Average Error: 12.8 → 1.9
Time: 2.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 9.154941957803031 \cdot 10^{-62} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.74805499515868977 \cdot 10^{289}\right):\\ \;\;\;\;x \cdot \left(1 \cdot \left(1 - \frac{z}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 9.154941957803031 \cdot 10^{-62} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.74805499515868977 \cdot 10^{289}\right):\\
\;\;\;\;x \cdot \left(1 \cdot \left(1 - \frac{z}{y}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{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 temp;
	if (((((x * (y - z)) / y) <= 9.154941957803031e-62) || !(((x * (y - z)) / y) <= 1.7480549951586898e+289))) {
		temp = (x * (1.0 * (1.0 - (z / y))));
	} else {
		temp = ((x * (y - z)) / y);
	}
	return temp;
}

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

Original12.8
Target3.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < 9.154941957803031e-62 or 1.7480549951586898e+289 < (/ (* x (- y z)) y)

    1. Initial program 17.0

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

    3. Applied *-un-lft-identity17.0

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

    4. Applied times-frac2.5

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}}\]

    5. Simplified2.5

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

    7. Applied *-un-lft-identity2.5

      \[\leadsto x \cdot \frac{y - z}{\color{blue}{1 \cdot y}}\]

    8. Applied *-un-lft-identity2.5

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

    9. Applied times-frac2.5

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

    10. Simplified2.5

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

    11. Simplified2.5

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

    if 9.154941957803031e-62 < (/ (* x (- y z)) y) < 1.7480549951586898e+289

    1. Initial program 0.3

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 9.154941957803031 \cdot 10^{-62} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.74805499515868977 \cdot 10^{289}\right):\\ \;\;\;\;x \cdot \left(1 \cdot \left(1 - \frac{z}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 +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))