Average Error: 0.1 → 0.1
Time: 4.8s
Precision: binary64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\frac{\frac{x + y}{t} - \frac{z}{t}}{2}\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{\frac{x + y}{t} - \frac{z}{t}}{2}
(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))
↓
(FPCore (x y z t) :precision binary64 (/ (- (/ (+ x y) t) (/ z t)) 2.0))
double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}
↓
double code(double x, double y, double z, double t) {
	return (((x + y) / t) - (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 0.1

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

  3. Applied associate-/r*_binary640.1

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

  5. Applied div-sub_binary640.1

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

  6. Final simplification0.1

    \[\leadsto \frac{\frac{x + y}{t} - \frac{z}{t}}{2}\]

Reproduce

herbie shell --seed 2020231 
(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)))