Average Error: 6.2 → 0.7
Time: 4.1s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.358863466710942 \cdot 10^{+243} \lor \neg \left(y \cdot \left(z - t\right) \leq 2.732902262531023 \cdot 10^{+128}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -3.358863466710942 \cdot 10^{+243} \lor \neg \left(y \cdot \left(z - t\right) \leq 2.732902262531023 \cdot 10^{+128}\right):\\
\;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\

\mathbf{else}:\\
\;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\

\end{array}
(FPCore (x y z t a) :precision binary64 (- x (/ (* y (- z t)) a)))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* y (- z t)) -3.358863466710942e+243)
         (not (<= (* y (- z t)) 2.732902262531023e+128)))
   (+ x (* (/ y a) (- t z)))
   (- x (* (* y (- z t)) (/ 1.0 a)))))
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)))) <= -3.358863466710942e+243) || !(((double) (y * ((double) (z - t)))) <= 2.732902262531023e+128))) {
		tmp = ((double) (x + ((double) ((y / a) * ((double) (t - z))))));
	} else {
		tmp = ((double) (x - ((double) (((double) (y * ((double) (z - t)))) * (1.0 / a)))));
	}
	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

Original6.2
Target0.8
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 2 regimes

  2. if (*.f64 y (-.f64 z t)) < -3.3588634667109421e243 or 2.73290226253102294e128 < (*.f64 y (-.f64 z t))

    1. Initial program 25.3

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

    3. Applied sub-neg_binary6425.3

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

    4. Simplified1.5

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

    if -3.3588634667109421e243 < (*.f64 y (-.f64 z t)) < 2.73290226253102294e128

    1. Initial program 0.4

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

    3. Applied div-inv_binary640.5

      \[\leadsto x - \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.358863466710942 \cdot 10^{+243} \lor \neg \left(y \cdot \left(z - t\right) \leq 2.732902262531023 \cdot 10^{+128}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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)))