Average Error: 6.3 → 1.5
Time: 3.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -9.794140385625607 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 1.1579583021138017 \cdot 10^{-73}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t \cdot \frac{1}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -9.794140385625607 \cdot 10^{+24}:\\
\;\;\;\;x + y \cdot \frac{z - x}{t}\\

\mathbf{elif}\;y \leq 1.1579583021138017 \cdot 10^{-73}:\\
\;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{t \cdot \frac{1}{z - x}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + (((double) (y * ((double) (z - x)))) / t)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((y <= -9.794140385625607e+24)) {
		VAR = ((double) (x + ((double) (y * (((double) (z - x)) / t)))));
	} else {
		double VAR_1;
		if ((y <= 1.1579583021138017e-73)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - x)))) * (1.0 / t)))));
		} else {
			VAR_1 = ((double) (x + (y / ((double) (t * (1.0 / ((double) (z - x))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.3
Target2.2
Herbie1.5
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if y < -9.7941403856256071e24

    1. Initial program Error: 16.6 bits

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

    2. SimplifiedError: 2.0 bits

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

    if -9.7941403856256071e24 < y < 1.1579583021138017e-73

    1. Initial program Error: 1.0 bits

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

    3. Applied div-invError: 1.0 bits

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

    if 1.1579583021138017e-73 < y

    1. Initial program Error: 11.1 bits

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

    3. Applied associate-/l*Error: 2.1 bits

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

    5. Applied div-invError: 2.1 bits

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

  4. Final simplificationError: 1.5 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.794140385625607 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 1.1579583021138017 \cdot 10^{-73}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t \cdot \frac{1}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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