Average Error: 0.0 → 0.0
Time: 4.4s
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 2019004 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))

Details

Time bar (total: 4.2s)Debug log

sample113.0ms

Algorithm
intervals

simplify32.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

32.0ms
(- (* re re) (* im im))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
1 → 13
Calls

1 calls. Slowest were:

7.0ms
(- (* re re) (* im im))

series40.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

39.0ms
(- (* re re) (* im im))

simplify62.0ms

Counts
6 → 16
Calls

6 calls. Slowest were:

38.0ms
(/ (exp (* re re)) (exp (* im im)))
8.0ms
(- (pow re 2) (pow im 2))
5.0ms
(- (pow re 2) (pow im 2))

prune120.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
1 → 29
Calls

1 calls. Slowest were:

8.0ms
(* (+ re im) (- re im))

series37.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify2.1s

Counts
27 → 32
Calls

27 calls. Slowest were:

565.0ms
(* (+ (pow re 3) (pow im 3)) (- (* re re) (* im im)))
362.0ms
(* (+ (* re re) (- (* im im) (* re im))) (+ (* re re) (+ (* im im) (* re im))))
200.0ms
(* (+ (pow re 3) (pow im 3)) (- (pow re 3) (pow im 3)))

prune192.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes126.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals