Average Error: 6.6 → 1.5
Time: 5.5s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.0932009212774863 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;t \le 5.3429070875297298 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.0932009212774863 \cdot 10^{-60}:\\
\;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\

\mathbf{elif}\;t \le 5.3429070875297298 \cdot 10^{-33}:\\
\;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\

\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 <= -1.0932009212774863e-60)) {
		VAR = ((double) (x + ((double) (((double) (z - x)) / ((double) (t / y))))));
	} else {
		double VAR_1;
		if ((t <= 5.34290708752973e-33)) {
			VAR_1 = ((double) (x + ((double) (1.0 / ((double) (t / ((double) (y * ((double) (z - x))))))))));
		} 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

Original6.6
Target2.1
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 < -1.0932009212774863e-60

    1. Initial program 8.4

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

    3. Applied clear-num8.4

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

    5. Applied associate-/r*1.2

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

    6. Taylor expanded around 0 8.4

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

    7. Simplified1.2

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

    if -1.0932009212774863e-60 < t < 5.3429070875297298e-33

    1. Initial program 2.1

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

    3. Applied clear-num2.1

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

    if 5.3429070875297298e-33 < t

    1. Initial program 8.8

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

    3. Applied associate-/l*1.3

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.0932009212774863 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;t \le 5.3429070875297298 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020171 
(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)))