Average Error: 12.7 → 0.4
Time: 11.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \le -2.523673116498965249180632340744567270682 \cdot 10^{284}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.256094014734885958876760293725805613458 \cdot 10^{-72}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 1.040091529858863440688059953611168253115 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 2.546060910949810566653930570467710796416 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \le -2.523673116498965249180632340744567270682 \cdot 10^{284}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.256094014734885958876760293725805613458 \cdot 10^{-72}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 1.040091529858863440688059953611168253115 \cdot 10^{-197}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 2.546060910949810566653930570467710796416 \cdot 10^{306}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r40990559 = x;
        double r40990560 = y;
        double r40990561 = z;
        double r40990562 = r40990560 - r40990561;
        double r40990563 = r40990559 * r40990562;
        double r40990564 = r40990563 / r40990560;
        return r40990564;
}
↓
double f(double x, double y, double z) {
        double r40990565 = y;
        double r40990566 = z;
        double r40990567 = r40990565 - r40990566;
        double r40990568 = x;
        double r40990569 = r40990567 * r40990568;
        double r40990570 = r40990569 / r40990565;
        double r40990571 = -2.5236731164989652e+284;
        bool r40990572 = r40990570 <= r40990571;
        double r40990573 = r40990565 / r40990567;
        double r40990574 = r40990568 / r40990573;
        double r40990575 = -3.256094014734886e-72;
        bool r40990576 = r40990570 <= r40990575;
        double r40990577 = 1.0400915298588634e-197;
        bool r40990578 = r40990570 <= r40990577;
        double r40990579 = 2.5460609109498106e+306;
        bool r40990580 = r40990570 <= r40990579;
        double r40990581 = r40990580 ? r40990570 : r40990574;
        double r40990582 = r40990578 ? r40990574 : r40990581;
        double r40990583 = r40990576 ? r40990570 : r40990582;
        double r40990584 = r40990572 ? r40990574 : r40990583;
        return r40990584;
}

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
Target3.2
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < -2.5236731164989652e+284 or -3.256094014734886e-72 < (/ (* x (- y z)) y) < 1.0400915298588634e-197 or 2.5460609109498106e+306 < (/ (* x (- y z)) y)

    1. Initial program 32.6

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

    3. Applied associate-/l*0.6

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

    if -2.5236731164989652e+284 < (/ (* x (- y z)) y) < -3.256094014734886e-72 or 1.0400915298588634e-197 < (/ (* x (- y z)) y) < 2.5460609109498106e+306

    1. Initial program 0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \le -2.523673116498965249180632340744567270682 \cdot 10^{284}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.256094014734885958876760293725805613458 \cdot 10^{-72}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 1.040091529858863440688059953611168253115 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 2.546060910949810566653930570467710796416 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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))