Average Error: 6.0 → 0.6
Time: 36.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -1.3475221070690317 \cdot 10^{+274}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.3829687109837004 \cdot 10^{+156}:\\ \;\;\;\;x + \left(\frac{y \cdot z}{a} - \frac{y \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -1.3475221070690317 \cdot 10^{+274}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.3829687109837004 \cdot 10^{+156}:\\
\;\;\;\;x + \left(\frac{y \cdot z}{a} - \frac{y \cdot t}{a}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z - t}{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)) -1.3475221070690317e+274)
   (+ x (/ y (/ a (- z t))))
   (if (<= (* y (- z t)) 1.3829687109837004e+156)
     (+ x (- (/ (* y z) a) (/ (* y t) a)))
     (+ x (* y (/ (- z t) 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)) <= -1.3475221070690317e+274) {
		tmp = x + (y / (a / (z - t)));
	} else if ((y * (z - t)) <= 1.3829687109837004e+156) {
		tmp = x + (((y * z) / a) - ((y * t) / a));
	} else {
		tmp = x + (y * ((z - t) / 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

Original6.0
Target0.8
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 y (-.f64 z t)) < -1.3475221070690317e274

    1. Initial program 47.7

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

    3. Applied associate-/l*_binary64_82070.2

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

    if -1.3475221070690317e274 < (*.f64 y (-.f64 z t)) < 1.3829687109837004e156

    1. Initial program 0.4

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

    2. Taylor expanded around 0 0.4

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

    if 1.3829687109837004e156 < (*.f64 y (-.f64 z t))

    1. Initial program 20.7

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

    3. Applied *-un-lft-identity_binary64_826220.7

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

    4. Applied times-frac_binary64_82682.0

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{z - t}{a}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -1.3475221070690317 \cdot 10^{+274}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 1.3829687109837004 \cdot 10^{+156}:\\ \;\;\;\;x + \left(\frac{y \cdot z}{a} - \frac{y \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2021090 
(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)))