Average Error: 5.8 → 0.7
Time: 4.3s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.144686656547863 \cdot 10^{+132}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 6.976797937108467 \cdot 10^{+210}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -3.144686656547863 \cdot 10^{+132}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 6.976797937108467 \cdot 10^{+210}:\\
\;\;\;\;x + \frac{-1}{\frac{a}{y \cdot \left(z - t\right)}}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (- x (/ (* y (- z t)) a)))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y (- z t)) -3.144686656547863e+132)
   (- x (/ y (/ a (- z t))))
   (if (<= (* y (- z t)) 6.976797937108467e+210)
     (+ x (/ -1.0 (/ a (* y (- z t)))))
     (+ x (* (/ y a) (- t z))))))
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 tmp;
	if ((((double) (y * ((double) (z - t)))) <= -3.144686656547863e+132)) {
		tmp = ((double) (x - (y / (a / ((double) (z - t))))));
	} else {
		double tmp_1;
		if ((((double) (y * ((double) (z - t)))) <= 6.976797937108467e+210)) {
			tmp_1 = ((double) (x + (-1.0 / (a / ((double) (y * ((double) (z - t))))))));
		} else {
			tmp_1 = ((double) (x + ((double) ((y / a) * ((double) (t - z))))));
		}
		tmp = tmp_1;
	}
	return tmp;
}

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

Original5.8
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -3.14468665654786308e132

    1. Initial program Error: 18.7 bits

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

    3. Applied associate-/l*Error: 1.7 bits

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

    if -3.14468665654786308e132 < (* y (- z t)) < 6.9767979371084669e210

    1. Initial program Error: 0.4 bits

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

    3. Applied clear-numError: 0.4 bits

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

    if 6.9767979371084669e210 < (* y (- z t))

    1. Initial program Error: 29.9 bits

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

    3. Applied sub-negError: 29.9 bits

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

    4. SimplifiedError: 0.7 bits

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

  4. Final simplificationError: 0.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.144686656547863 \cdot 10^{+132}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 6.976797937108467 \cdot 10^{+210}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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)))