Average Error: 0.0 → 0.0
Time: 605.0ms
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[im \cdot \mathsf{fma}\left(re, 1, re\right)\]
re \cdot im + im \cdot re
↓
im \cdot \mathsf{fma}\left(re, 1, re\right)
double code(double re, double im) {
	return ((double) (((double) (re * im)) + ((double) (im * re))));
}
↓
double code(double re, double im) {
	return ((double) (im * ((double) fma(re, 1.0, re))));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot im + im \cdot re\]
  2. Using strategy rm

  3. Applied *-commutative0.0

    \[\leadsto \color{blue}{im \cdot re} + im \cdot re\]

  4. Applied distribute-lft-out0.0

    \[\leadsto \color{blue}{im \cdot \left(re + re\right)}\]

  5. Simplified0.0

    \[\leadsto im \cdot \color{blue}{\mathsf{fma}\left(re, 1, re\right)}\]

  6. Final simplification0.0

    \[\leadsto im \cdot \mathsf{fma}\left(re, 1, re\right)\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))