Average Error: 6.3 → 0.5
Time: 4.1min
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -7.70801392572327344 \cdot 10^{222}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.31644994767174427 \cdot 10^{172}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -7.70801392572327344 \cdot 10^{222}:\\
\;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.31644994767174427 \cdot 10^{172}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(t - z\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)))) <= -7.708013925723273e+222)) {
		VAR = ((double) (x + (((double) (t - z)) / (a / y))));
	} else {
		double VAR_1;
		if ((((double) (y * ((double) (z - t)))) <= 1.3164499476717443e+172)) {
			VAR_1 = ((double) (x - (((double) (y * ((double) (z - t)))) / a)));
		} else {
			VAR_1 = ((double) (x + ((double) ((y / a) * ((double) (t - z))))));
		}
		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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -7.70801392572327344e222

    1. Initial program 31.6

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

    3. Applied *-un-lft-identity31.6

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

    4. Applied times-frac0.8

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

    5. Simplified0.8

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

    7. Applied sub-neg0.8

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

    8. Simplified0.8

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

    if -7.70801392572327344e222 < (* y (- z t)) < 1.31644994767174427e172

    1. Initial program 0.4

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

    if 1.31644994767174427e172 < (* y (- z t))

    1. Initial program 24.5

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

    3. Applied sub-neg24.5

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

    4. Simplified1.2

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -7.70801392572327344 \cdot 10^{222}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.31644994767174427 \cdot 10^{172}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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)))