Average Error: 6.1 → 2.0
Time: 7.5s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.93771321468104164 \cdot 10^{-120} \lor \neg \left(x \le -2.3612955667005291 \cdot 10^{-303}\right):\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.93771321468104164 \cdot 10^{-120} \lor \neg \left(x \le -2.3612955667005291 \cdot 10^{-303}\right):\\
\;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{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 (((x <= -1.9377132146810416e-120) || !(x <= -2.361295566700529e-303))) {
		VAR = ((double) (x + ((double) (((double) (z - x)) / ((double) (t / y))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - x)))) * ((double) (1.0 / t))))));
	}
	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

Original6.1
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.93771321468104164e-120 or -2.3612955667005291e-303 < x

    1. Initial program 6.4

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

    3. Applied clear-num6.4

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

    5. Applied associate-/r*1.5

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

    6. Taylor expanded around 0 6.4

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

    7. Simplified1.4

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

    if -1.93771321468104164e-120 < x < -2.3612955667005291e-303

    1. Initial program 4.9

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

    3. Applied div-inv5.0

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.93771321468104164 \cdot 10^{-120} \lor \neg \left(x \le -2.3612955667005291 \cdot 10^{-303}\right):\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \end{array}\]

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)))