Average Error: 12.7 → 3.1
Time: 1.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -7.5792715376466816 \cdot 10^{186} \lor \neg \left(z \le 3.69561090197641088 \cdot 10^{128}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -7.5792715376466816 \cdot 10^{186} \lor \neg \left(z \le 3.69561090197641088 \cdot 10^{128}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (y - z)))) / y));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -7.579271537646682e+186) || !(z <= 3.695610901976411e+128))) {
		VAR = ((double) (((double) (x / y)) * ((double) (y - z))));
	} else {
		VAR = ((double) (x / ((double) (y / ((double) (y - z))))));
	}
	return VAR;
}

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
Target3.0
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.579271537646682e+186 or 3.695610901976411e+128 < z

    1. Initial program 13.5

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

    3. Applied associate-/l*11.2

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

    5. Applied associate-/r/11.3

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

    if -7.579271537646682e+186 < z < 3.695610901976411e+128

    1. Initial program 12.6

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

    3. Applied associate-/l*1.3

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.5792715376466816 \cdot 10^{186} \lor \neg \left(z \le 3.69561090197641088 \cdot 10^{128}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020129 
(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))