Average Error: 6.2 → 1.2
Time: 4.6s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -0.0:\\ \;\;\;\;x - \left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 1.08793558090891271 \cdot 10^{303}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -0.0:\\
\;\;\;\;x - \left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}}}\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 1.08793558090891271 \cdot 10^{303}:\\
\;\;\;\;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 ((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) (((double) (y * ((double) (z - t)))) / a)) <= -0.0)) {
		VAR = ((double) (x - ((double) (((double) (((double) (y / ((double) (((double) cbrt(a)) * ((double) cbrt(a)))))) * ((double) (((double) (((double) cbrt(((double) (z - t)))) * ((double) cbrt(((double) (z - t)))))) / ((double) (((double) cbrt(((double) cbrt(a)))) * ((double) cbrt(((double) cbrt(a)))))))))) * ((double) (((double) cbrt(((double) (z - t)))) / ((double) cbrt(((double) cbrt(a))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (y * ((double) (z - t)))) / a)) <= 1.0879355809089127e+303)) {
			VAR_1 = ((double) (x - ((double) (((double) (y * ((double) (z - t)))) / a))));
		} else {
			VAR_1 = ((double) (x - ((double) (y / ((double) (a / ((double) (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

Original6.2
Target0.7
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* y (- z t)) a) < -0.0

    1. Initial program 5.5

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

    3. Applied add-cube-cbrt5.9

      \[\leadsto x - \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\]

    4. Applied times-frac3.0

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

    6. Applied add-cube-cbrt3.2

      \[\leadsto x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right) \cdot \sqrt[3]{\sqrt[3]{a}}}}\]

    7. Applied add-cube-cbrt3.2

      \[\leadsto x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right) \cdot \sqrt[3]{\sqrt[3]{a}}}\]

    8. Applied times-frac3.2

      \[\leadsto x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \color{blue}{\left(\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}}}\right)}\]

    9. Applied associate-*r*1.9

      \[\leadsto x - \color{blue}{\left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}}}}\]

    if -0.0 < (/ (* y (- z t)) a) < 1.08793558090891271e303

    1. Initial program 0.1

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

    if 1.08793558090891271e303 < (/ (* y (- z t)) a)

    1. Initial program 61.0

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

    3. Applied associate-/l*1.8

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -0.0:\\ \;\;\;\;x - \left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a}}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \le 1.08793558090891271 \cdot 10^{303}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020149 
(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 (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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