Average Error: 5.9 → 0.5
Time: 3.2s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -7.2242271345987932 \cdot 10^{168}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - z, x\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.63793512063663311 \cdot 10^{269}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -7.2242271345987932 \cdot 10^{168}:\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - z, x\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 2.63793512063663311 \cdot 10^{269}:\\
\;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\

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

\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 ((((double) (y * ((double) (z - t)))) <= -7.224227134598793e+168)) {
		VAR = ((double) fma(((double) (y / a)), ((double) (t - z)), x));
	} else {
		double VAR_1;
		if ((((double) (y * ((double) (z - t)))) <= 2.637935120636633e+269)) {
			VAR_1 = ((double) (x - ((double) (((double) (y * ((double) (z - t)))) * ((double) (1.0 / a))))));
		} else {
			VAR_1 = ((double) (x - ((double) (y / ((double) (a / ((double) (z - t))))))));
		}
		VAR = VAR_1;
	}
	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

Original5.9
Target0.7
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -7.224227134598793e+168

    1. Initial program 24.0

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

    2. Simplified1.3

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

    if -7.224227134598793e+168 < (* y (- z t)) < 2.637935120636633e+269

    1. Initial program 0.4

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

    3. Applied div-inv0.5

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

    if 2.637935120636633e+269 < (* y (- z t))

    1. Initial program 46.2

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

    3. Applied associate-/l*0.2

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -7.2242271345987932 \cdot 10^{168}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - z, x\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.63793512063663311 \cdot 10^{269}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020113 +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)))