Average Error: 12.5 → 2.6
Time: 16.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.153708350718751 \cdot 10^{119} \lor \neg \left(x \le 1.7856545451239248 \cdot 10^{-270}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.153708350718751 \cdot 10^{119} \lor \neg \left(x \le 1.7856545451239248 \cdot 10^{-270}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

\end{array}
double f(double x, double y, double z) {
        double r541191 = x;
        double r541192 = y;
        double r541193 = z;
        double r541194 = r541192 - r541193;
        double r541195 = r541191 * r541194;
        double r541196 = r541195 / r541192;
        return r541196;
}
↓
double f(double x, double y, double z) {
        double r541197 = x;
        double r541198 = -1.153708350718751e+119;
        bool r541199 = r541197 <= r541198;
        double r541200 = 1.7856545451239248e-270;
        bool r541201 = r541197 <= r541200;
        double r541202 = !r541201;
        bool r541203 = r541199 || r541202;
        double r541204 = y;
        double r541205 = z;
        double r541206 = r541204 - r541205;
        double r541207 = r541204 / r541206;
        double r541208 = r541197 / r541207;
        double r541209 = r541197 * r541205;
        double r541210 = r541209 / r541204;
        double r541211 = r541197 - r541210;
        double r541212 = r541203 ? r541208 : r541211;
        return r541212;
}

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

Original12.5
Target3.4
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.153708350718751e+119 or 1.7856545451239248e-270 < x

    1. Initial program 16.2

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

    3. Applied associate-/l*2.1

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

    if -1.153708350718751e+119 < x < 1.7856545451239248e-270

    1. Initial program 7.3

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

    3. Applied associate-/l*4.6

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

    4. Taylor expanded around 0 3.3

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.153708350718751 \cdot 10^{119} \lor \neg \left(x \le 1.7856545451239248 \cdot 10^{-270}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 +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))