Average Error: 12.7 → 1.7
Time: 9.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 4.37247531142817321365398637170882177174 \cdot 10^{-32} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.200133185098060603983055402191501639186 \cdot 10^{302}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 4.37247531142817321365398637170882177174 \cdot 10^{-32} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.200133185098060603983055402191501639186 \cdot 10^{302}\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 r540366 = x;
        double r540367 = y;
        double r540368 = z;
        double r540369 = r540367 - r540368;
        double r540370 = r540366 * r540369;
        double r540371 = r540370 / r540367;
        return r540371;
}
↓
double f(double x, double y, double z) {
        double r540372 = x;
        double r540373 = y;
        double r540374 = z;
        double r540375 = r540373 - r540374;
        double r540376 = r540372 * r540375;
        double r540377 = r540376 / r540373;
        double r540378 = 4.372475311428173e-32;
        bool r540379 = r540377 <= r540378;
        double r540380 = 1.2001331850980606e+302;
        bool r540381 = r540377 <= r540380;
        double r540382 = !r540381;
        bool r540383 = r540379 || r540382;
        double r540384 = r540373 / r540375;
        double r540385 = r540372 / r540384;
        double r540386 = r540383 ? r540385 : r540377;
        return r540386;
}

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

Original12.7
Target3.2
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < 4.372475311428173e-32 or 1.2001331850980606e+302 < (/ (* x (- y z)) y)

    1. Initial program 16.5

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

    3. Applied associate-/l*2.1

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

    if 4.372475311428173e-32 < (/ (* x (- y z)) y) < 1.2001331850980606e+302

    1. Initial program 0.2

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 4.37247531142817321365398637170882177174 \cdot 10^{-32} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.200133185098060603983055402191501639186 \cdot 10^{302}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e104) (- x (/ (* z x) y)) (if (< z 1.69397660138285259e213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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