Average Error: 0.1 → 0.0
Time: 4.2s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\frac{y - z}{t} + \frac{x}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\frac{y - z}{t} + \frac{x}{t}\right)
(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))
↓
(FPCore (x y z t) :precision binary64 (* 0.5 (+ (/ (- y z) t) (/ x t))))
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 0.5 * (((y - z) / t) + (x / t));
}

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 div-sub_binary640.1

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

  4. Simplified0.1

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

  5. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y}{t}\right) - 0.5 \cdot \frac{z}{t}}\]

  6. Simplified0.4

    \[\leadsto \color{blue}{\frac{0.5}{\frac{t}{\left(x + y\right) - z}}}\]

  7. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \frac{y}{t} + 0.5 \cdot \frac{x}{t}\right) - 0.5 \cdot \frac{z}{t}}\]

  8. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\frac{y - z}{t} + \frac{x}{t}\right)}\]

  9. Final simplification0.0

    \[\leadsto 0.5 \cdot \left(\frac{y - z}{t} + \frac{x}{t}\right)\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(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)))