Average Error: 0.1 → 0.0
Time: 2.5s
Precision: binary64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right)
(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))
↓
(FPCore (x y z t) :precision binary64 (* 0.5 (+ (/ y t) (- (/ x t) (/ z 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 / t) + ((x / t) - (z / 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 add-sqr-sqrt_binary6431.9

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

  4. Applied times-frac_binary6431.9

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

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020233 
(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)))