Average Error: 10.5 → 4.4
Time: 13.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 8.509729486679155842541870672204874453908 \cdot 10^{45} \lor \neg \left(z \le 2.771023612321592625881472298763729634882 \cdot 10^{231}\right):\\ \;\;\;\;y + \frac{x - y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left({y}^{2} + y\right) \cdot \frac{z}{x} + \frac{z}{x}} + y\\ \end{array}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le 8.509729486679155842541870672204874453908 \cdot 10^{45} \lor \neg \left(z \le 2.771023612321592625881472298763729634882 \cdot 10^{231}\right):\\
\;\;\;\;y + \frac{x - y \cdot x}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\left({y}^{2} + y\right) \cdot \frac{z}{x} + \frac{z}{x}} + y\\

\end{array}
double f(double x, double y, double z) {
        double r697303 = x;
        double r697304 = y;
        double r697305 = z;
        double r697306 = r697305 - r697303;
        double r697307 = r697304 * r697306;
        double r697308 = r697303 + r697307;
        double r697309 = r697308 / r697305;
        return r697309;
}
↓
double f(double x, double y, double z) {
        double r697310 = z;
        double r697311 = 8.509729486679156e+45;
        bool r697312 = r697310 <= r697311;
        double r697313 = 2.7710236123215926e+231;
        bool r697314 = r697310 <= r697313;
        double r697315 = !r697314;
        bool r697316 = r697312 || r697315;
        double r697317 = y;
        double r697318 = x;
        double r697319 = r697317 * r697318;
        double r697320 = r697318 - r697319;
        double r697321 = r697320 / r697310;
        double r697322 = r697317 + r697321;
        double r697323 = 1.0;
        double r697324 = 2.0;
        double r697325 = pow(r697317, r697324);
        double r697326 = r697325 + r697317;
        double r697327 = r697310 / r697318;
        double r697328 = r697326 * r697327;
        double r697329 = r697328 + r697327;
        double r697330 = r697323 / r697329;
        double r697331 = r697330 + r697317;
        double r697332 = r697316 ? r697322 : r697331;
        return r697332;
}

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

Original10.5
Target0.0
Herbie4.4
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < 8.509729486679156e+45 or 2.7710236123215926e+231 < z

    1. Initial program 9.3

      \[\frac{x + y \cdot \left(z - x\right)}{z}\]

    2. Simplified3.0

      \[\leadsto \color{blue}{y + \frac{x - x \cdot y}{z}}\]

    if 8.509729486679156e+45 < z < 2.7710236123215926e+231

    1. Initial program 15.9

      \[\frac{x + y \cdot \left(z - x\right)}{z}\]

    2. Simplified5.4

      \[\leadsto \color{blue}{y + \frac{x - x \cdot y}{z}}\]
    3. Using strategy rm

    4. Applied clear-num5.5

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

    5. Taylor expanded around 0 17.6

      \[\leadsto y + \frac{1}{\color{blue}{\frac{z \cdot y}{x} + \left(\frac{z}{x} + \frac{z \cdot {y}^{2}}{x}\right)}}\]

    6. Simplified21.9

      \[\leadsto y + \frac{1}{\color{blue}{\left(\frac{z}{x} + \frac{z}{x} \cdot y\right) + \frac{z}{x} \cdot \left(y \cdot y\right)}}\]
    7. Using strategy rm

    8. Applied associate-+l+21.9

      \[\leadsto y + \frac{1}{\color{blue}{\frac{z}{x} + \left(\frac{z}{x} \cdot y + \frac{z}{x} \cdot \left(y \cdot y\right)\right)}}\]

    9. Simplified11.3

      \[\leadsto y + \frac{1}{\frac{z}{x} + \color{blue}{\frac{z}{x} \cdot \left({y}^{2} + y\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 8.509729486679155842541870672204874453908 \cdot 10^{45} \lor \neg \left(z \le 2.771023612321592625881472298763729634882 \cdot 10^{231}\right):\\ \;\;\;\;y + \frac{x - y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left({y}^{2} + y\right) \cdot \frac{z}{x} + \frac{z}{x}} + y\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

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