Average Error: 2.7 → 0.0
Time: 5.2s
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 r497289 = x;
        double r497290 = y;
        double r497291 = 1.1283791670955126;
        double r497292 = z;
        double r497293 = exp(r497292);
        double r497294 = r497291 * r497293;
        double r497295 = r497289 * r497290;
        double r497296 = r497294 - r497295;
        double r497297 = r497290 / r497296;
        double r497298 = r497289 + r497297;
        return r497298;
}
↓
double f(double x, double y, double z) {
        double r497299 = x;
        double r497300 = 1.0;
        double r497301 = 1.1283791670955126;
        double r497302 = z;
        double r497303 = exp(r497302);
        double r497304 = r497301 * r497303;
        double r497305 = y;
        double r497306 = r497304 / r497305;
        double r497307 = r497306 - r497299;
        double r497308 = r497300 / r497307;
        double r497309 = r497299 + r497308;
        return r497309;
}

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

Original2.7
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

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

  3. Applied clear-num2.7

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

  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 2020046 +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)))))