Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
Internal Precision: 128
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]

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

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

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

    \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019007 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))

Details

Time bar (total: 1.8s)Debug log

sample193.0ms

Algorithm
intervals

simplify19.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

18.0ms
(- (* re re) (* im im))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* re re) (* im im))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

3.0ms
(- (* re re) (* im im))

series37.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

37.0ms
(- (* re re) (* im im))

simplify37.0ms

Counts
6 → 16
Calls

6 calls. Slowest were:

19.0ms
(/ (exp (* re re)) (exp (* im im)))
5.0ms
(- (pow re 2) (pow im 2))
5.0ms
(- (pow re 2) (pow im 2))

prune95.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune3.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.4s

Algorithm
intervals