Average Error: 6.1 → 1.0
Time: 2.8s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.39267331937567577 \cdot 10^{-17} \lor \neg \left(y \le 4.7790321465538917 \cdot 10^{-95}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.39267331937567577 \cdot 10^{-17} \lor \neg \left(y \le 4.7790321465538917 \cdot 10^{-95}\right):\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

\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 (((y <= -1.3926733193756758e-17) || !(y <= 4.779032146553892e-95))) {
		temp = (x - (y / (a / (z - t))));
	} else {
		temp = (x - (1.0 / (a / (y * (z - t)))));
	}
	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
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.3926733193756758e-17 or 4.779032146553892e-95 < y

    1. Initial program 12.0

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

    3. Applied associate-/l*1.3

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

    if -1.3926733193756758e-17 < y < 4.779032146553892e-95

    1. Initial program 0.7

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

    3. Applied clear-num0.7

      \[\leadsto x - \color{blue}{\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.39267331937567577 \cdot 10^{-17} \lor \neg \left(y \le 4.7790321465538917 \cdot 10^{-95}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]

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, F"
  :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)))