Details

analyze426.0ms (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 29 to 21 computations (27.6% saved)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
3.0ms	36×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify253.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5740	19

prune5.0ms (0.1%)

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: 31.8b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
29.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_420`
22×	`log-pow_binary64_500`
21×	`pow1_binary64_472`
17×	`add-sqr-sqrt_binary64_435`
16×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
6×	`sqrt-pow1_binary64_431` `pow1/2_binary64_491` `associate-/l*_binary64_361`
5×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
4×	`sqrt-div_binary64_430` `associate-/r*_binary64_360`
3×	`flip3-+_binary64_417` `sqrt-prod_binary64_429` `flip-+_binary64_388`
2×	`log-div_binary64_498` `div-sub_binary64_419`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `+-commutative_binary64_346` `cbrt-undiv_binary64_445` `frac-2neg_binary64_425` `sum-log_binary64_502` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

3 → 74

Calls

3 calls:

8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series278.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

191.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
45.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
41.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5721	1833

prune100.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	72	13	85

Merged error: 6.2b

Counts

85 → 13

Compiler

Compiled 1791 to 463 computations (74.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
30.6b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_420`
72×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
47×	`pow1_binary64_472`
43×	`log-pow_binary64_500`
24×	`associate-/r*_binary64_360`
12×	`add-exp-log_binary64_449`
11×	`add-cbrt-cube_binary64_447`
7×	`associate-/l*_binary64_361`
6×	`div-inv_binary64_411` `add-log-exp_binary64_450`
4×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
3×	`log-prod_binary64_497`
2×	`clear-num_binary64_413` `flip3-+_binary64_417` `log-div_binary64_498` `flip-+_binary64_388` `frac-2neg_binary64_425`
1×	`associate-/r/_binary64_362` `rem-log-exp_binary64_452` `+-commutative_binary64_346` `sum-log_binary64_502`

Counts

4 → 159

Calls

4 calls:

8.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series552.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
215.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
66.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
37.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5984	4862

prune161.0ms (2.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	170	14	184

Merged error: 6.2b

Counts

184 → 14

Compiler

Compiled 4145 to 1112 computations (73.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
30.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
12×	`times-frac_binary64_420`
9×	`cbrt-prod_binary64_442`
8×	`pow1_binary64_472`
6×	`cbrt-div_binary64_443` `associate-+r+_binary64_348` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `log-prod_binary64_497`
5×	`flip3-+_binary64_417` `add-log-exp_binary64_450` `flip-+_binary64_388`
4×	`log-pow_binary64_500` `associate-/l*_binary64_361`
3×	`associate-/r*_binary64_360`
2×	`associate-/r/_binary64_362` `associate-+r-_binary64_350` `log-div_binary64_498` `pow1/3_binary64_493`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `+-commutative_binary64_346` `cbrt-undiv_binary64_445` `frac-2neg_binary64_425` `sum-log_binary64_502` `div-exp_binary64_462`

Counts

4 → 78

Calls

4 calls:

11.0ms	(+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
10.0ms	(/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series782.0ms (13.7%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(/.f64 (log.f64 base) (+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
151.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
144.0ms	(+.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 2) (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
129.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4850	2265
1	4850	2265

prune111.0ms (1.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	89	15	104

Merged error: 6.2b

Counts

104 → 15

Compiler

Compiled 2975 to 1045 computations (64.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(pow.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 3)
30.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.5b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
9×	`cbrt-prod_binary64_442`
7×	`pow1_binary64_472`
6×	`cbrt-div_binary64_443`
5×	`cube-prod_binary64_439` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `unpow-prod-down_binary64_490` `pow1/3_binary64_493`
4×	`log-pow_binary64_500` `add-log-exp_binary64_450`
3×	`flip3-+_binary64_417` `pow-unpow_binary64_488` `flip-+_binary64_388`
1×	`cube-mult_binary64_441` `sqr-pow_binary64_386` `pow-pow_binary64_483` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `unpow3_binary64_477` `rem-cube-cbrt_binary64_436`

Counts

4 → 66

Calls

4 calls:

4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(pow.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 3)

series611.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(pow.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 3)
141.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
141.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
129.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4865	1434
1	4865	1434

prune112.0ms (2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	76	17	93

Merged error: 6.1b

Counts

93 → 17

Compiler

Compiled 3570 to 1131 computations (68.3% saved)

regimes232.0ms (4%)

Compiler: Compiled 1498 to 938 computations (37.4% saved)

bsearch92.0ms (1.6%)

Steps

Iters	Range		Point
8	3.9941090885542994e+105	1.105004037435333e+109	9.280062418099048e+107
6	-3.2294302163354224e+66	-7.608403370815523e+65	-3.1460850084900386e+66

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	78
1	36	78

end0.0ms (0%)

sample1.5s (25.6%)

Algorithm

1×

intervals

Results

815.0ms	8000×	body	128	valid
91.0ms	986×	body	128	nan

Compiler

Compiled 451 to 283 computations (37.3% saved)

Details

analyze426.0ms (7.4%)

sample41.0ms (0.7%)

simplify253.0ms (4.4%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

rewrite24.0ms (0.4%)

series278.0ms (4.8%)

simplify78.0ms (1.4%)

prune100.0ms (1.7%)

localize11.0ms (0.2%)

rewrite39.0ms (0.7%)

series552.0ms (9.6%)

simplify94.0ms (1.6%)

prune161.0ms (2.8%)

localize15.0ms (0.3%)

rewrite40.0ms (0.7%)

series782.0ms (13.7%)

simplify73.0ms (1.3%)

prune111.0ms (1.9%)

localize20.0ms (0.3%)

rewrite26.0ms (0.5%)

series611.0ms (10.7%)

simplify71.0ms (1.2%)

prune112.0ms (2%)

regimes232.0ms (4%)

bsearch92.0ms (1.6%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (25.6%)

Profiling