Average Error: 2.9 → 0.0
Time: 15.0s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}
double f(double x, double y, double z) {
        double r19160311 = x;
        double r19160312 = y;
        double r19160313 = 1.1283791670955126;
        double r19160314 = z;
        double r19160315 = exp(r19160314);
        double r19160316 = r19160313 * r19160315;
        double r19160317 = r19160311 * r19160312;
        double r19160318 = r19160316 - r19160317;
        double r19160319 = r19160312 / r19160318;
        double r19160320 = r19160311 + r19160319;
        return r19160320;
}
↓
double f(double x, double y, double z) {
        double r19160321 = x;
        double r19160322 = 1.0;
        double r19160323 = z;
        double r19160324 = exp(r19160323);
        double r19160325 = 1.1283791670955126;
        double r19160326 = y;
        double r19160327 = r19160325 / r19160326;
        double r19160328 = r19160324 * r19160327;
        double r19160329 = r19160328 - r19160321;
        double r19160330 = r19160322 / r19160329;
        double r19160331 = r19160321 + r19160330;
        return r19160331;
}

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

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}{1}}}\]

  6. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}}\]

  7. Final simplification0.0

    \[\leadsto x + \frac{1}{e^{z} \cdot \frac{1.1283791670955126}{y} - x}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))