Average Error: 6.3 → 0.4
Time: 8.6s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.140199905049377 \cdot 10^{+275}:\\ \;\;\;\;x - y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.286315470243138 \cdot 10^{+250}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -3.140199905049377 \cdot 10^{+275}:\\
\;\;\;\;x - y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.286315470243138 \cdot 10^{+250}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (- x (/ (* y (- z t)) a)))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y (- z t)) -3.140199905049377e+275)
   (- x (* y (* (- z t) (/ 1.0 a))))
   (if (<= (* y (- z t)) 1.286315470243138e+250)
     (- x (/ (* y (- z t)) a))
     (- x (/ y (/ a (- z t)))))))
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 tmp;
	if ((y * (z - t)) <= -3.140199905049377e+275) {
		tmp = x - (y * ((z - t) * (1.0 / a)));
	} else if ((y * (z - t)) <= 1.286315470243138e+250) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

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

Original6.3
Target0.6
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 y (-.f64 z t)) < -3.14019990504937724e275

    1. Initial program 49.5

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

    3. Applied add-cube-cbrt_binary64_1136649.7

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

    4. Applied times-frac_binary64_113371.1

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

    6. Applied div-inv_binary64_113281.1

      \[\leadsto x - \color{blue}{\left(y \cdot \frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right)} \cdot \frac{z - t}{\sqrt[3]{a}}\]

    7. Applied associate-*l*_binary64_112721.1

      \[\leadsto x - \color{blue}{y \cdot \left(\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)}\]

    8. Simplified0.3

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

    if -3.14019990504937724e275 < (*.f64 y (-.f64 z t)) < 1.28631547024313807e250

    1. Initial program 0.4

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

    if 1.28631547024313807e250 < (*.f64 y (-.f64 z t))

    1. Initial program 41.3

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

    3. Applied associate-/l*_binary64_112760.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.140199905049377 \cdot 10^{+275}:\\ \;\;\;\;x - y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.286315470243138 \cdot 10^{+250}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(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)))