Average Error: 6.4 → 1.6
Time: 3.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.9938512783487052 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{elif}\;t \le 1.96080948284751819 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.9938512783487052 \cdot 10^{-18}:\\
\;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\

\mathbf{elif}\;t \le 1.96080948284751819 \cdot 10^{-66}:\\
\;\;\;\;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 <= -1.993851278348705e-18)) {
		VAR = ((double) (x + ((double) (((double) (y / t)) * ((double) (z - x))))));
	} else {
		double VAR_1;
		if ((t <= 1.9608094828475182e-66)) {
			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

Original6.4
Target2.1
Herbie1.6
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.9938512783487052e-18

    1. Initial program 8.6

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

    3. Applied associate-/l*1.4

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

    5. Applied associate-/r/1.0

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

    if -1.9938512783487052e-18 < t < 1.96080948284751819e-66

    1. Initial program 2.4

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

    if 1.96080948284751819e-66 < t

    1. Initial program 7.8

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
    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 simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.9938512783487052 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{elif}\;t \le 1.96080948284751819 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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)))