Average Error: 2.8 → 0.0
Time: 9.5s
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 r1071325 = x;
        double r1071326 = y;
        double r1071327 = 1.1283791670955126;
        double r1071328 = z;
        double r1071329 = exp(r1071328);
        double r1071330 = r1071327 * r1071329;
        double r1071331 = r1071325 * r1071326;
        double r1071332 = r1071330 - r1071331;
        double r1071333 = r1071326 / r1071332;
        double r1071334 = r1071325 + r1071333;
        return r1071334;
}
↓
double f(double x, double y, double z) {
        double r1071335 = x;
        double r1071336 = 1.0;
        double r1071337 = 1.1283791670955126;
        double r1071338 = z;
        double r1071339 = exp(r1071338);
        double r1071340 = r1071337 * r1071339;
        double r1071341 = y;
        double r1071342 = r1071340 / r1071341;
        double r1071343 = r1071342 - r1071335;
        double r1071344 = r1071336 / r1071343;
        double r1071345 = r1071335 + r1071344;
        return r1071345;
}

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 
(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)))))