Average Error: 5.9 → 0.6
Time: 3.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.85374084693398804 \cdot 10^{89}:\\ \;\;\;\;x + \left(-\frac{y}{a}\right) \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.2051286431763556 \cdot 10^{287}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -3.85374084693398804 \cdot 10^{89}:\\
\;\;\;\;x + \left(-\frac{y}{a}\right) \cdot \left(z - t\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.2051286431763556 \cdot 10^{287}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\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 (((y * (z - t)) <= -3.853740846933988e+89)) {
		VAR = (x + (-(y / a) * (z - t)));
	} else {
		double VAR_1;
		if (((y * (z - t)) <= 1.2051286431763556e+287)) {
			VAR_1 = (x - ((y * (z - t)) / a));
		} else {
			VAR_1 = (x - (y / (a / (z - t))));
		}
		VAR = VAR_1;
	}
	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
Target0.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -3.853740846933988e+89

    1. Initial program 15.0

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

    3. Applied clear-num15.0

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

    5. Applied sub-neg15.0

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

    6. Simplified2.0

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

    if -3.853740846933988e+89 < (* y (- z t)) < 1.2051286431763556e+287

    1. Initial program 0.3

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

    if 1.2051286431763556e+287 < (* y (- z t))

    1. Initial program 51.7

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

    3. Applied associate-/l*0.2

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.85374084693398804 \cdot 10^{89}:\\ \;\;\;\;x + \left(-\frac{y}{a}\right) \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.2051286431763556 \cdot 10^{287}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 
(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)))