Details

sample37.0ms

Algorithm

intervals

Results

8.0ms	177×	body	80	valid
7.0ms	28×	body	2560	valid
4.0ms	12×	body	640	valid
4.0ms	20×	body	1280	valid
3.0ms	11×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

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)))

series248.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
43.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	244	351
1	743	325
2	2278	315
3	5001	312

prune136.0ms

Filtered

49 candidates to 42 candidates (85.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 19.3b

Counts

50 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.1b	(sqrt (+ (* re re) (* im im)))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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)))))
14.0ms	(+ (* (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)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
44.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune254.0ms

Filtered

136 candidates to 73 candidates (53.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 19.3b

Counts

143 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
7.1b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
29.1b	(cbrt (+ (* re re) (* im im)))
29.1b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
78.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
91.0ms	(cbrt (+ (* re re) (* im im)))
90.0ms	(cbrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	323	928
1	1214	868
2	5002	841

prune267.0ms

Filtered

77 candidates to 66 candidates (85.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 19.3b

Counts

85 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

29.1b	(cbrt (+ (* re re) (* im im)))
29.1b	(cbrt (+ (* re re) (* im im)))
29.1b	(cbrt (+ (* re re) (* im im)))
29.1b	(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ (* re re) (* im im)))
91.0ms	(cbrt (+ (* re re) (* im im)))
90.0ms	(cbrt (+ (* re re) (* im im)))
91.0ms	(cbrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1386	444
3	5001	444

prune323.0ms

Filtered

64 candidates to 60 candidates (93.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	64	8	72

Merged error: 19.3b

Counts

72 → 8

Details

sample37.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite18.0ms

series248.0ms

simplify66.0ms

prune136.0ms

localize15.0ms

rewrite41.0ms

series153.0ms

simplify48.0ms

prune254.0ms

localize14.0ms

rewrite25.0ms

series365.0ms

simplify46.0ms

prune267.0ms

localize20.0ms

rewrite16.0ms

series363.0ms

simplify52.0ms

prune323.0ms

regimes191.0ms

bsearch3.0ms

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