Average Error: 12.8 → 3.0
Time: 14.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.565615297402513793822059617442033581563 \cdot 10^{-201} \lor \neg \left(y \le 1.727845853063427358970787003444816519654 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.565615297402513793822059617442033581563 \cdot 10^{-201} \lor \neg \left(y \le 1.727845853063427358970787003444816519654 \cdot 10^{-151}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r820393 = x;
        double r820394 = y;
        double r820395 = z;
        double r820396 = r820394 - r820395;
        double r820397 = r820393 * r820396;
        double r820398 = r820397 / r820394;
        return r820398;
}
↓
double f(double x, double y, double z) {
        double r820399 = y;
        double r820400 = -4.565615297402514e-201;
        bool r820401 = r820399 <= r820400;
        double r820402 = 1.7278458530634274e-151;
        bool r820403 = r820399 <= r820402;
        double r820404 = !r820403;
        bool r820405 = r820401 || r820404;
        double r820406 = x;
        double r820407 = z;
        double r820408 = r820399 - r820407;
        double r820409 = r820399 / r820408;
        double r820410 = r820406 / r820409;
        double r820411 = 1.0;
        double r820412 = r820406 * r820408;
        double r820413 = r820399 / r820412;
        double r820414 = r820411 / r820413;
        double r820415 = r820405 ? r820410 : r820414;
        return r820415;
}

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

Original12.8
Target3.2
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.565615297402514e-201 or 1.7278458530634274e-151 < y

    1. Initial program 13.0

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

    3. Applied associate-/l*1.4

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

    if -4.565615297402514e-201 < y < 1.7278458530634274e-151

    1. Initial program 11.9

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

    3. Applied clear-num12.0

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

    4. Simplified12.0

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.565615297402513793822059617442033581563 \cdot 10^{-201} \lor \neg \left(y \le 1.727845853063427358970787003444816519654 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :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))