Average Error: 12.2 → 1.9
Time: 10.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.842562368772701429645805907300691455493 \cdot 10^{-91} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 3.432540453061663231003216489606318759457 \cdot 10^{307}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.842562368772701429645805907300691455493 \cdot 10^{-91} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 3.432540453061663231003216489606318759457 \cdot 10^{307}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r448514 = x;
        double r448515 = y;
        double r448516 = z;
        double r448517 = r448515 - r448516;
        double r448518 = r448514 * r448517;
        double r448519 = r448518 / r448515;
        return r448519;
}
↓
double f(double x, double y, double z) {
        double r448520 = x;
        double r448521 = y;
        double r448522 = z;
        double r448523 = r448521 - r448522;
        double r448524 = r448520 * r448523;
        double r448525 = r448524 / r448521;
        double r448526 = 2.8425623687727014e-91;
        bool r448527 = r448525 <= r448526;
        double r448528 = 3.432540453061663e+307;
        bool r448529 = r448525 <= r448528;
        double r448530 = !r448529;
        bool r448531 = r448527 || r448530;
        double r448532 = r448521 / r448523;
        double r448533 = r448520 / r448532;
        double r448534 = r448531 ? r448533 : r448525;
        return r448534;
}

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

Original12.2
Target3.3
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < 2.8425623687727014e-91 or 3.432540453061663e+307 < (/ (* x (- y z)) y)

    1. Initial program 16.9

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

    3. Applied associate-/l*2.5

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

    if 2.8425623687727014e-91 < (/ (* x (- y z)) y) < 3.432540453061663e+307

    1. Initial program 0.3

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.842562368772701429645805907300691455493 \cdot 10^{-91} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 3.432540453061663231003216489606318759457 \cdot 10^{307}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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