Average Error: 6.6 → 1.0
Time: 4.3s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -7.40472292056332088 \cdot 10^{-19} \lor \neg \left(a \le 1.9997637455986459 \cdot 10^{-98}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -7.40472292056332088 \cdot 10^{-19} \lor \neg \left(a \le 1.9997637455986459 \cdot 10^{-98}\right):\\
\;\;\;\;x + y \cdot \frac{t - z}{a}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(t - z\right)}{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 (((a <= -7.404722920563321e-19) || !(a <= 1.999763745598646e-98))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (t - z)) / a))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (t - z)))) / a))));
	}
	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

Original6.6
Target0.6
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 a < -7.40472292056332088e-19 or 1.9997637455986459e-98 < a

    1. Initial program 8.9

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

    2. Simplified1.1

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

    if -7.40472292056332088e-19 < a < 1.9997637455986459e-98

    1. Initial program 0.8

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.40472292056332088 \cdot 10^{-19} \lor \neg \left(a \le 1.9997637455986459 \cdot 10^{-98}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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)))