Average Error: 7.0 → 1.5
Time: 3.6s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.3369112523988943 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(\left(z - x\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;t \le 4.4413768369798711 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.3369112523988943 \cdot 10^{-11}:\\
\;\;\;\;x + y \cdot \left(\left(z - x\right) \cdot \frac{1}{t}\right)\\

\mathbf{elif}\;t \le 4.4413768369798711 \cdot 10^{-58}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\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 ((t <= -5.336911252398894e-11)) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - x)) * ((double) (1.0 / t))))))));
	} else {
		double VAR_1;
		if ((t <= 4.441376836979871e-58)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
		} else {
			VAR_1 = ((double) (x + ((double) (y / ((double) (t / ((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

Original7.0
Target2.0
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 t < -5.3369112523988943e-11

    1. Initial program 9.5

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

    2. Simplified1.1

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

    4. Applied div-inv1.1

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

    if -5.3369112523988943e-11 < t < 4.4413768369798711e-58

    1. Initial program 2.1

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

    if 4.4413768369798711e-58 < t

    1. Initial program 9.2

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

    3. Applied associate-/l*1.4

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.3369112523988943 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \left(\left(z - x\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;t \le 4.4413768369798711 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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)))