Average Error: 2.7 → 0.0
Time: 10.9s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\frac{e^{z}}{\frac{y}{1.12837916709551256}} - x} + x\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\frac{e^{z}}{\frac{y}{1.12837916709551256}} - x} + x
double f(double x, double y, double z) {
        double r449161 = x;
        double r449162 = y;
        double r449163 = 1.1283791670955126;
        double r449164 = z;
        double r449165 = exp(r449164);
        double r449166 = r449163 * r449165;
        double r449167 = r449161 * r449162;
        double r449168 = r449166 - r449167;
        double r449169 = r449162 / r449168;
        double r449170 = r449161 + r449169;
        return r449170;
}
↓
double f(double x, double y, double z) {
        double r449171 = 1.0;
        double r449172 = z;
        double r449173 = exp(r449172);
        double r449174 = y;
        double r449175 = 1.1283791670955126;
        double r449176 = r449174 / r449175;
        double r449177 = r449173 / r449176;
        double r449178 = x;
        double r449179 = r449177 - r449178;
        double r449180 = r449171 / r449179;
        double r449181 = r449180 + r449178;
        return r449181;
}

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. Using strategy rm

  5. Applied div-sub2.7

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

  6. Simplified2.7

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +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)))))