Details

analyze432.0ms (10.5%)

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

sample37.0ms (0.9%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	35×	body	80	nan

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

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: 32.4b

Counts

2 → 1

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`pow1_binary64` `add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`times-frac_binary64`
8×	`associate-r_binary64`
6×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 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)))

series74.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0.0 0.0)))
23.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
13.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4986	2010
1	4986	2010

prune242.0ms (5.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	105	17	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	17	123

Merged error: 7.3b

Counts

123 → 17

localize24.0ms (0.6%)

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))
0.5b	(pow.f64 (log.f64 base) 2)
0.5b	(*.f64 (log.f64 base) (log.f64 base))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`pow1_binary64`
22×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
11×	`log-pow_binary64`
10×	`associate-l_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64` `add-cbrt-cube_binary64`
6×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64`
3×	`pow-unpow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-prod-up_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow-exp_binary64` `pow2_binary64`

Counts

4 → 98

Calls

4 calls:

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))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(pow.f64 (log.f64 base) 2)

series58.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
15.0ms	(pow.f64 (log.f64 base) 2)
13.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4819	923
1	4819	923

prune212.0ms (5.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	110	17	127

Merged error: 7.3b

Counts

127 → 17

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))) (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (*.f64 0.0 0.0)))))
0.5b	(pow.f64 (log.f64 base) 2)
0.5b	(pow.f64 (log.f64 base) 2)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite50.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
32×	`sqrt-prod_binary64`
28×	`add-exp-log_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
16×	`add-cbrt-cube_binary64`
15×	`unswap-sqr_binary64`
11×	`pow1_binary64`
8×	`unpow-prod-down_binary64` `prod-exp_binary64` `div-exp_binary64`
6×	`pow-unpow_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 140

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))) (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (*.f64 0.0 0.0)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(pow.f64 (log.f64 base) 2)
3.0ms	(pow.f64 (log.f64 base) 2)

series72.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (.f64 0.0 0.0)))) (/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (sqrt.f64 (+.f64 (pow.f64 (log.f64 base) 2) (*.f64 0.0 0.0)))))
13.0ms	(pow.f64 (log.f64 base) 2)
13.0ms	(pow.f64 (log.f64 base) 2)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify58.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4957	4112
1	4957	4112

prune357.0ms (8.7%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	150	19	169

Merged error: 7.2b

Counts

169 → 19

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (-.f64 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4)))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
0.8b	(pow.f64 (log.f64 base) 4)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
45×	`times-frac_binary64`
44×	`unpow-prod-down_binary64`
36×	`difference-of-squares_binary64`
33×	`add-cube-cbrt_binary64`
25×	`sqr-pow_binary64`
24×	`pow1_binary64`
15×	`associate-/r*_binary64`
12×	`distribute-lft-out--_binary64`
11×	`log-pow_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`swap-sqr_binary64` `log-prod_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`pow-unpow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `pow-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 148

Calls

4 calls:

16.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (-.f64 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4)))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(pow.f64 (log.f64 base) 4)

series80.0ms (2%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0.0)) (-.f64 (pow.f64 (log.f64 base) 4) (pow.f64 0.0 4)))
17.0ms	(pow.f64 (log.f64 base) 4)
13.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify87.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4981	3959
1	4981	3959

prune273.0ms (6.7%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	154	6	160
Fresh	2	14	16
Picked	1	0	1
Done	0	2	2
Total	157	22	179

Merged error: 7.2b

Counts

179 → 22

regimes538.0ms (13.1%)

Accuracy

Total 10.4b remaining (57.8%)

Threshold costs 0b (0%)

bsearch154.0ms (3.7%)

Steps

Iters	Range		Point
9	2.742846384821079e+28	2.573805552041366e+35	2.5362193761446767e+35
9	9.317771181504113e-281	5.196805194780243e-272	8.950330598317258e-276
6	-5.093211122374936e-261	-3.65607763076758e-262	-4.337372021152796e-262
8	-2.1915322657080793e+63	-2.1090434721521167e+59	-1.8073559612423165e+63

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	99	137
1	99	137

end0.0ms (0%)

sample1.1s (25.7%)

Algorithm

1×

intervals

Results

757.0ms	8000×	body	80	valid
88.0ms	975×	body	80	nan

Details

analyze432.0ms (10.5%)

sample37.0ms (0.9%)

simplify5.0ms (0.1%)

prune9.0ms (0.2%)

localize18.0ms (0.4%)

rewrite31.0ms (0.7%)

series74.0ms (1.8%)

simplify73.0ms (1.8%)

prune242.0ms (5.9%)

localize24.0ms (0.6%)

rewrite21.0ms (0.5%)

series58.0ms (1.4%)

simplify57.0ms (1.4%)

prune212.0ms (5.2%)

localize23.0ms (0.5%)

rewrite50.0ms (1.2%)

series72.0ms (1.7%)

simplify58.0ms (1.4%)

prune357.0ms (8.7%)

localize24.0ms (0.6%)

rewrite37.0ms (0.9%)

series80.0ms (2%)

simplify87.0ms (2.1%)

prune273.0ms (6.7%)

regimes538.0ms (13.1%)

bsearch154.0ms (3.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (25.7%)

Profiling