Average Error: 0.0 → 0.0
Time: 1.1s
Precision: binary64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\frac{x}{2} + \left(x \cdot y + z\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\frac{x}{2} + \left(x \cdot y + z\right)
(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))
↓
(FPCore (x y z) :precision binary64 (+ (/ x 2.0) (+ (* x y) z)))
double code(double x, double y, double z) {
	return ((double) (((double) ((x / 2.0) + ((double) (y * x)))) + z));
}
↓
double code(double x, double y, double z) {
	return ((double) ((x / 2.0) + ((double) (((double) (x * y)) + 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

    \[\left(\frac{x}{2} + y \cdot x\right) + z\]
  2. Using strategy rm

  3. Applied associate-+l+_binary640.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto \frac{x}{2} + \left(x \cdot y + z\right)\]

Reproduce

herbie shell --seed 2020219 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))