Average Error: 6.3 → 0.9
Time: 5.2s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.7727444625810444 \cdot 10^{-43} \lor \neg \left(y \leq 4.0872069085301 \cdot 10^{-69}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.7727444625810444 \cdot 10^{-43} \lor \neg \left(y \leq 4.0872069085301 \cdot 10^{-69}\right):\\
\;\;\;\;x + y \cdot \frac{t - z}{a}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(t - z\right)}{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 -1.7727444625810444e-43) (not (<= y 4.0872069085301e-69)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ (* y (- t z)) 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 VAR;
	if (((y <= -1.7727444625810444e-43) || !(y <= 4.0872069085301e-69))) {
		VAR = ((double) (x + ((double) (y * (((double) (t - z)) / a)))));
	} else {
		VAR = ((double) (x + (((double) (y * ((double) (t - z)))) / a)));
	}
	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
Target0.8
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.7727444625810444e-43 or 4.0872069085300999e-69 < y

    1. Initial program 12.3

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

    2. Simplified1.2

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

    if -1.7727444625810444e-43 < y < 4.0872069085300999e-69

    1. Initial program 0.6

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7727444625810444 \cdot 10^{-43} \lor \neg \left(y \leq 4.0872069085301 \cdot 10^{-69}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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)))