Details

analyze2.2s (21.1%)

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
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
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample137.0ms (1.3%)

Algorithm

1×

intervals

Results

59.0ms	75×	body	1280	valid
33.0ms	53×	body	640	valid
13.0ms	100×	body	80	valid
6.0ms	16×	body	320	valid
5.0ms	43×	body	80	invalid
3.0ms	12×	body	160	valid
2.0ms	6×	body	320	invalid
2.0ms	3×	body	640	invalid
1.0ms	3×	body	160	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5167	35

prune10.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.1b

Counts

2 → 1

Compiler

Compiled 46 to 38 computations (17.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.4b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
14.7b	(/.f64 (pow.f64 t 3) (*.f64 l l))
16.7b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-exp-log_binary64`
58×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
28×	`times-frac_binary64`
26×	`cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
24×	`div-exp_binary64`
20×	`pow1_binary64`
19×	`*-un-lft-identity_binary64`
18×	`associate-l_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-*l/_binary64`
12×	`associate-/l*_binary64`
10×	`pow-prod-down_binary64` `associate-r_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `frac-times_binary64`
8×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `pow-exp_binary64` `tan-quot_binary64`
6×	`associate-*r/_binary64`
5×	`unswap-sqr_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `flip-+_binary64`
3×	`unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
2×	`div-inv_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 159

Calls

4 calls:

22.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
12.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
10.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
8.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series157.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
41.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
20.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5447	3703

prune216.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Merged error: 17.3b

Counts

172 → 9

Compiler

Compiled 5028 to 2755 computations (45.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (/.f64 (.f64 t t) l))) (tan.f64 k))
4.9b	(.f64 (sin.f64 k) (/.f64 (.f64 t t) l))
5.5b	(/.f64 (*.f64 t t) l)
16.7b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (/.f64 (*.f64 t t) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite65.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
65×	`cbrt-unprod_binary64` `prod-exp_binary64`
34×	`frac-times_binary64`
31×	`associate-*r/_binary64`
29×	`pow1_binary64`
27×	`associate-*l/_binary64`
20×	`cbrt-undiv_binary64` `div-exp_binary64`
17×	`pow-prod-down_binary64`
16×	`tan-quot_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`times-frac_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`

Counts

4 → 151

Calls

4 calls:

29.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (/.f64 (*.f64 t t) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
15.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (/.f64 (.f64 t t) l))) (tan.f64 k))
8.0ms	(.f64 (sin.f64 k) (/.f64 (.f64 t t) l))
5.0ms	(/.f64 (*.f64 t t) l)

series153.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (/.f64 (*.f64 t t) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
41.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (sin.f64 k) (/.f64 (.f64 t t) l))) (tan.f64 k))
18.0ms	(.f64 (sin.f64 k) (/.f64 (.f64 t t) l))
4.0ms	(/.f64 (*.f64 t t) l)

simplify135.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4973	4043
1	4973	4043

prune186.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	159	13	172

Merged error: 12.1b

Counts

172 → 13

Compiler

Compiled 5076 to 2571 computations (49.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
1.5b	(.f64 (.f64 t (sin.f64 k)) (/.f64 t l))
2.7b	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k))
16.7b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite97.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

215×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
129×	`cbrt-unprod_binary64` `prod-exp_binary64`
63×	`frac-times_binary64`
54×	`associate-*r/_binary64`
49×	`associate-*l/_binary64`
43×	`pow1_binary64`
42×	`cbrt-undiv_binary64` `div-exp_binary64`
28×	`pow-prod-down_binary64` `tan-quot_binary64`
23×	`associate-/r/_binary64`
20×	`associate-r_binary64`
17×	`*-un-lft-identity_binary64`
16×	`flip3-+_binary64` `flip-+_binary64`
15×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`times-frac_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `associate-/l_binary64` `-commutative_binary64`
2×	`div-inv_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 211

Calls

4 calls:

31.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
28.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
15.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k))
8.0ms	(.f64 (.f64 t (sin.f64 k)) (/.f64 t l))

series218.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
71.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
42.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (sin.f64 k)) (/.f64 t l))) (tan.f64 k))
14.0ms	(.f64 (.f64 t (sin.f64 k)) (/.f64 t l))

simplify163.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4963	7001
1	4963	7001

prune225.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	215	8	223
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	222	14	236

Merged error: 9.9b

Counts

236 → 14

Compiler

Compiled 7111 to 2880 computations (59.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 (/.f64 t l) (.f64 t (sin.f64 k)))
1.8b	(.f64 (/.f64 t l) (.f64 (.f64 (/.f64 t l) (.f64 t (sin.f64 k))) (tan.f64 k)))
4.2b	(.f64 (.f64 (/.f64 t l) (*.f64 t (sin.f64 k))) (tan.f64 k))
16.7b	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 (/.f64 t l) (*.f64 t (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite73.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

160×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
98×	`cbrt-unprod_binary64` `prod-exp_binary64`
52×	`pow1_binary64`
39×	`associate-*l/_binary64`
35×	`frac-times_binary64`
34×	`pow-prod-down_binary64`
28×	`associate-l_binary64`
24×	`cbrt-undiv_binary64` `div-exp_binary64`
23×	`associate-*r/_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`times-frac_binary64` `tan-quot_binary64`
9×	`associate-r_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
2×	`div-inv_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 187

Calls

4 calls:

27.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 (/.f64 t l) (*.f64 t (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
16.0ms	(.f64 (/.f64 t l) (.f64 (.f64 (/.f64 t l) (.f64 t (sin.f64 k))) (tan.f64 k)))
11.0ms	(.f64 (.f64 (/.f64 t l) (*.f64 t (sin.f64 k))) (tan.f64 k))
8.0ms	(.f64 (/.f64 t l) (.f64 t (sin.f64 k)))

series185.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 (/.f64 t l) (*.f64 t (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
43.0ms	(.f64 (/.f64 t l) (.f64 (.f64 (/.f64 t l) (.f64 t (sin.f64 k))) (tan.f64 k)))
39.0ms	(.f64 (.f64 (/.f64 t l) (*.f64 t (sin.f64 k))) (tan.f64 k))
15.0ms	(.f64 (/.f64 t l) (.f64 t (sin.f64 k)))

simplify115.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5177	5150

prune171.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	199	14	213

Merged error: 9.9b

Counts

213 → 14

Compiler

Compiled 5773 to 2606 computations (54.9% saved)

regimes334.0ms (3.3%)

Compiler: Compiled 1540 to 1142 computations (25.8% saved)

bsearch202.0ms (2%)

Steps

Iters	Range		Point
10	2.0428536821452525e-175	1.4710700831047654e-162	1.4895900323393487e-174
7	-3.0035489332934224e-232	-3.62019715772937e-234	-2.882279254698786e-232

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	54	109
1	54	109

end0.0ms (0%)

sample4.9s (48.1%)

Algorithm

1×

intervals

Results

1.6s	2046×	body	1280	valid
852.0ms	1596×	body	640	valid
438.0ms	3291×	body	80	valid
276.0ms	712×	body	320	valid
172.0ms	1341×	body	80	invalid
101.0ms	355×	body	160	valid
68.0ms	122×	body	640	invalid
44.0ms	117×	body	320	invalid
24.0ms	82×	body	160	invalid
16.0ms	21×	body	1280	invalid

Compiler

Compiled 468 to 340 computations (27.4% saved)

Details

analyze2.2s (21.1%)

sample137.0ms (1.3%)

simplify77.0ms (0.8%)

prune10.0ms (0.1%)

localize19.0ms (0.2%)

rewrite59.0ms (0.6%)

series157.0ms (1.5%)

simplify83.0ms (0.8%)

prune216.0ms (2.1%)

localize19.0ms (0.2%)

rewrite65.0ms (0.6%)

series153.0ms (1.5%)

simplify135.0ms (1.3%)

prune186.0ms (1.8%)

localize18.0ms (0.2%)

rewrite97.0ms (1%)

series218.0ms (2.1%)

simplify163.0ms (1.6%)

prune225.0ms (2.2%)

localize20.0ms (0.2%)

rewrite73.0ms (0.7%)

series185.0ms (1.8%)

simplify115.0ms (1.1%)

prune171.0ms (1.7%)

regimes334.0ms (3.3%)

bsearch202.0ms (2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.9s (48.1%)

Profiling