Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\mathsf{fma}\left(x, \frac{1}{2} + y, z\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\mathsf{fma}\left(x, \frac{1}{2} + y, z\right)
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x / 2.0)) + ((double) (y * x)))) + z));
}
↓
double code(double x, double y, double z) {
	return ((double) fma(x, ((double) (((double) (1.0 / 2.0)) + 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 *-commutative0.0

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

  4. Applied div-inv0.0

    \[\leadsto \left(\color{blue}{x \cdot \frac{1}{2}} + x \cdot y\right) + z\]

  5. Applied distribute-lft-out0.0

    \[\leadsto \color{blue}{x \cdot \left(\frac{1}{2} + y\right)} + z\]

  6. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{1}{2} + y, z\right)}\]

  7. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, \frac{1}{2} + y, z\right)\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))