Average Error: 12.3 → 2.0
Time: 1.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.88974202997066505 \cdot 10^{-158} \lor \neg \left(x \le 1.07737698380717868 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -9.88974202997066505 \cdot 10^{-158} \lor \neg \left(x \le 1.07737698380717868 \cdot 10^{-151}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((x * (y - z)) / y);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((x <= -9.889742029970665e-158) || !(x <= 1.0773769838071787e-151))) {
		VAR = (x / (y / (y - z)));
	} else {
		VAR = (x - ((x * z) / y));
	}
	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

Original12.3
Target3.0
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -9.889742029970665e-158 or 1.0773769838071787e-151 < x

    1. Initial program 14.6

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

    3. Applied associate-/l*1.3

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

    if -9.889742029970665e-158 < x < 1.0773769838071787e-151

    1. Initial program 7.0

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

    2. Taylor expanded around 0 3.4

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.88974202997066505 \cdot 10^{-158} \lor \neg \left(x \le 1.07737698380717868 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020071 +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))