Average Error: 6.6 → 1.8
Time: 3.7s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -5.036521477223781 \cdot 10^{-192} \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.3627586753872378 \cdot 10^{-79}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -5.036521477223781 \cdot 10^{-192} \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.3627586753872378 \cdot 10^{-79}\right):\\
\;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\

\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) (y * ((double) (z - x)))) / t)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x + (((double) (y * ((double) (z - x)))) / t))) <= -5.036521477223781e-192) || !(((double) (x + (((double) (y * ((double) (z - x)))) / t))) <= 2.3627586753872378e-79))) {
		VAR = ((double) (x + (1.0 / ((t / y) / ((double) (z - x))))));
	} else {
		VAR = ((double) (x + (y / (t / ((double) (z - x))))));
	}
	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
Target1.8
Herbie1.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -5.03652147722378098e-192 or 2.36275867538723784e-79 < (+ x (/ (* y (- z x)) t))

    1. Initial program 6.7

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

    3. Applied clear-num6.8

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

    5. Applied associate-/r*1.7

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

    if -5.03652147722378098e-192 < (+ x (/ (* y (- z x)) t)) < 2.36275867538723784e-79

    1. Initial program 5.5

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

    3. Applied associate-/l*2.4

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -5.036521477223781 \cdot 10^{-192} \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.3627586753872378 \cdot 10^{-79}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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)))