Average Error: 6.0 → 0.8
Time: 4.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -32476558814886848 \lor \neg \left(a \le 3.28528990138168409 \cdot 10^{-63}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -32476558814886848 \lor \neg \left(a \le 3.28528990138168409 \cdot 10^{-63}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (x + ((y * (z - t)) / a));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((a <= -3.247655881488685e+16) || !(a <= 3.285289901381684e-63))) {
		VAR = (x + (y * ((z - t) / a)));
	} else {
		VAR = (x + (1.0 / (a / (y * (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

Original6.0
Target0.6
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -3.247655881488685e+16 or 3.285289901381684e-63 < a

    1. Initial program 8.9

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

    3. Applied *-un-lft-identity8.9

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

    4. Applied times-frac0.8

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

    5. Simplified0.8

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

    if -3.247655881488685e+16 < a < 3.285289901381684e-63

    1. Initial program 0.8

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

    3. Applied clear-num0.9

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -32476558814886848 \lor \neg \left(a \le 3.28528990138168409 \cdot 10^{-63}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))