Details

analyze412.0ms (7.5%)

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)

sample37.0ms (0.7%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
3.0ms	31×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify199.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5740	19

prune4.0ms (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

Error

29.4b

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))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
27.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (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:

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))

series152.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

106.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5313	1833

prune92.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	72	11	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	73	12	85

Error

7.7b

Counts

85 → 12

Compiler

Compiled 1742 to 455 computations (73.9% 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)))))
0.3b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
28.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite38.0ms (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	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series296.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
110.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
34.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
23.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5141	4862

prune168.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	168	15	183

Error

7.7b

Counts

183 → 15

Compiler

Compiled 4132 to 1136 computations (72.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (log.f64 base))
0.4b	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
28.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84` `*-un-lft-identity_binary64_78`
16×	`associate-l_binary64_19`
15×	`pow1_binary64_139`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
9×	`log-prod_binary64_164` `log-pow_binary64_167`
6×	`add-log-exp_binary64_117`
4×	`associate-r_binary64_18` `associate-/r*_binary64_22`
3×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `associate-/l*_binary64_23`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `flip-+_binary64_52` `div-inv_binary64_75` `unswap-sqr_binary64_46` `log-div_binary64_165` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `frac-2neg_binary64_89` `associate-l/_binary64_21` `rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

4 → 98

Calls

4 calls:

12.0ms	(.f64 (/.f64 1/2 (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)))
3.0ms	(/.f64 1/2 (log.f64 base))

series256.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
87.0ms	(/.f64 1/2 (log.f64 base))
34.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4996	1931
1	4996	1931

prune108.0ms (2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	107	18	125

Error

7.7b

Counts

125 → 18

Compiler

Compiled 2328 to 919 computations (60.5% saved)

localize14.0ms (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))))))
28.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.2b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite36.0ms (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:

10.0ms	(+.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)))

series456.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.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))))))
84.0ms	(+.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)))))
79.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
75.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5564	2267

prune98.0ms (1.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	15	16
Picked	0	1	1
Done	1	0	1
Total	91	17	108

Error

7.7b

Counts

108 → 17

Compiler

Compiled 2702 to 880 computations (67.4% saved)

regimes737.0ms (13.3%)

Accuracy

Total 10.3b remaining (58.8%)

Threshold costs 0b (0%)

Compiler

Compiled 4671 to 3376 computations (27.7% saved)

bsearch78.0ms (1.4%)

Steps

Iters	Range		Point
7	4.371470645634199e+48	4.051965958269525e+50	3.955690204860042e+50
7	-1.6828150234725596e+126	-1.4945821875336624e+124	-5.756623360562739e+124

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	37	55
1	37	55

end0.0ms (0%)

sample1.9s (35.3%)

Algorithm

1×

intervals

Results

773.0ms	8000×	body	128	valid
88.0ms	983×	body	128	nan

Compiler

Compiled 985 to 711 computations (27.8% saved)

Details

analyze412.0ms (7.5%)

sample37.0ms (0.7%)

simplify199.0ms (3.6%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite24.0ms (0.4%)

series152.0ms (2.7%)

simplify79.0ms (1.4%)

prune92.0ms (1.7%)

localize11.0ms (0.2%)

rewrite38.0ms (0.7%)

series296.0ms (5.4%)

simplify93.0ms (1.7%)

prune168.0ms (3%)

localize13.0ms (0.2%)

rewrite32.0ms (0.6%)

series256.0ms (4.6%)

simplify50.0ms (0.9%)

prune108.0ms (2%)

localize14.0ms (0.3%)

rewrite36.0ms (0.7%)

series456.0ms (8.3%)

simplify79.0ms (1.4%)

prune98.0ms (1.8%)

regimes737.0ms (13.3%)

bsearch78.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (35.3%)

Profiling