Details

analyze428.0ms (7%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
3.0ms	32×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify264.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

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: 33.6b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_757`
22×	`log-pow_binary64_837`
20×	`pow1_binary64_809`
16×	`add-sqr-sqrt_binary64_772`
15×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
6×	`pow1/2_binary64_828` `associate-/l*_binary64_698` `sqrt-pow1_binary64_768`
4×	`associate-/r*_binary64_697` `sqrt-div_binary64_767` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`sqrt-prod_binary64_766`
2×	`log-div_binary64_835` `flip3-+_binary64_754` `div-sub_binary64_756` `add-log-exp_binary64_787` `flip-+_binary64_725`
1×	`rem-sqrt-square_binary64_764` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `div-exp_binary64_799`

Counts

2 → 63

Calls

2 calls:

9.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series236.0ms (3.9%)

Counts

2 → 6

Calls

2 calls:

187.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
49.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5747	1640

prune88.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	58	13	71

Merged error: 9.0b

Counts

71 → 13

Compiler

Compiled 1517 to 390 computations (74.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) (log.f64 base))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite99.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

194×	`sqrt-pow1_binary64_768`
175×	`pow1_binary64_809`
136×	`log-pow_binary64_837`
100×	`times-frac_binary64_757`
98×	`pow1/2_binary64_828`
81×	`add-sqr-sqrt_binary64_772`
72×	`sqrt-prod_binary64_766`
54×	`pow-prod-up_binary64_818`
52×	`sqrt-div_binary64_767`
49×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
30×	`pow-sqr_binary64_724` `pow-prod-down_binary64_819`
25×	`associate-/l*_binary64_698`
15×	`swap-sqr_binary64_718`
14×	`flip3-+_binary64_754` `flip-+_binary64_725`
9×	`unswap-sqr_binary64_719` `associate-l_binary64_694` `associate-r_binary64_693`
8×	`frac-times_binary64_761` `log-div_binary64_835` `div-sub_binary64_756` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
6×	`pow-plus_binary64_811` `pow2_binary64_829`
4×	`associate-/r_binary64_697` `add-log-exp_binary64_787` `associate-r/_binary64_695` `associate-*l/_binary64_696`
2×	`rem-sqrt-square_binary64_764`
1×	`prod-exp_binary64_797` `rem-square-sqrt_binary64_763` `*-commutative_binary64_684` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `cbrt-unprod_binary64_781` `clear-num_binary64_750` `sqrt-unprod_binary64_770` `div-exp_binary64_799`

Counts

4 → 262

Calls

4 calls:

24.0ms	(/.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) (log.f64 base))
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series346.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(/.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))) (log.f64 base))
57.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
45.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4921	6206
1	4921	6206

prune225.0ms (3.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	273	14	287

Merged error: 9.0b

Counts

287 → 14

Compiler

Compiled 6130 to 1379 computations (77.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 (log.f64 base) (log.f64 (+.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)))))
32.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_757`
71×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
46×	`pow1_binary64_809`
43×	`log-pow_binary64_837`
24×	`associate-/r*_binary64_697`
11×	`add-exp-log_binary64_786`
10×	`add-cbrt-cube_binary64_784`
7×	`associate-/l*_binary64_698`
6×	`div-inv_binary64_748`
4×	`cbrt-undiv_binary64_782` `div-exp_binary64_799`
3×	`add-log-exp_binary64_787` `log-prod_binary64_834`
2×	`log-div_binary64_835` `frac-2neg_binary64_762` `clear-num_binary64_750`
1×	`rem-log-exp_binary64_789` `flip3-+_binary64_754` `associate-/r/_binary64_699` `flip-+_binary64_725`

Counts

3 → 148

Calls

3 calls:

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

series486.0ms (8%)

Counts

3 → 9

Calls

3 calls:

215.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
214.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
56.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify88.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5410	4669

prune170.0ms (2.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	150	7	157
Fresh	6	6	12
Picked	1	0	1
Done	0	1	1
Total	157	14	171

Merged error: 8.9b

Counts

171 → 14

Compiler

Compiled 3870 to 1027 computations (73.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.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))))))
0.3b	(/.f64 1/2 (/.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)))))))
32.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
32.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64_757`
66×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
21×	`associate-/r*_binary64_697`
20×	`pow1_binary64_809`
16×	`log-pow_binary64_837`
11×	`add-cbrt-cube_binary64_784` `associate-/r/_binary64_699` `add-exp-log_binary64_786`
7×	`flip3-+_binary64_754` `associate-/l*_binary64_698` `flip-+_binary64_725`
6×	`cbrt-prod_binary64_779` `div-inv_binary64_748`
4×	`add-log-exp_binary64_787` `cbrt-undiv_binary64_782` `cbrt-div_binary64_780` `div-exp_binary64_799`
2×	`pow1/3_binary64_830` `frac-2neg_binary64_762` `clear-num_binary64_750`

Counts

4 → 149

Calls

4 calls:

11.0ms	(/.f64 1/2 (/.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)))))))
8.0ms	(/.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)))

series901.0ms (14.8%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(/.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))))))
286.0ms	(/.f64 1/2 (/.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)))))))
142.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
130.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5350	5819

prune194.0ms (3.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	161	14	175

Merged error: 8.9b

Counts

175 → 14

Compiler

Compiled 5287 to 1796 computations (66% saved)

regimes456.0ms (7.5%)

Compiler: Compiled 1246 to 916 computations (26.5% saved)

bsearch187.0ms (3.1%)

Steps

Iters	Range		Point
4	1.9530496141444853e+62	3.1555099882568186e+62	3.1146883802374637e+62
8	1.8718016354406046e-239	2.4776342703605906e-235	1.977245760406704e-239
12	-5.220048298073483e-164	-5.403045257775847e-240	-1.1637338402804801e-200
8	-1.583170481407227e+121	-6.124267486961955e+118	-1.1631929203516236e+119

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	130
1	46	130

end0.0ms (0%)

sample1.4s (23.2%)

Algorithm

1×

intervals

Results

804.0ms	8000×	body	128	valid
98.0ms	1020×	body	128	nan

Compiler

Compiled 347 to 229 computations (34% saved)

Details

analyze428.0ms (7%)

sample39.0ms (0.6%)

simplify264.0ms (4.3%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite19.0ms (0.3%)

series236.0ms (3.9%)

simplify66.0ms (1.1%)

prune88.0ms (1.4%)

localize15.0ms (0.2%)

rewrite99.0ms (1.6%)

series346.0ms (5.7%)

simplify118.0ms (1.9%)

prune225.0ms (3.7%)

localize11.0ms (0.2%)

rewrite36.0ms (0.6%)

series486.0ms (8%)

simplify88.0ms (1.5%)

prune170.0ms (2.8%)

localize15.0ms (0.2%)

rewrite54.0ms (0.9%)

series901.0ms (14.8%)

simplify118.0ms (1.9%)

prune194.0ms (3.2%)

regimes456.0ms (7.5%)

bsearch187.0ms (3.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (23.2%)

Profiling