Average Error: 6.1 → 1.2
Time: 3.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -5.028213798595296 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 6.020779023830261 \cdot 10^{-201}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \leq -5.028213798595296 \cdot 10^{+22}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;a \leq 6.020779023830261 \cdot 10^{-201}:\\
\;\;\;\;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 (<= a -5.028213798595296e+22)
   (+ x (* y (/ (- z t) a)))
   (if (<= a 6.020779023830261e-201)
     (+ 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 (a <= -5.028213798595296e+22) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 6.020779023830261e-201) {
		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

Original6.1
Target0.6
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -5.02821379859529586e22

    1. Initial program 9.5

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

    3. Applied *-un-lft-identity_binary649.5

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

    4. Applied times-frac_binary640.5

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

    5. Simplified0.5

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

    if -5.02821379859529586e22 < a < 6.0207790238302608e-201

    1. Initial program 0.8

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

    if 6.0207790238302608e-201 < a

    1. Initial program 6.8

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

    3. Applied add-cube-cbrt_binary647.2

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

    4. Applied times-frac_binary642.6

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

    6. Applied pow1_binary642.6

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

    7. Applied pow1_binary642.6

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

    8. Applied pow-prod-down_binary642.6

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

    9. Simplified1.9

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.028213798595296 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 6.020779023830261 \cdot 10^{-201}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020231 
(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)))