Average Error: 0.0 → 0.0
Time: 4.9s
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 2019004 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))

Details

Time bar (total: 4.6s)Debug log

sample171.0ms

Algorithm
intervals

simplify36.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

35.0ms
(- (* re re) (* im im))

prune10.0ms

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))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series48.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

48.0ms
(- (* re re) (* im im))

simplify98.0ms

Counts
8 → 20
Calls

8 calls. Slowest were:

37.0ms
(/ (exp (* re re)) (exp (* im im)))
17.0ms
(fma re re (- (* im im)))
10.0ms
(- (pow re 2) (pow im 2))

prune179.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 31
Calls

1 calls. Slowest were:

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

series44.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

44.0ms
(* (+ re im) (- re im))

simplify2.3s

Counts
27 → 34
Calls

27 calls. Slowest were:

591.0ms
(* (+ (* re re) (- (* im im) (* re im))) (+ (* re re) (+ (* im im) (* re im))))
377.0ms
(* (+ (pow re 3) (pow im 3)) (- (pow re 3) (pow im 3)))
178.0ms
(* (- re im) (+ (* re re) (+ (* im im) (* re im))))

prune240.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes137.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals