Average Error: 12.5 → 3.4
Time: 3.4s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.9947624096786527 \cdot 10^{201}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{elif}\;z \le 3.5640512405086981 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.9947624096786527 \cdot 10^{201}:\\
\;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\

\mathbf{elif}\;z \le 3.5640512405086981 \cdot 10^{131}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\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 <= -2.9947624096786527e+201)) {
		VAR = ((double) (1.0 / ((double) (y / ((double) (x * ((double) (y - z))))))));
	} else {
		double VAR_1;
		if ((z <= 3.564051240508698e+131)) {
			VAR_1 = ((double) (x / ((double) (y / ((double) (y - z))))));
		} else {
			VAR_1 = ((double) (((double) (x / y)) * ((double) (y - z))));
		}
		VAR = VAR_1;
	}
	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

Original12.5
Target3.2
Herbie3.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -2.9947624096786527e201

    1. Initial program 16.9

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

    3. Applied clear-num16.9

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}}\]

    if -2.9947624096786527e201 < z < 3.5640512405086981e131

    1. Initial program 12.0

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

    3. Applied associate-/l*1.3

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

    if 3.5640512405086981e131 < z

    1. Initial program 13.9

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

    3. Applied associate-/l*10.1

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

    5. Applied associate-/r/11.5

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

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.9947624096786527 \cdot 10^{201}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{elif}\;z \le 3.5640512405086981 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020168 
(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))