Average Error: 6.4 → 2.8
Time: 3.5s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -2.586633332464155 \cdot 10^{-162}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -2.586633332464155 \cdot 10^{-162}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.586633332464155e-162)
   (+ x (/ y (/ t (- z x))))
   (+ x (/ (/ y t) (/ 1.0 (- z x))))))
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 tmp;
	if ((t <= -2.586633332464155e-162)) {
		tmp = ((double) (x + (y / (t / ((double) (z - x))))));
	} else {
		tmp = ((double) (x + ((y / t) / (1.0 / ((double) (z - x))))));
	}
	return tmp;
}

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
Herbie2.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.586633332464155e-162

    1. Initial program Error: 6.8 bits

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

    3. Applied associate-/l*Error: 3.0 bits

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

    if -2.586633332464155e-162 < t

    1. Initial program Error: 6.1 bits

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

    3. Applied associate-/l*Error: 8.1 bits

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

    5. Applied div-invError: 8.2 bits

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

    6. Applied associate-/r*Error: 2.7 bits

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

  4. Final simplificationError: 2.8 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.586633332464155 \cdot 10^{-162}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(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)))