Average Error: 2.7 → 0.0
Time: 10.7s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{e^{z} \cdot \frac{1.12837916709551256}{y} - x}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{e^{z} \cdot \frac{1.12837916709551256}{y} - x}
double f(double x, double y, double z) {
        double r445323 = x;
        double r445324 = y;
        double r445325 = 1.1283791670955126;
        double r445326 = z;
        double r445327 = exp(r445326);
        double r445328 = r445325 * r445327;
        double r445329 = r445323 * r445324;
        double r445330 = r445328 - r445329;
        double r445331 = r445324 / r445330;
        double r445332 = r445323 + r445331;
        return r445332;
}
↓
double f(double x, double y, double z) {
        double r445333 = x;
        double r445334 = 1.0;
        double r445335 = z;
        double r445336 = exp(r445335);
        double r445337 = 1.1283791670955126;
        double r445338 = y;
        double r445339 = r445337 / r445338;
        double r445340 = r445336 * r445339;
        double r445341 = r445340 - r445333;
        double r445342 = r445334 / r445341;
        double r445343 = r445333 + r445342;
        return r445343;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(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)))))