Average Error: 6.2 → 0.8
Time: 4.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.6539155517775925 \cdot 10^{+134}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2.6317952106013106 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -2.6539155517775925 \cdot 10^{+134}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 2.6317952106013106 \cdot 10^{+162}:\\
\;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

\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)) -2.6539155517775925e+134)
   (+ x (/ y (/ a (- z t))))
   (if (<= (* y (- z t)) 2.6317952106013106e+162)
     (+ x (/ 1.0 (/ a (* y (- z t)))))
     (+ x (* (- z t) (/ y a))))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (y * ((double) (z - t)))) / a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((double) (y * ((double) (z - t)))) <= -2.6539155517775925e+134)) {
		tmp = ((double) (x + (y / (a / ((double) (z - t))))));
	} else {
		double tmp_1;
		if ((((double) (y * ((double) (z - t)))) <= 2.6317952106013106e+162)) {
			tmp_1 = ((double) (x + (1.0 / (a / ((double) (y * ((double) (z - t))))))));
		} else {
			tmp_1 = ((double) (x + ((double) (((double) (z - t)) * (y / a)))));
		}
		tmp = tmp_1;
	}
	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

Original6.2
Target0.8
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 y (-.f64 z t)) < -2.6539155517775925e134

    1. Initial program 19.2

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

    3. Applied associate-/l*_binary642.1

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

    if -2.6539155517775925e134 < (*.f64 y (-.f64 z t)) < 2.6317952106013106e162

    1. Initial program 0.5

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

    3. Applied clear-num_binary640.5

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

    if 2.6317952106013106e162 < (*.f64 y (-.f64 z t))

    1. Initial program 22.0

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

    3. Applied associate-/l*_binary641.7

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/_binary640.8

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.6539155517775925 \cdot 10^{+134}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2.6317952106013106 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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)))