Average Error: 6.5 → 0.5
Time: 3.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.961337850366166 \cdot 10^{+222}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.2914759979061437 \cdot 10^{+248}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -2.961337850366166 \cdot 10^{+222}:\\
\;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.2914759979061437 \cdot 10^{+248}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\

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

\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)))) <= -2.961337850366166e+222)) {
		VAR = ((double) (x + ((double) (((double) (z - t)) * (y / a)))));
	} else {
		double VAR_1;
		if ((((double) (y * ((double) (z - t)))) <= 1.2914759979061437e+248)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) * (1.0 / a)))));
		} else {
			VAR_1 = ((double) (x + ((double) (y * ((double) ((z / a) - (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

Original6.5
Target0.8
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -2.96133785036616623e222

    1. Initial program 33.3

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

    2. Simplified0.5

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

    4. Applied div-sub0.5

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

    6. Applied div-inv0.5

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

    7. Applied div-inv0.6

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

    8. Applied distribute-rgt-out--0.6

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

    9. Applied associate-*r*0.5

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

    10. Simplified0.4

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

    if -2.96133785036616623e222 < (* y (- z t)) < 1.29147599790614367e248

    1. Initial program 0.5

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

    2. Simplified7.0

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

    4. Applied div-inv7.0

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

    5. Applied associate-*r*0.5

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

    if 1.29147599790614367e248 < (* y (- z t))

    1. Initial program 39.5

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

    2. Simplified0.4

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

    4. Applied div-sub0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.961337850366166 \cdot 10^{+222}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.2914759979061437 \cdot 10^{+248}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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)))