Average Error: 0.0 → 0.0
Time: 4.1s
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

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

Runtime

Time bar (total: 4.1s)Debug log

start205.0ms

Algorithm
intervals

setup35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

4.0ms
(- (* re re) (* im im))

series456.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

456.0ms
(- (* re re) (* im im))

simplify64.0ms

Counts
8 → 20
Calls

8 calls. Slowest were:

27.0ms
(/ (exp (* re re)) (exp (* im im)))
10.0ms
(fma re re (- (* im im)))
7.0ms
(- (pow re 2) (pow im 2))

prune164.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

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:

prune10.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

herbie shell --seed 2018359 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))