Average Error: 12.4 → 3.6
Time: 5.3s
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 r795949 = x;
        double r795950 = y;
        double r795951 = z;
        double r795952 = r795950 - r795951;
        double r795953 = r795949 * r795952;
        double r795954 = r795953 / r795950;
        return r795954;
}
↓
double f(double x, double y, double z) {
        double r795955 = x;
        double r795956 = -9.434850190373923e-51;
        bool r795957 = r795955 <= r795956;
        double r795958 = -1.276743401231038e-140;
        bool r795959 = r795955 <= r795958;
        double r795960 = !r795959;
        bool r795961 = r795957 || r795960;
        double r795962 = y;
        double r795963 = -r795962;
        double r795964 = z;
        double r795965 = r795962 - r795964;
        double r795966 = -r795965;
        double r795967 = r795963 / r795966;
        double r795968 = r795955 / r795967;
        double r795969 = r795955 / r795962;
        double r795970 = r795969 * r795965;
        double r795971 = r795961 ? r795968 : r795970;
        return r795971;
}

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 +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))