Details

Time bar (total: 2.2s)

sample33.0ms

Algorithm
intervals
Results
8.0ms187×body80valid
5.0ms19×body2560valid
4.0ms13×body5120valid
4.0ms18×body1280valid
2.0ms12×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.7b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b
(+ (sqrt (+ (* re re) (* im im))) re)
29.7b
(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt sqrt-div sqrt-prod
3×add-exp-log sqrt-pow1 flip3-+ add-cbrt-cube flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log distribute-lft-out
Counts
3 → 40
Calls
3 calls:
8.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series262.0ms

Counts
3 → 9
Calls
3 calls:
178.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0244351
1743325
22278315
35001312

prune149.0ms

Filtered
49 candidates to 42 candidates (85.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New42749
Fresh000
Picked011
Done000
Total42850

Merged error: 19.0b

Counts
50 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.3b
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.7b
(sqrt (+ (* re re) (* im im)))
29.7b
(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
15.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series161.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
51.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
34.0ms
(sqrt (+ (* re re) (* im im)))
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
02671096
1974974
25001950

prune267.0ms

Filtered
136 candidates to 72 candidates (52.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1342136
Fresh246
Picked011
Done011
Total1368144

Merged error: 19.0b

Counts
144 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
12.3b
(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
29.7b
(sqrt (+ (* re re) (* im im)))
29.7b
(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
17×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod
11×sqrt-pow1
10×pow1 sqrt-div
7×pow-pow
6×add-log-exp
5×add-exp-log pow1/2 add-cbrt-cube
4×flip3-+ flip-+
3×pow-unpow
2×cube-div rem-sqrt-square
1×+-commutative cube-mult pow-to-exp unpow3 pow-exp sum-log sqrt-pow2 rem-cube-cbrt sqr-pow
Counts
4 → 91
Calls
4 calls:
8.0ms
(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
21.0ms
(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
46.0ms
(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
42.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0394992
11342878
25001845

prune303.0ms

Filtered
103 candidates to 66 candidates (64.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1021103
Fresh055
Picked101
Done022
Total1038111

Merged error: 19.0b

Counts
111 → 8

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New000
Fresh055
Picked011
Done022
Total088

Merged error: 19.0b

Counts
8 → 8

regimes458.0ms

bsearch5.0ms

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