Average Error: 2.8 → 0.9
Time: 2.2s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -959124237.32905316:\\ \;\;\;\;x - \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\\ \end{array}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -959124237.32905316:\\
\;\;\;\;x - \frac{1}{x}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\\

\end{array}
double f(double x, double y, double z) {
        double r483240 = x;
        double r483241 = y;
        double r483242 = 1.1283791670955126;
        double r483243 = z;
        double r483244 = exp(r483243);
        double r483245 = r483242 * r483244;
        double r483246 = r483240 * r483241;
        double r483247 = r483245 - r483246;
        double r483248 = r483241 / r483247;
        double r483249 = r483240 + r483248;
        return r483249;
}
↓
double f(double x, double y, double z) {
        double r483250 = z;
        double r483251 = -959124237.3290532;
        bool r483252 = r483250 <= r483251;
        double r483253 = x;
        double r483254 = 1.0;
        double r483255 = r483254 / r483253;
        double r483256 = r483253 - r483255;
        double r483257 = y;
        double r483258 = 1.1283791670955126;
        double r483259 = exp(r483250);
        double r483260 = r483258 * r483259;
        double r483261 = r483253 * r483257;
        double r483262 = r483260 - r483261;
        double r483263 = r483257 / r483262;
        double r483264 = r483253 + r483263;
        double r483265 = r483252 ? r483256 : r483264;
        return r483265;
}

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
Target0.1
Herbie0.9
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -959124237.3290532

    1. Initial program 7.9

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

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{x - \frac{1}{x}}\]

    if -959124237.3290532 < z

    1. Initial program 1.2

      \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -959124237.32905316:\\ \;\;\;\;x - \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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)))))