Average Error: 2.7 → 0.9
Time: 3.1s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y} \le 6.080526524810317350601311198697643594969 \cdot 10^{291}:\\ \;\;\;\;x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{x}\\ \end{array}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y} \le 6.080526524810317350601311198697643594969 \cdot 10^{291}:\\
\;\;\;\;x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r387257 = x;
        double r387258 = y;
        double r387259 = 1.1283791670955126;
        double r387260 = z;
        double r387261 = exp(r387260);
        double r387262 = r387259 * r387261;
        double r387263 = r387257 * r387258;
        double r387264 = r387262 - r387263;
        double r387265 = r387258 / r387264;
        double r387266 = r387257 + r387265;
        return r387266;
}
↓
double f(double x, double y, double z) {
        double r387267 = x;
        double r387268 = y;
        double r387269 = 1.1283791670955126;
        double r387270 = z;
        double r387271 = exp(r387270);
        double r387272 = r387269 * r387271;
        double r387273 = r387267 * r387268;
        double r387274 = r387272 - r387273;
        double r387275 = r387268 / r387274;
        double r387276 = r387267 + r387275;
        double r387277 = 6.080526524810317e+291;
        bool r387278 = r387276 <= r387277;
        double r387279 = 1.0;
        double r387280 = r387279 / r387267;
        double r387281 = r387267 - r387280;
        double r387282 = r387278 ? r387276 : r387281;
        return r387282;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))) < 6.080526524810317e+291

    1. Initial program 0.9

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

    if 6.080526524810317e+291 < (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y))))

    1. Initial program 41.8

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

    2. Taylor expanded around inf 0.3

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y} \le 6.080526524810317350601311198697643594969 \cdot 10^{291}:\\ \;\;\;\;x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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)))))