Average Error: 6.1 → 1.0
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.46399435477971523 \cdot 10^{251}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 5.02388448113049226 \cdot 10^{87}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -5.46399435477971523 \cdot 10^{251}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 5.02388448113049226 \cdot 10^{87}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\

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

\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)))) <= -5.463994354779715e+251)) {
		VAR = ((double) (x + ((double) (((double) (y / a)) * ((double) (z - t))))));
	} else {
		double VAR_1;
		if ((((double) (y * ((double) (z - t)))) <= 5.023884481130492e+87)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / a))));
		} else {
			VAR_1 = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / a))))));
		}
		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

Original6.1
Target0.8
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -5.463994354779715e+251

    1. Initial program 40.7

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

    3. Applied clear-num40.7

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}}\]
    4. Using strategy rm

    5. Applied associate-/r*0.3

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

    7. Applied div-inv0.3

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

    8. Applied add-cube-cbrt0.3

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{a}{y} \cdot \frac{1}{z - t}}\]

    9. Applied times-frac0.4

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{a}{y}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{z - t}}}\]

    10. Simplified0.3

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{z - t}}\]

    11. Simplified0.2

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

    if -5.463994354779715e+251 < (* y (- z t)) < 5.023884481130492e+87

    1. Initial program 0.5

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

    if 5.023884481130492e+87 < (* y (- z t))

    1. Initial program 15.1

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

    3. Applied *-un-lft-identity15.1

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

    4. Applied times-frac3.4

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

    5. Simplified3.4

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.46399435477971523 \cdot 10^{251}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 5.02388448113049226 \cdot 10^{87}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020121 
(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 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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