Average Error: 0.0 → 0.0
Time: 2.6s
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 2019016 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))

Details

Time bar (total: 2.4s)Debug log

sample196.0ms

Algorithm
intervals
Results
455×(pre true 80)
455×(body real 80)

simplify27.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
26.0ms
(- (* re re) (* im im))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×difference-of-squares
1×flip--
1×log1p-expm1-u
1×add-cube-cbrt
1×add-exp-log
1×prod-diff
1×diff-log
1×fma-neg
1×add-cbrt-cube
1×flip3--
1×*-un-lft-identity
1×sub-neg
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 17
Calls
1 calls:
Slowest
7.0ms
(- (* re re) (* im im))

series76.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
76.0ms
(- (* re re) (* im im))

simplify203.0ms

Counts
8 → 20
Calls
8 calls:
Slowest
83.0ms
(/ (exp (* re re)) (exp (* im im)))
47.0ms
(- (pow re 2) (pow im 2))
23.0ms
(- (pow re 2) (pow im 2))
21.0ms
(fma re re (- (* im im)))
12.0ms
(- (pow re 2) (pow im 2))

prune129.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune4.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.7s

Algorithm
intervals
Results
14260×(pre true 80)
14260×(body real 80)