Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[x + \frac{y - x}{z}\]
↓
\[x + \left(\frac{y}{z} - \frac{x}{z}\right)\]
x + \frac{y - x}{z}
↓
x + \left(\frac{y}{z} - \frac{x}{z}\right)
(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))
↓
(FPCore (x y z) :precision binary64 (+ x (- (/ y z) (/ x z))))
double code(double x, double y, double z) {
	return ((double) (x + (((double) (y - x)) / z)));
}
↓
double code(double x, double y, double z) {
	return ((double) (x + ((double) ((y / z) - (x / z)))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x + \frac{y - x}{z}\]
  2. Using strategy rm

  3. Applied div-sub0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020198 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))