Average Error: 6.5 → 0.5
Time: 4.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -6.10307666411289603 \cdot 10^{197}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.2518092491125354 \cdot 10^{192}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -6.10307666411289603 \cdot 10^{197}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.2518092491125354 \cdot 10^{192}:\\
\;\;\;\;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) (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)))) <= -6.103076664112896e+197)) {
		VAR = ((double) (x + ((double) (y * (((double) (z - t)) / a)))));
	} else {
		double VAR_1;
		if ((((double) (y * ((double) (z - t)))) <= 1.2518092491125354e+192)) {
			VAR_1 = ((double) (x + (((double) (y * ((double) (z - t)))) / a)));
		} else {
			VAR_1 = ((double) (x + (y / (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

Original6.5
Target0.7
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -6.10307666411289603e197

    1. Initial program 29.4

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

    2. Simplified0.6

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

    if -6.10307666411289603e197 < (* y (- z t)) < 1.2518092491125354e192

    1. Initial program 0.4

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

    if 1.2518092491125354e192 < (* y (- z t))

    1. Initial program 27.8

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

    2. Simplified0.8

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

    4. Applied clear-num0.8

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a}{z - t}}}\]
    5. Using strategy rm

    6. Applied un-div-inv0.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -6.10307666411289603 \cdot 10^{197}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.2518092491125354 \cdot 10^{192}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))