↓
double f(double x, double y, double z) {
        double r407319 = x;
        double r407320 = 1.0;
        double r407321 = 1.1283791670955126;
        double r407322 = z;
        double r407323 = exp(r407322);
        double r407324 = r407321 * r407323;
        double r407325 = y;
        double r407326 = r407324 / r407325;
        double r407327 = r407326 - r407319;
        double r407328 = r407320 / r407327;
        double r407329 = r407319 + r407328;
        return r407329;
}

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

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))))