Details

analyze423.0ms (7.8%)

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)

sample36.0ms (0.7%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
2.0ms	23×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify189.0ms (3.5%)

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: 30.1b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
27.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_84`
22×	`log-pow_binary64_167`
21×	`pow1_binary64_139`
17×	`add-sqr-sqrt_binary64_100`
16×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`sqrt-pow1_binary64_96` `associate-/l*_binary64_23` `pow1/2_binary64_158`
5×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
4×	`associate-/r*_binary64_22` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `flip-+_binary64_52` `flip3-+_binary64_81`
2×	`log-div_binary64_165` `div-sub_binary64_83`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

3 → 74

Calls

3 calls:

7.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series141.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

97.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5313	1833

prune93.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 6.7b

Counts

85 → 10

Compiler

Compiled 1726 to 419 computations (75.7% saved)

localize14.0ms (0.3%)

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)))))
0.3b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
29.0b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_84`
72×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
47×	`pow1_binary64_139`
43×	`log-pow_binary64_167`
24×	`associate-/r*_binary64_22`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
7×	`associate-/l*_binary64_23`
6×	`add-log-exp_binary64_117` `div-inv_binary64_75`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`log-prod_binary64_164`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `log-div_binary64_165` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `rem-log-exp_binary64_119` `associate-/r/_binary64_24` `sum-log_binary64_169`

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))))

series289.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
112.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
32.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5141	4862

prune165.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	163	8	171
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	166	15	181

Merged error: 6.6b

Counts

181 → 15

Compiler

Compiled 4153 to 1139 computations (72.6% 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)))))
0.3b	(/.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))))))
28.9b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.9b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
12×	`times-frac_binary64_84`
9×	`cbrt-prod_binary64_109`
8×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `associate-+r+_binary64_10` `log-prod_binary64_164` `add-exp-log_binary64_116`
5×	`add-log-exp_binary64_117` `flip-+_binary64_52` `flip3-+_binary64_81`
4×	`associate-/l*_binary64_23` `log-pow_binary64_167`
3×	`associate-/r*_binary64_22`
2×	`associate-+r-_binary64_12` `pow1/3_binary64_160` `log-div_binary64_165` `associate-/r/_binary64_24`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

4 → 78

Calls

4 calls:

13.0ms	(+.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)))))
7.0ms	(/.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)))

series450.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.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))))))
83.0ms	(+.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)))))
74.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
71.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5564	2267

prune110.0ms (2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	90	15	105

Merged error: 6.6b

Counts

105 → 15

Compiler

Compiled 2916 to 1050 computations (64% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.4b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
27.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_100`
25×	`*-un-lft-identity_binary64_78`
23×	`add-cube-cbrt_binary64_113` `pow1_binary64_139`
12×	`log-prod_binary64_164`
10×	`add-cbrt-cube_binary64_114` `associate-l_binary64_19` `add-exp-log_binary64_116` `log-pow_binary64_167`
9×	`times-frac_binary64_84`
8×	`associate-r_binary64_18`
6×	`distribute-lft-in_binary64_27` `swap-sqr_binary64_45` `distribute-rgt-in_binary64_28`
4×	`add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `flip-+_binary64_52` `associate-/l_binary64_23` `associate-/r_binary64_22` `flip3-+_binary64_81`
2×	`*-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `sqrt-div_binary64_95` `associate-/r/_binary64_24` `associate-/l/_binary64_25` `pow1/2_binary64_158`
1×	`pow2_binary64_159` `pow-sqr_binary64_51` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `pow-prod-up_binary64_148` `clear-num_binary64_77` `pow-plus_binary64_141`

Counts

4 → 110

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series261.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
72.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
65.0ms	(*.f64 (log.f64 base) (log.f64 base))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5236	2387

prune126.0ms (2.3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	120	17	137

Merged error: 6.6b

Counts

137 → 17

Compiler

Compiled 3801 to 1228 computations (67.7% saved)

regimes619.0ms (11.4%)

Compiler: Compiled 4836 to 3311 computations (31.5% saved)

bsearch96.0ms (1.8%)

Steps

Iters	Range		Point
9	3.6701391401380136e+40	7.562495526946566e+45	7.464152480213898e+45
8	-3.8843656189335154e+76	-8.421015650252839e+72	-3.6782753198332146e+76

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	49
1	31	49

end0.0ms (0%)

sample1.9s (35.3%)

Algorithm

1×

intervals

Results

781.0ms	8000×	body	128	valid
94.0ms	979×	body	128	nan

Compiler

Compiled 1014 to 694 computations (31.6% saved)

Details

analyze423.0ms (7.8%)

sample36.0ms (0.7%)

simplify189.0ms (3.5%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite21.0ms (0.4%)

series141.0ms (2.6%)

simplify80.0ms (1.5%)

prune93.0ms (1.7%)

localize14.0ms (0.3%)

rewrite37.0ms (0.7%)

series289.0ms (5.3%)

simplify98.0ms (1.8%)

prune165.0ms (3%)

localize15.0ms (0.3%)

rewrite37.0ms (0.7%)

series450.0ms (8.3%)

simplify76.0ms (1.4%)

prune110.0ms (2%)

localize19.0ms (0.3%)

rewrite38.0ms (0.7%)

series261.0ms (4.8%)

simplify78.0ms (1.4%)

prune126.0ms (2.3%)

regimes619.0ms (11.4%)

bsearch96.0ms (1.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (35.3%)

Profiling