Average Error: 6.1 → 1.5
Time: 3.0s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.5555026040340327 \cdot 10^{-76} \lor \neg \left(y \le 236520.52657286497\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.5555026040340327 \cdot 10^{-76} \lor \neg \left(y \le 236520.52657286497\right):\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

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

\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 (((y <= -2.5555026040340327e-76) || !(y <= 236520.52657286497))) {
		VAR = ((double) (x - ((double) (y * ((double) (((double) (z - t)) / a))))));
	} else {
		VAR = ((double) (x - ((double) (((double) (y / a)) * ((double) (z - t))))));
	}
	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

Original6.1
Target0.8
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.5555026040340327e-76 or 236520.52657286497 < y

    1. Initial program 12.8

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

    3. Applied *-un-lft-identity12.8

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

    4. Applied times-frac1.3

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

    5. Simplified1.3

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

    if -2.5555026040340327e-76 < y < 236520.52657286497

    1. Initial program 0.6

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

    3. Applied associate-/l*9.5

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

    5. Applied associate-/r/1.7

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.5555026040340327 \cdot 10^{-76} \lor \neg \left(y \le 236520.52657286497\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020121 
(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 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))