Average Error: 2.8 → 0.0
Time: 12.1s
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 r1155283 = x;
        double r1155284 = y;
        double r1155285 = 1.1283791670955126;
        double r1155286 = z;
        double r1155287 = exp(r1155286);
        double r1155288 = r1155285 * r1155287;
        double r1155289 = r1155283 * r1155284;
        double r1155290 = r1155288 - r1155289;
        double r1155291 = r1155284 / r1155290;
        double r1155292 = r1155283 + r1155291;
        return r1155292;
}
↓
double f(double x, double y, double z) {
        double r1155293 = x;
        double r1155294 = 1.0;
        double r1155295 = 1.1283791670955126;
        double r1155296 = z;
        double r1155297 = exp(r1155296);
        double r1155298 = r1155295 * r1155297;
        double r1155299 = y;
        double r1155300 = r1155298 / r1155299;
        double r1155301 = r1155300 - r1155293;
        double r1155302 = r1155294 / r1155301;
        double r1155303 = r1155293 + r1155302;
        return r1155303;
}

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)))))