Average Error: 12.4 → 3.6
Time: 4.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.43485019037392297 \cdot 10^{-51} \lor \neg \left(x \le -1.276743401231038 \cdot 10^{-140}\right):\\ \;\;\;\;\frac{x}{\frac{-y}{-\left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -9.43485019037392297 \cdot 10^{-51} \lor \neg \left(x \le -1.276743401231038 \cdot 10^{-140}\right):\\
\;\;\;\;\frac{x}{\frac{-y}{-\left(y - z\right)}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r781184 = x;
        double r781185 = y;
        double r781186 = z;
        double r781187 = r781185 - r781186;
        double r781188 = r781184 * r781187;
        double r781189 = r781188 / r781185;
        return r781189;
}
↓
double f(double x, double y, double z) {
        double r781190 = x;
        double r781191 = -9.434850190373923e-51;
        bool r781192 = r781190 <= r781191;
        double r781193 = -1.276743401231038e-140;
        bool r781194 = r781190 <= r781193;
        double r781195 = !r781194;
        bool r781196 = r781192 || r781195;
        double r781197 = y;
        double r781198 = -r781197;
        double r781199 = z;
        double r781200 = r781197 - r781199;
        double r781201 = -r781200;
        double r781202 = r781198 / r781201;
        double r781203 = r781190 / r781202;
        double r781204 = r781190 / r781197;
        double r781205 = r781204 * r781200;
        double r781206 = r781196 ? r781203 : r781205;
        return r781206;
}

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

Original12.4
Target3.0
Herbie3.6
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -9.434850190373923e-51 or -1.276743401231038e-140 < x

    1. Initial program 13.3

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

    3. Applied associate-/l*3.0

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}}\]
    4. Using strategy rm

    5. Applied frac-2neg3.0

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

    if -9.434850190373923e-51 < x < -1.276743401231038e-140

    1. Initial program 2.1

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

    3. Applied associate-/l*5.1

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}}\]
    4. Using strategy rm

    5. Applied associate-/r/10.0

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

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.43485019037392297 \cdot 10^{-51} \lor \neg \left(x \le -1.276743401231038 \cdot 10^{-140}\right):\\ \;\;\;\;\frac{x}{\frac{-y}{-\left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))