Average Error: 0.0 → 0.0
Time: 3.4s
Precision: binary64
\[x + \frac{y - x}{z}\]
↓
\[\left(\frac{y}{z} + x\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(\frac{y}{z} + x\right) - \frac{x}{z}
(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))
↓
(FPCore (x y z) :precision binary64 (- (+ (/ y z) x) (/ x z)))
double code(double x, double y, double z) {
	return x + ((y - x) / z);
}
↓
double code(double x, double y, double z) {
	return ((y / z) + x) - (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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021174 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))