Average Error: 6.2 → 0.9
Time: 5.1s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x - \frac{y \cdot \left(z - t\right)}{a} = -inf.0:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;x - \frac{y \cdot \left(z - t\right)}{a} \le 115946595681813742000:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;x - \frac{y \cdot \left(z - t\right)}{a} = -inf.0:\\
\;\;\;\;x + y \cdot \frac{t - z}{a}\\

\mathbf{elif}\;x - \frac{y \cdot \left(z - t\right)}{a} \le 115946595681813742000:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

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

\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) (x - ((double) (((double) (y * ((double) (z - t)))) / a)))) <= -inf.0)) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (t - z)) / a))))));
	} else {
		double VAR_1;
		if ((((double) (x - ((double) (((double) (y * ((double) (z - t)))) / a)))) <= 1.1594659568181374e+20)) {
			VAR_1 = ((double) (x - ((double) (((double) (y * ((double) (z - t)))) / a))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (t - z)) * ((double) (y / a))))));
		}
		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

Original6.2
Target0.7
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- x (/ (* y (- z t)) a)) < -inf.0

    1. Initial program 64.0

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

    2. Simplified0.2

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

    if -inf.0 < (- x (/ (* y (- z t)) a)) < 115946595681813742000

    1. Initial program 0.4

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

    if 115946595681813742000 < (- x (/ (* y (- z t)) a))

    1. Initial program 8.0

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

    2. Taylor expanded around 0 8.0

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

    3. Simplified1.8

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{y \cdot \left(z - t\right)}{a} = -inf.0:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;x - \frac{y \cdot \left(z - t\right)}{a} \le 115946595681813742000:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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 (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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