Average Error: 9.4 → 0.2
Time: 13.3s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le -6.297922194041028 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\ \mathbf{elif}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le 2.1642747315993925 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1.0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le -6.297922194041028 \cdot 10^{+43}:\\
\;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\

\mathbf{elif}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le 2.1642747315993925 \cdot 10^{-80}:\\
\;\;\;\;x \cdot \frac{\left(y - z\right) + 1.0}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\

\end{array}
double f(double x, double y, double z) {
        double r31670286 = x;
        double r31670287 = y;
        double r31670288 = z;
        double r31670289 = r31670287 - r31670288;
        double r31670290 = 1.0;
        double r31670291 = r31670289 + r31670290;
        double r31670292 = r31670286 * r31670291;
        double r31670293 = r31670292 / r31670288;
        return r31670293;
}
↓
double f(double x, double y, double z) {
        double r31670294 = y;
        double r31670295 = z;
        double r31670296 = r31670294 - r31670295;
        double r31670297 = 1.0;
        double r31670298 = r31670296 + r31670297;
        double r31670299 = x;
        double r31670300 = r31670298 * r31670299;
        double r31670301 = r31670300 / r31670295;
        double r31670302 = -6.297922194041028e+43;
        bool r31670303 = r31670301 <= r31670302;
        double r31670304 = r31670299 / r31670295;
        double r31670305 = r31670294 + r31670297;
        double r31670306 = r31670304 * r31670305;
        double r31670307 = r31670306 - r31670299;
        double r31670308 = 2.1642747315993925e-80;
        bool r31670309 = r31670301 <= r31670308;
        double r31670310 = r31670298 / r31670295;
        double r31670311 = r31670299 * r31670310;
        double r31670312 = r31670309 ? r31670311 : r31670307;
        double r31670313 = r31670303 ? r31670307 : r31670312;
        return r31670313;
}

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

Original9.4
Target0.4
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1.0\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ (- y z) 1.0)) z) < -6.297922194041028e+43 or 2.1642747315993925e-80 < (/ (* x (+ (- y z) 1.0)) z)

    1. Initial program 14.6

      \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity14.6

      \[\leadsto \frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac5.2

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{\left(y - z\right) + 1.0}{z}}\]

    5. Simplified5.2

      \[\leadsto \color{blue}{x} \cdot \frac{\left(y - z\right) + 1.0}{z}\]

    6. Taylor expanded around 0 4.9

      \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + 1.0 \cdot \frac{x}{z}\right) - x}\]

    7. Simplified0.2

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y + 1.0\right) - x}\]

    if -6.297922194041028e+43 < (/ (* x (+ (- y z) 1.0)) z) < 2.1642747315993925e-80

    1. Initial program 0.1

      \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity0.1

      \[\leadsto \frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac0.3

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{\left(y - z\right) + 1.0}{z}}\]

    5. Simplified0.3

      \[\leadsto \color{blue}{x} \cdot \frac{\left(y - z\right) + 1.0}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le -6.297922194041028 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\ \mathbf{elif}\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z} \le 2.1642747315993925 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1.0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))