Average Error: 5.9 → 0.3
Time: 5.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.5251367727114 \cdot 10^{+288} \lor \neg \left(y \cdot \left(z - t\right) \leq 2.17459616770256 \cdot 10^{+291}\right):\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -2.5251367727114 \cdot 10^{+288} \lor \neg \left(y \cdot \left(z - t\right) \leq 2.17459616770256 \cdot 10^{+291}\right):\\
\;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\

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

\end{array}
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 (((((double) (y * ((double) (z - t)))) <= -2.5251367727114e+288) || !(((double) (y * ((double) (z - t)))) <= 2.17459616770256e+291))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) * (1.0 / a)))))));
	} else {
		VAR = ((double) (x + (((double) (y * ((double) (z - t)))) / 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
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -2.5251367727114001e288 or 2.17459616770256e291 < (* y (- z t))

    1. Initial program Error: 54.8 bits

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

    2. SimplifiedError: 0.2 bits

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

    4. Applied div-invError: 0.3 bits

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

    if -2.5251367727114001e288 < (* y (- z t)) < 2.17459616770256e291

    1. Initial program Error: 0.3 bits

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

  4. Final simplificationError: 0.3 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.5251367727114 \cdot 10^{+288} \lor \neg \left(y \cdot \left(z - t\right) \leq 2.17459616770256 \cdot 10^{+291}\right):\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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 (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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