Details

analyze5.0ms (0.1%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 25 to 23 computations (8% saved)

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

prune3.0ms (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

Error

33.3b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.6b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite21.0ms (0.3%)

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 10))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series120.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

74.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4966	1833
1	4966	1833

prune109.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Error

7.3b

Counts

84 → 13

Compiler

Compiled 1822 to 783 computations (57% saved)

localize10.0ms (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 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.5b	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
32.0b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.5%)

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:

7.0ms	(/.f64 1/2 (/.f64 (log.f64 10) (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 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series227.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
77.0ms	(/.f64 1/2 (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
30.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
19.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4952	4862
1	4952	4862

prune196.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	164	7	171
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	172	12	184

Error

7.2b

Counts

184 → 12

Compiler

Compiled 4088 to 1891 computations (53.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2))))
0.5b	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2))
0.7b	(/.f64 (log.f64 10) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2)))
32.0b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`times-frac_binary64_84`
46×	`add-sqr-sqrt_binary64_100`
42×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
31×	`sqrt-prod_binary64_94`
21×	`add-exp-log_binary64_116`
20×	`add-cbrt-cube_binary64_114`
17×	`pow1_binary64_139`
11×	`log-pow_binary64_167`
10×	`associate-/l*_binary64_23`
9×	`div-inv_binary64_75` `associate-/r*_binary64_22`
7×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
6×	`associate-r_binary64_18`
4×	`associate-l_binary64_19` `add-log-exp_binary64_117`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `log-prod_binary64_164`
2×	`frac-2neg_binary64_89` `unswap-sqr_binary64_46` `log-div_binary64_165` `clear-num_binary64_77`
1×	`*-commutative_binary64_9` `flip-+_binary64_52` `rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `associate-/r/_binary64_24` `flip3-+_binary64_81`

Counts

4 → 139

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2))))
6.0ms	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2))
5.0ms	(/.f64 (log.f64 10) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2)))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series326.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(/.f64 (log.f64 10) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2)))
113.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2))))
50.0ms	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 1/2))
29.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4993	4225
1	4993	4225

prune187.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	149	14	163

Error

7.1b

Counts

163 → 14

Compiler

Compiled 3689 to 2181 computations (40.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2)))))
0.7b	(/.f64 (log.f64 10) (log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2))))
13.8b	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2))
20.6b	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2)))

rewrite52.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

248×	`times-frac_binary64_84`
124×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
67×	`log-pow_binary64_167`
66×	`sqrt-prod_binary64_94`
38×	`pow1_binary64_139`
24×	`associate-/r*_binary64_22`
14×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
10×	`associate-/l*_binary64_23`
9×	`div-inv_binary64_75`
7×	`log-prod_binary64_164`
6×	`unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`rem-log-exp_binary64_119`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `clear-num_binary64_77`
1×	`pow-pow_binary64_150` `associate-/r/_binary64_24`

Counts

4 → 235

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2)))))
6.0ms	(/.f64 (log.f64 10) (log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2))))
5.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2))
5.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2)))

series557.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 (log.f64 10) (log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2))))
163.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2)))))
96.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2))
90.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (sqrt.f64 1/2)))

simplify138.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4997	9659
1	4997	9659

prune402.0ms (6.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	245	16	261

Error

7.1b

Counts

261 → 16

Compiler

Compiled 7156 to 4155 computations (41.9% saved)

regimes1.5s (23.8%)

Accuracy

Total 10.1b remaining (59.3%)

Threshold costs 0b (0%)

Compiler

Compiled 12672 to 9088 computations (28.3% saved)

bsearch47.0ms (0.8%)

Steps

Iters	Range		Point
6	5.767514674511149e+98	8.300775693211392e+99	8.169445472099669e+99
10	-2.5624171412581313e+112	-2.8795429740246812e+94	-1.0759262699953573e+106

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	84
1	40	84

end0.0ms (0%)

sample1.8s (29.5%)

Algorithm

1×

intervals

Results

501.0ms

8000×

body

128

valid

Compiler

Compiled 1174 to 877 computations (25.3% saved)

Details

analyze5.0ms (0.1%)

sample22.0ms (0.4%)

simplify99.0ms (1.6%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite21.0ms (0.3%)

series120.0ms (1.9%)

simplify78.0ms (1.3%)

prune109.0ms (1.8%)

localize10.0ms (0.2%)

rewrite34.0ms (0.5%)

series227.0ms (3.6%)

simplify96.0ms (1.5%)

prune196.0ms (3.1%)

localize13.0ms (0.2%)

rewrite37.0ms (0.6%)

series326.0ms (5.2%)

simplify99.0ms (1.6%)

prune187.0ms (3%)

localize15.0ms (0.2%)

rewrite52.0ms (0.8%)

series557.0ms (8.9%)

simplify138.0ms (2.2%)

prune402.0ms (6.5%)

regimes1.5s (23.8%)

bsearch47.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (29.5%)

Profiling