Average Error: 6.1 → 0.8
Time: 4.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -7.9936955577655023 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \le 9.83225554937983249 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot 1}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -7.9936955577655023 \cdot 10^{-36}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;a \le 9.83225554937983249 \cdot 10^{-19}:\\
\;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot 1}{\frac{a}{z - t}}\\

\end{array}
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 temp;
	if ((a <= -7.993695557765502e-36)) {
		temp = (x + (y * ((z - t) / a)));
	} else {
		double temp_1;
		if ((a <= 9.832255549379832e-19)) {
			temp_1 = (x + (1.0 / (a / (y * (z - t)))));
		} else {
			temp_1 = (x + ((y * 1.0) / (a / (z - t))));
		}
		temp = temp_1;
	}
	return temp;
}

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
Target0.7
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -7.993695557765502e-36

    1. Initial program 8.6

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

    3. Applied *-un-lft-identity8.6

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

    4. Applied times-frac0.7

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

    5. Simplified0.7

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

    if -7.993695557765502e-36 < a < 9.832255549379832e-19

    1. Initial program 1.0

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

    3. Applied clear-num1.1

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

    if 9.832255549379832e-19 < a

    1. Initial program 8.8

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

    3. Applied *-un-lft-identity8.8

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

    4. Applied associate-*r*8.8

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

    5. Applied associate-/l*0.5

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.9936955577655023 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \le 9.83225554937983249 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot 1}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(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 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))