Average Error: 5.9 → 0.4
Time: 4.1s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -7.329837396606733 \cdot 10^{+256}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5.351143384782188 \cdot 10^{+233}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -7.329837396606733 \cdot 10^{+256}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 5.351143384782188 \cdot 10^{+233}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

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

\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)) -7.329837396606733e+256)
   (- x (/ y (/ a (- z t))))
   (if (<= (* y (- z t)) 5.351143384782188e+233)
     (- x (/ (* y (- z t)) a))
     (- x (* (- z t) (/ y a))))))
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)) <= -7.329837396606733e+256) {
		tmp = x - (y / (a / (z - t)));
	} else if ((y * (z - t)) <= 5.351143384782188e+233) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - ((z - t) * (y / a));
	}
	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

Original5.9
Target0.8
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)) < -7.3298373966067332e256

    1. Initial program 41.8

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

    3. Applied associate-/l*_binary64_105940.2

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

    if -7.3298373966067332e256 < (*.f64 y (-.f64 z t)) < 5.3511433847821882e233

    1. Initial program 0.4

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

    if 5.3511433847821882e233 < (*.f64 y (-.f64 z t))

    1. Initial program 33.4

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

    3. Applied add-cube-cbrt_binary64_1068433.8

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

    4. Applied associate-/r*_binary64_1059333.8

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

    5. Simplified8.4

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

    7. Applied *-un-lft-identity_binary64_106498.4

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

    8. Applied times-frac_binary64_106551.0

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

    9. Simplified1.0

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

    10. Simplified0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -7.329837396606733 \cdot 10^{+256}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5.351143384782188 \cdot 10^{+233}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020355 
(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)))