Average Error: 6.0 → 0.6
Time: 5.2s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} = -inf.0:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{a}{t - z}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 5.72597468503871405 \cdot 10^{222}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} = -inf.0:\\
\;\;\;\;x + y \cdot \frac{1}{\frac{a}{t - z}}\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 5.72597468503871405 \cdot 10^{222}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

\mathbf{else}:\\
\;\;\;\;x + \left(t - z\right) \cdot \frac{y}{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) (((double) (y * ((double) (z - t)))) / a)) <= -inf.0)) {
		VAR = ((double) (x + ((double) (y * ((double) (1.0 / ((double) (a / ((double) (t - z))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y * ((double) (z - t)))) / a)) <= 5.725974685038714e+222)) {
			VAR_1 = ((double) (x - ((double) (((double) (y * ((double) (z - t)))) / a))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (t - z)) * ((double) (y / 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

Original6.0
Target0.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* y (- z t)) a) < -inf.0

    1. Initial program 64.0

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

    2. Simplified0.2

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

    4. Applied clear-num0.3

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

    if -inf.0 < (/ (* y (- z t)) a) < 5.72597468503871405e222

    1. Initial program 0.3

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

    if 5.72597468503871405e222 < (/ (* y (- z t)) a)

    1. Initial program 31.6

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

    2. Simplified12.7

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

    4. Applied clear-num12.7

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

    6. Applied associate-/r/12.7

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

    7. Applied associate-*r*4.1

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

    8. Simplified4.0

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} = -inf.0:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{a}{t - z}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 5.72597468503871405 \cdot 10^{222}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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)))