Average Error: 6.4 → 1.7
Time: 4.5s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.0142020729490171 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;y \le 3.9095692807924123 \cdot 10^{135}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.0142020729490171 \cdot 10^{-97}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;y \le 3.9095692807924123 \cdot 10^{135}:\\
\;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((y <= -8.014202072949017e-97)) {
		VAR = ((double) (x + ((double) (y / ((double) (t / ((double) (z - x))))))));
	} else {
		double VAR_1;
		if ((y <= 3.909569280792412e+135)) {
			VAR_1 = ((double) (x + ((double) (((double) (y / t)) / ((double) (1.0 / ((double) (z - x))))))));
		} else {
			VAR_1 = ((double) (x + ((double) (y * ((double) (((double) (z - x)) / t))))));
		}
		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

Original6.4
Target2.1
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if y < -8.0142020729490171e-97

    1. Initial program 10.5

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

    3. Applied associate-/l*2.5

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

    if -8.0142020729490171e-97 < y < 3.9095692807924123e135

    1. Initial program 2.7

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

    3. Applied associate-/l*8.1

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

    5. Applied div-inv8.1

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

    6. Applied associate-/r*1.2

      \[\leadsto x + \color{blue}{\frac{\frac{y}{t}}{\frac{1}{z - x}}}\]

    if 3.9095692807924123e135 < y

    1. Initial program 21.3

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

    2. Simplified2.6

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.0142020729490171 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;y \le 3.9095692807924123 \cdot 10^{135}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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)) (* (neg z) (/ y t))))

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