Average Error: 0.1 → 0.0
Time: 3.3s
Precision: binary64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\frac{\frac{x + \left(y - z\right)}{t}}{2}\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{\frac{x + \left(y - z\right)}{t}}{2}
(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))
↓
(FPCore (x y z t) :precision binary64 (/ (/ (+ x (- y z)) t) 2.0))
double code(double x, double y, double z, double t) {
	return (((double) (((double) (x + y)) - z)) / ((double) (t * 2.0)));
}
↓
double code(double x, double y, double z, double t) {
	return ((((double) (x + ((double) (y - z)))) / t) / 2.0);
}

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

Derivation

  1. Initial program Error: 0.1 bits

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

  3. Applied associate-/r*Error: 0.0 bits

    \[\leadsto \color{blue}{\frac{\frac{\left(x + y\right) - z}{t}}{2}}\]

  4. SimplifiedError: 0.0 bits

    \[\leadsto \frac{\color{blue}{\frac{x + \left(y - z\right)}{t}}}{2}\]

  5. Final simplificationError: 0.0 bits

    \[\leadsto \frac{\frac{x + \left(y - z\right)}{t}}{2}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))