Average Error: 6.3 → 0.9
Time: 3.5s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.87721871110522447 \cdot 10^{164}:\\ \;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.16545704575117748 \cdot 10^{121}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -5.87721871110522447 \cdot 10^{164}:\\
\;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.16545704575117748 \cdot 10^{121}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

\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 ((((double) (y * ((double) (z - t)))) <= -5.877218711105224e+164)) {
		VAR = ((double) (x - ((double) (((double) (y / a)) / ((double) (1.0 / ((double) (z - t))))))));
	} else {
		double VAR_1;
		if ((((double) (y * ((double) (z - t)))) <= 1.1654570457511775e+121)) {
			VAR_1 = ((double) (x - ((double) (((double) (y * ((double) (z - t)))) / a))));
		} else {
			VAR_1 = ((double) (x - ((double) (y / ((double) (a / ((double) (z - t))))))));
		}
		VAR = VAR_1;
	}
	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

Original6.3
Target0.7
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -5.877218711105224e+164

    1. Initial program 23.6

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

    3. Applied associate-/l*1.3

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

    5. Applied div-inv1.3

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

    6. Applied associate-/r*0.8

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

    if -5.877218711105224e+164 < (* y (- z t)) < 1.1654570457511775e+121

    1. Initial program 0.5

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

    if 1.1654570457511775e+121 < (* y (- z t))

    1. Initial program 18.2

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

    3. Applied associate-/l*2.9

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.87721871110522447 \cdot 10^{164}:\\ \;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.16545704575117748 \cdot 10^{121}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020123 
(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 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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