Average Error: 12.7 → 0.4
Time: 2.8s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.74240735694960229 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.74240735694960229 \cdot 10^{-106}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r1009145 = x;
        double r1009146 = y;
        double r1009147 = z;
        double r1009148 = r1009146 - r1009147;
        double r1009149 = r1009145 * r1009148;
        double r1009150 = r1009149 / r1009146;
        return r1009150;
}
↓
double f(double x, double y, double z) {
        double r1009151 = x;
        double r1009152 = y;
        double r1009153 = z;
        double r1009154 = r1009152 - r1009153;
        double r1009155 = r1009151 * r1009154;
        double r1009156 = r1009155 / r1009152;
        double r1009157 = -inf.0;
        bool r1009158 = r1009156 <= r1009157;
        double r1009159 = r1009152 / r1009154;
        double r1009160 = r1009151 / r1009159;
        double r1009161 = -5.742407356949602e-106;
        bool r1009162 = r1009156 <= r1009161;
        double r1009163 = 1.0101904628573289e+139;
        bool r1009164 = r1009156 <= r1009163;
        double r1009165 = 3.1488091740454137e+307;
        bool r1009166 = r1009156 <= r1009165;
        double r1009167 = r1009151 / r1009152;
        double r1009168 = r1009167 * r1009154;
        double r1009169 = r1009166 ? r1009156 : r1009168;
        double r1009170 = r1009164 ? r1009160 : r1009169;
        double r1009171 = r1009162 ? r1009156 : r1009170;
        double r1009172 = r1009158 ? r1009160 : r1009171;
        return r1009172;
}

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
Target3.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -inf.0 or -5.742407356949602e-106 < (/ (* x (- y z)) y) < 1.0101904628573289e+139

    1. Initial program 14.1

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

    3. Applied associate-/l*0.6

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

    if -inf.0 < (/ (* x (- y z)) y) < -5.742407356949602e-106 or 1.0101904628573289e+139 < (/ (* x (- y z)) y) < 3.1488091740454137e+307

    1. Initial program 0.3

      \[\frac{x \cdot \left(y - z\right)}{y}\]

    if 3.1488091740454137e+307 < (/ (* x (- y z)) y)

    1. Initial program 63.7

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

    3. Applied associate-/l*0.3

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

    5. Applied associate-/r/0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.74240735694960229 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +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))