Average Error: 6.1 → 0.7
Time: 7.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.371682285636237 \cdot 10^{+219}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5.845663913548385 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -3.371682285636237 \cdot 10^{+219}:\\
\;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 5.845663913548385 \cdot 10^{+126}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\

\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)) -3.371682285636237e+219)
   (+ x (* (- z t) (/ y a)))
   (if (<= (* y (- z t)) 5.845663913548385e+126)
     (+ x (/ (* y (- z 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)) <= -3.371682285636237e+219) {
		tmp = x + ((z - t) * (y / a));
	} else if ((y * (z - t)) <= 5.845663913548385e+126) {
		tmp = x + ((y * (z - 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

Original6.1
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 y (-.f64 z t)) < -3.37168228563623683e219

    1. Initial program 33.1

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

    3. Applied associate-/l*_binary64_85480.7

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

    5. Applied associate-/r/_binary64_85490.5

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

    if -3.37168228563623683e219 < (*.f64 y (-.f64 z t)) < 5.84566391354838511e126

    1. Initial program 0.5

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

    if 5.84566391354838511e126 < (*.f64 y (-.f64 z t))

    1. Initial program 18.0

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

    3. Applied *-un-lft-identity_binary64_860318.0

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

    4. Applied times-frac_binary64_86092.2

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

    5. Simplified2.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -3.371682285636237 \cdot 10^{+219}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5.845663913548385 \cdot 10^{+126}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(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)))