Average Error: 2.7 → 0.9
Time: 5.5s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y}{\frac{5081767996463981}{4503599627370496} \cdot e^{z} - x \cdot y} \le 7.692267140979724484480008976812300814177 \cdot 10^{263}:\\ \;\;\;\;x + \frac{y}{\frac{5081767996463981}{4503599627370496} \cdot e^{z} - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{x}\\ \end{array}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y}{\frac{5081767996463981}{4503599627370496} \cdot e^{z} - x \cdot y} \le 7.692267140979724484480008976812300814177 \cdot 10^{263}:\\
\;\;\;\;x + \frac{y}{\frac{5081767996463981}{4503599627370496} \cdot e^{z} - x \cdot y}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{1}{x}\\

\end{array}
double f(double x, double y, double z) {
        double r301313 = x;
        double r301314 = y;
        double r301315 = 1.1283791670955126;
        double r301316 = z;
        double r301317 = exp(r301316);
        double r301318 = r301315 * r301317;
        double r301319 = r301313 * r301314;
        double r301320 = r301318 - r301319;
        double r301321 = r301314 / r301320;
        double r301322 = r301313 + r301321;
        return r301322;
}
↓
double f(double x, double y, double z) {
        double r301323 = x;
        double r301324 = y;
        double r301325 = 5081767996463981.0;
        double r301326 = 4503599627370496.0;
        double r301327 = r301325 / r301326;
        double r301328 = z;
        double r301329 = exp(r301328);
        double r301330 = r301327 * r301329;
        double r301331 = r301323 * r301324;
        double r301332 = r301330 - r301331;
        double r301333 = r301324 / r301332;
        double r301334 = r301323 + r301333;
        double r301335 = 7.692267140979724e+263;
        bool r301336 = r301334 <= r301335;
        double r301337 = 1.0;
        double r301338 = r301337 / r301323;
        double r301339 = r301323 - r301338;
        double r301340 = r301336 ? r301334 : r301339;
        return r301340;
}

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
Target0.1
Herbie0.9
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))) < 7.692267140979724e+263

    1. Initial program 1.0

      \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]

    if 7.692267140979724e+263 < (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))

    1. Initial program 26.2

      \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]

    2. Taylor expanded around inf 0.6

      \[\leadsto \color{blue}{x - \frac{1}{x}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y}{\frac{5081767996463981}{4503599627370496} \cdot e^{z} - x \cdot y} \le 7.692267140979724484480008976812300814177 \cdot 10^{263}:\\ \;\;\;\;x + \frac{y}{\frac{5081767996463981}{4503599627370496} \cdot e^{z} - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.12837916709551256 y) (exp z)) x)))

  (+ x (/ y (- (* 1.12837916709551256 (exp z)) (* x y)))))