Average Error: 5.9 → 0.4
Time: 3.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8774048015909977 \cdot 10^{237} \lor \neg \left(y \cdot \left(z - t\right) \le 2.37303420758733905 \cdot 10^{217}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.8774048015909977 \cdot 10^{237} \lor \neg \left(y \cdot \left(z - t\right) \le 2.37303420758733905 \cdot 10^{217}\right):\\
\;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\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 (((((double) (y * ((double) (z - t)))) <= -1.8774048015909977e+237) || !(((double) (y * ((double) (z - t)))) <= 2.373034207587339e+217))) {
		VAR = ((double) (x + ((double) (((double) (z - t)) * ((double) (y / a))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (z * y)) / a)) - ((double) (((double) (t * y)) / 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

Original5.9
Target0.7
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -1.8774048015909977e+237 or 2.373034207587339e+217 < (* y (- z t))

    1. Initial program 33.6

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

    3. Applied *-un-lft-identity33.6

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

    4. Applied *-commutative33.6

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

    5. Applied times-frac0.6

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

    6. Simplified0.6

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

    if -1.8774048015909977e+237 < (* y (- z t)) < 2.373034207587339e+217

    1. Initial program 0.4

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

    3. Applied *-commutative0.4

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

    4. Applied associate-/l*2.6

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

    6. Applied div-sub2.6

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

    7. Simplified2.2

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

    8. Simplified0.4

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8774048015909977 \cdot 10^{237} \lor \neg \left(y \cdot \left(z - t\right) \le 2.37303420758733905 \cdot 10^{217}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020113 
(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)))