Details

analyze1.7s (16%)

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
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample105.0ms (1%)

Algorithm

1×

intervals

Results

44.0ms	78×	body	1024	valid
22.0ms	121×	body	128	valid
15.0ms	38×	body	512	valid
5.0ms	18×	body	256	valid
2.0ms	16×	body	128	invalid
1.0ms	1×	body	2048	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify236.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune15.0ms (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

14.4b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
6.7b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
19.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

series400.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
120.0ms	(/.f64 x (tan.f64 B))
81.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
51.0ms	(/.f64 F (sin.f64 B))

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4933	2525
1	4933	2525

prune208.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	13	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Error

0.0b

Counts

129 → 13

Compiler

Compiled 3860 to 1879 computations (51.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
19.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite55.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
11.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
3.0ms	(/.f64 x (tan.f64 B))

series444.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
129.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
112.0ms	(/.f64 x (tan.f64 B))
65.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4950	3927
1	4950	3927

prune228.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	150	13	163

Error

0.0b

Counts

163 → 13

Compiler

Compiled 4954 to 2649 computations (46.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
19.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
3.0ms	(/.f64 x (tan.f64 B))

series351.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
112.0ms	(/.f64 x (tan.f64 B))
60.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
46.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4978	2141
1	4978	2141

prune137.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	105	13	118

Error

0.0b

Counts

118 → 13

Compiler

Compiled 3116 to 1686 computations (45.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
0.3b	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
0.3b	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
19.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite113.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

332×	`times-frac_binary64`
199×	`add-sqr-sqrt_binary64`
177×	`*-un-lft-identity_binary64`
173×	`add-cube-cbrt_binary64`
80×	`associate-r_binary64` `unpow-prod-down_binary64`
68×	`add-exp-log_binary64`
37×	`div-exp_binary64`
32×	`associate-/r*_binary64`
28×	`sqr-pow_binary64`
20×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
10×	`div-inv_binary64`
9×	`unswap-sqr_binary64`
8×	`pow-to-exp_binary64` `pow1_binary64` `1-exp_binary64` `rec-exp_binary64` `pow-exp_binary64`
7×	`cbrt-undiv_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
2×	`associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `inv-pow_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 311

Calls

4 calls:

33.0ms	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
15.0ms	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
11.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series423.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
122.0ms	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
106.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
57.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify175.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4933	10988
1	4933	10988

prune671.0ms (6.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	323	13	336

Error

0.0b

Counts

336 → 13

Compiler

Compiled 11774 to 6511 computations (44.7% saved)

regimes704.0ms (6.5%)

Accuracy

Total 0.2b remaining (91.9%)

Threshold costs 0.2b (91.9%)

Compiler

Compiled 6944 to 5184 computations (25.3% saved)

bsearch143.0ms (1.3%)

Steps

Iters	Range		Point
7	1034183379.180392	27458847009.08069	1043981270.3907567
9	-118910369492.71365	-363746.96536039544	-7600355.253758293

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	90
1	67	90

end0.0ms (0%)

sample4.3s (39.5%)

Algorithm

1×

intervals

Results

1.2s	2201×	body	1024	valid
541.0ms	4114×	body	128	valid
431.0ms	1114×	body	512	valid
146.0ms	567×	body	256	valid
84.0ms	648×	body	128	invalid
12.0ms	112×	body	128	nan
4.0ms	4×	body	2048	valid

Compiler

Compiled 1808 to 1342 computations (25.8% saved)

Details

analyze1.7s (16%)

sample105.0ms (1%)

simplify236.0ms (2.2%)

prune15.0ms (0.1%)

localize19.0ms (0.2%)

rewrite42.0ms (0.4%)

series400.0ms (3.7%)

simplify84.0ms (0.8%)

prune208.0ms (1.9%)

localize17.0ms (0.2%)

rewrite55.0ms (0.5%)

series444.0ms (4.1%)

simplify97.0ms (0.9%)

prune228.0ms (2.1%)

localize21.0ms (0.2%)

rewrite43.0ms (0.4%)

series351.0ms (3.2%)

simplify79.0ms (0.7%)

prune137.0ms (1.3%)

localize21.0ms (0.2%)

rewrite113.0ms (1%)

series423.0ms (3.9%)

simplify175.0ms (1.6%)

prune671.0ms (6.2%)

regimes704.0ms (6.5%)

bsearch143.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.3s (39.5%)

Profiling