Average Error: 12.5 → 1.9
Time: 2.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.10254487981744727 \cdot 10^{288} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -1.88409447397914514 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.10254487981744727 \cdot 10^{288} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -1.88409447397914514 \cdot 10^{-83}\right):\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r2245192 = x;
        double r2245193 = y;
        double r2245194 = z;
        double r2245195 = r2245193 - r2245194;
        double r2245196 = r2245192 * r2245195;
        double r2245197 = r2245196 / r2245193;
        return r2245197;
}
↓
double f(double x, double y, double z) {
        double r2245198 = x;
        double r2245199 = y;
        double r2245200 = z;
        double r2245201 = r2245199 - r2245200;
        double r2245202 = r2245198 * r2245201;
        double r2245203 = r2245202 / r2245199;
        double r2245204 = -1.1025448798174473e+288;
        bool r2245205 = r2245203 <= r2245204;
        double r2245206 = -1.884094473979145e-83;
        bool r2245207 = r2245203 <= r2245206;
        double r2245208 = !r2245207;
        bool r2245209 = r2245205 || r2245208;
        double r2245210 = r2245201 / r2245199;
        double r2245211 = r2245198 * r2245210;
        double r2245212 = r2245209 ? r2245211 : r2245203;
        return r2245212;
}

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
Target3.2
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < -1.1025448798174473e+288 or -1.884094473979145e-83 < (/ (* x (- y z)) y)

    1. Initial program 17.0

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

    3. Applied *-un-lft-identity17.0

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

    4. Applied times-frac2.5

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}}\]

    5. Simplified2.5

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

    if -1.1025448798174473e+288 < (/ (* x (- y z)) y) < -1.884094473979145e-83

    1. Initial program 0.3

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.10254487981744727 \cdot 10^{288} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -1.88409447397914514 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 +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 -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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