Details

analyze422.0ms (7.7%)

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)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
1.0ms	14×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify258.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5740	19

prune9.0ms (0.2%)

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: 28.3b

Counts

2 → 2

Compiler

Compiled 92 to 70 computations (23.9% saved)

localize11.0ms (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))
26.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_85`
22×	`log-pow_binary64_168`
21×	`pow1_binary64_140`
17×	`add-sqr-sqrt_binary64_101`
16×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
6×	`associate-/l*_binary64_24` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`
5×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
4×	`associate-/r*_binary64_23` `sqrt-div_binary64_96`
3×	`sqrt-prod_binary64_95` `flip-+_binary64_53` `flip3-+_binary64_82`
2×	`div-sub_binary64_84` `log-div_binary64_166`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `sum-log_binary64_170` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `clear-num_binary64_78` `frac-2neg_binary64_90`

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))

series274.0ms (5%)

Counts

3 → 9

Calls

3 calls:

182.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
51.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
40.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5385	1833

prune290.0ms (5.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	72	13	85

Merged error: 6.7b

Counts

85 → 13

Compiler

Compiled 5585 to 2681 computations (52% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
27.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`times-frac_binary64_85`
14×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101` `pow1_binary64_140` `*-un-lft-identity_binary64_79`
11×	`log-pow_binary64_168`
6×	`add-exp-log_binary64_117`
5×	`add-cbrt-cube_binary64_115` `add-log-exp_binary64_118`
4×	`associate-/r_binary64_23` `associate-/l_binary64_24` `log-div_binary64_166`
3×	`flip-+_binary64_53` `log-prod_binary64_165` `flip3-+_binary64_82`
2×	`div-sub_binary64_84`
1×	`rem-log-exp_binary64_120` `cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `sum-log_binary64_170` `+-commutative_binary64_9` `clear-num_binary64_78` `frac-2neg_binary64_90`

Counts

3 → 63

Calls

3 calls:

7.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
6.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series256.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

158.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (log.f64 base))
60.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
38.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4932	1536
1	4932	1536

prune174.0ms (3.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	73	12	85

Merged error: 6.7b

Counts

85 → 12

Compiler

Compiled 3442 to 1650 computations (52.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(/.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))))
27.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_85`
72×	`add-cube-cbrt_binary64_114` `add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
47×	`pow1_binary64_140`
43×	`log-pow_binary64_168`
24×	`associate-/r*_binary64_23`
12×	`add-exp-log_binary64_117`
11×	`add-cbrt-cube_binary64_115`
7×	`associate-/l*_binary64_24`
6×	`div-inv_binary64_76` `add-log-exp_binary64_118`
4×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
3×	`log-prod_binary64_165`
2×	`flip-+_binary64_53` `log-div_binary64_166` `clear-num_binary64_78` `flip3-+_binary64_82` `frac-2neg_binary64_90`
1×	`rem-log-exp_binary64_120` `sum-log_binary64_170` `+-commutative_binary64_9` `associate-/r/_binary64_25`

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

series505.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
197.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
61.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
37.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6042	4862

prune314.0ms (5.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	167	16	183

Merged error: 6.6b

Counts

183 → 16

Compiler

Compiled 6607 to 2891 computations (56.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/2 (.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
0.3b	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.4b	(.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
27.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64_117`
32×	`add-sqr-sqrt_binary64_101`
29×	`times-frac_binary64_85`
26×	`*-un-lft-identity_binary64_79`
25×	`add-cube-cbrt_binary64_114`
20×	`add-cbrt-cube_binary64_115`
16×	`pow1_binary64_140` `associate-r_binary64_19`
11×	`div-exp_binary64_130`
9×	`log-pow_binary64_168`
8×	`prod-exp_binary64_128`
6×	`cbrt-undiv_binary64_113` `associate-/l*_binary64_24`
5×	`associate-/r*_binary64_23`
4×	`associate-l_binary64_20` `cbrt-unprod_binary64_112` `add-log-exp_binary64_118`
3×	`1-exp_binary64_123` `div-inv_binary64_76` `rec-exp_binary64_129` `log-prod_binary64_165` `unswap-sqr_binary64_47`
2×	`un-div-inv_binary64_77` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `log-div_binary64_166` `clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`rem-log-exp_binary64_120` `flip-+_binary64_53` `inv-pow_binary64_164` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `flip3-+_binary64_82` `pow-flip_binary64_153`

Counts

4 → 116

Calls

4 calls:

10.0ms	(.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
8.0ms	(/.f64 1/2 (.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series584.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
190.0ms	(/.f64 1/2 (.f64 (log.f64 base) (/.f64 1 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
118.0ms	(/.f64 1 (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
57.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5426	2440

prune185.0ms (3.4%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	127	17	144

Merged error: 6.6b

Counts

144 → 17

Compiler

Compiled 3732 to 1789 computations (52.1% saved)

regimes195.0ms (3.6%)

Compiler: Compiled 970 to 766 computations (21% saved)

bsearch81.0ms (1.5%)

Steps

Iters	Range		Point
8	2.0355860987462653e+130	2.2371059522363548e+133	8.138679595525005e+130
6	-4.15452649581536e+72	-5.971042625070159e+71	-1.4606828681743375e+72

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	33	50
1	33	50

end0.0ms (0%)

sample1.4s (25.9%)

Algorithm

1×

intervals

Results

811.0ms	8000×	body	128	valid
95.0ms	1017×	body	128	nan

Compiler

Compiled 301 to 231 computations (23.3% saved)

Details

analyze422.0ms (7.7%)

sample38.0ms (0.7%)

simplify258.0ms (4.7%)

prune9.0ms (0.2%)

localize11.0ms (0.2%)

rewrite24.0ms (0.4%)

series274.0ms (5%)

simplify76.0ms (1.4%)

prune290.0ms (5.3%)

localize11.0ms (0.2%)

rewrite24.0ms (0.4%)

series256.0ms (4.7%)

simplify54.0ms (1%)

prune174.0ms (3.2%)

localize11.0ms (0.2%)

rewrite38.0ms (0.7%)

series505.0ms (9.2%)

simplify96.0ms (1.8%)

prune314.0ms (5.7%)

localize12.0ms (0.2%)

rewrite39.0ms (0.7%)

series584.0ms (10.7%)

simplify71.0ms (1.3%)

prune185.0ms (3.4%)

regimes195.0ms (3.6%)

bsearch81.0ms (1.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (25.9%)

Profiling