Average Error: 6.1 → 1.5
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.072638126039449 \cdot 10^{-79} \lor \neg \left(y \le 236520.52657286497\right):\\ \;\;\;\;y \cdot \frac{z - t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.072638126039449 \cdot 10^{-79} \lor \neg \left(y \le 236520.52657286497\right):\\
\;\;\;\;y \cdot \frac{z - t}{a} + x\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / a))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((y <= -6.072638126039449e-79) || !(y <= 236520.52657286497))) {
		VAR = ((double) (((double) (y * ((double) (((double) (z - t)) / a)))) + x));
	} else {
		VAR = ((double) (((double) (((double) (y / a)) * ((double) (z - t)))) + x));
	}
	return VAR;
}

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
Target0.8
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.072638126039449e-79 or 236520.52657286497 < y

    1. Initial program 12.7

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

    2. Simplified3.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef3.1

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

    6. Applied div-inv3.2

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

    7. Applied associate-*l*1.4

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

    8. Simplified1.3

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

    if -6.072638126039449e-79 < y < 236520.52657286497

    1. Initial program 0.6

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

    2. Simplified1.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef1.7

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.072638126039449 \cdot 10^{-79} \lor \neg \left(y \le 236520.52657286497\right):\\ \;\;\;\;y \cdot \frac{z - t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020121 +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)))