Average Error: 5.9 → 0.6
Time: 4.4s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -2.7341664699093905 \cdot 10^{-15} \lor \neg \left(a \leq 3.6035247661278024 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(t - z\right)\right) \cdot \frac{1}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \leq -2.7341664699093905 \cdot 10^{-15} \lor \neg \left(a \leq 3.6035247661278024 \cdot 10^{-16}\right):\\
\;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x - (((double) (y * ((double) (z - t)))) / a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((a <= -2.7341664699093905e-15) || !(a <= 3.6035247661278024e-16))) {
		VAR = ((double) (x + (y / (a / ((double) (t - z))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (t - z)))) * (1.0 / 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

Original5.9
Target0.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.7341664699093905e-15 or 3.6035247661278024e-16 < a

    1. Initial program Error: 8.7 bits

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

    2. SimplifiedError: 0.5 bits

      \[\leadsto \color{blue}{x + y \cdot \frac{t - z}{a}}\]
    3. Using strategy rm

    4. Applied clear-numError: 0.5 bits

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a}{t - z}}}\]
    5. Using strategy rm

    6. Applied un-div-invError: 0.5 bits

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

    if -2.7341664699093905e-15 < a < 3.6035247661278024e-16

    1. Initial program Error: 0.8 bits

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

    2. SimplifiedError: 16.5 bits

      \[\leadsto \color{blue}{x + y \cdot \frac{t - z}{a}}\]
    3. Using strategy rm

    4. Applied div-invError: 16.5 bits

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

    5. Applied associate-*r*Error: 0.9 bits

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

  4. Final simplificationError: 0.6 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7341664699093905 \cdot 10^{-15} \lor \neg \left(a \leq 3.6035247661278024 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(t - z\right)\right) \cdot \frac{1}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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)))