Average Error: 5.8 → 2.2
Time: 9.7s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.27783139542532109 \cdot 10^{-292} \lor \neg \left(t \le 2.03120907708558159 \cdot 10^{-227}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.27783139542532109 \cdot 10^{-292} \lor \neg \left(t \le 2.03120907708558159 \cdot 10^{-227}\right):\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x - ((double) (((double) (y * ((double) (z - t)))) / a))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((t <= -4.277831395425321e-292) || !(t <= 2.0312090770855816e-227))) {
		VAR = ((double) (x - ((double) (((double) (y / a)) * ((double) (z - t))))));
	} else {
		VAR = ((double) (x - ((double) (y / ((double) (a / ((double) (z - t))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target0.7
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.27783139542532109e-292 or 2.03120907708558159e-227 < t

    1. Initial program 6.0

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

    3. Applied associate-/l*6.1

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

    5. Applied associate-/r/2.2

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

    if -4.27783139542532109e-292 < t < 2.03120907708558159e-227

    1. Initial program 4.0

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

    3. Applied associate-/l*2.7

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.27783139542532109 \cdot 10^{-292} \lor \neg \left(t \le 2.03120907708558159 \cdot 10^{-227}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))