Average Error: 6.5 → 2.4
Time: 4.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -8.77907409067161722 \cdot 10^{-14} \lor \neg \left(y \cdot \left(z - t\right) \le 2.98120741983821543 \cdot 10^{186}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -8.77907409067161722 \cdot 10^{-14} \lor \neg \left(y \cdot \left(z - t\right) \le 2.98120741983821543 \cdot 10^{186}\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 ((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)))) <= -8.779074090671617e-14) || !(((double) (y * ((double) (z - t)))) <= 2.9812074198382154e+186))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / a))))));
	} else {
		VAR = ((double) (x + ((double) (1.0 / ((double) (a / ((double) (y * ((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

Original6.5
Target0.8
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -8.77907409067161722e-14 or 2.98120741983821543e186 < (* y (- z t))

    1. Initial program 15.0

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

    2. Simplified4.8

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

    if -8.77907409067161722e-14 < (* y (- z t)) < 2.98120741983821543e186

    1. Initial program 0.6

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

    3. Applied clear-num0.7

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -8.77907409067161722 \cdot 10^{-14} \lor \neg \left(y \cdot \left(z - t\right) \le 2.98120741983821543 \cdot 10^{186}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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)))