Average Error: 0.0 → 0.0
Time: 5.6s
Precision: binary64
\[x + \frac{y - x}{z}\]
↓
\[\frac{y}{z} + \left(x - \frac{x}{z}\right)\]
x + \frac{y - x}{z}
↓
\frac{y}{z} + \left(x - \frac{x}{z}\right)
(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. Using strategy rm

  3. Applied div-sub_binary64_830.0

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

  4. Applied associate-+r-_binary64_120.0

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

  5. Simplified0.0

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

  7. Applied associate--l+_binary64_150.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))