Details

analyze2.6s (11.3%)

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%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.5%	0.5%	11
0%	99.1%	0.9%	12
0.4%	97.3%	2.3%	13
0.7%	95.8%	3.5%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample482.0ms (2.1%)

Algorithm

1×

intervals

Results

133.0ms	28×	body	5120	invalid
97.0ms	37×	body	2560	invalid
85.0ms	105×	body	1280	valid
36.0ms	69×	body	640	valid
29.0ms	28×	body	1280	invalid
29.0ms	23×	body	2560	valid
20.0ms	6×	body	5120	valid
12.0ms	25×	body	640	invalid
7.0ms	18×	body	320	valid
5.0ms	13×	body	320	invalid
4.0ms	30×	body	80	invalid
3.0ms	24×	body	80	valid
3.0ms	11×	body	160	valid
2.0ms	9×	body	160	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4907	32
1	4907	32

prune11.0ms (0%)

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: 42.1b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
0.5b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
19.5b	(/.f64 (pow.f64 t 3) (*.f64 l l))
29.0b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite74.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

396×	`add-exp-log_binary64`
229×	`prod-exp_binary64`
115×	`div-exp_binary64`
65×	`add-cbrt-cube_binary64`
56×	`pow-exp_binary64`
40×	`times-frac_binary64`
38×	`pow-to-exp_binary64`
34×	`add-sqr-sqrt_binary64`
31×	`cbrt-unprod_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
23×	`unpow-prod-down_binary64`
21×	`associate-r_binary64`
17×	`associate-l_binary64`
15×	`associate-/l*_binary64`
14×	`cbrt-undiv_binary64`
13×	`associate-*l/_binary64`
10×	`cube-prod_binary64`
6×	`pow1_binary64`
5×	`sqr-pow_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `tan-quot_binary64`
3×	`associate-/r/_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`associate-/r_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `unpow2_binary64`

Counts

4 → 221

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
19.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
10.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series166.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
71.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
17.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify121.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5109	5826

prune280.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	219	14	233
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	220	14	234

Merged error: 17.6b

Counts

234 → 14

Compiler

Compiled 6220 to 3211 computations (48.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
1.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
8.8b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
23.0b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite60.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`add-exp-log_binary64`
183×	`prod-exp_binary64`
173×	`add-cbrt-cube_binary64`
87×	`cbrt-unprod_binary64`
82×	`div-exp_binary64`
46×	`cbrt-undiv_binary64`
23×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`pow-to-exp_binary64` `pow-exp_binary64`
9×	`pow1_binary64` `associate-r_binary64`
6×	`associate-/r*_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64`
3×	`pow-prod-down_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/r/_binary64`

Counts

4 → 184

Calls

4 calls:

15.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
15.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
9.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

series122.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
38.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
13.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
10.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify136.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4977	5207
1	4977	5207

prune198.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	188	8	196
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	193	17	210

Merged error: 11.6b

Counts

210 → 17

Compiler

Compiled 5001 to 2304 computations (53.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.5b	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
1.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
23.0b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-exp-log_binary64`
128×	`add-cbrt-cube_binary64`
111×	`prod-exp_binary64`
61×	`cbrt-unprod_binary64`
55×	`div-exp_binary64`
37×	`cbrt-undiv_binary64`
25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow-to-exp_binary64` `associate-r_binary64` `pow-exp_binary64`
7×	`unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `*-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

15.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
15.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series113.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
41.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
10.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(pow.f64 (sin.f64 k) 2)

simplify106.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4988	4249
1	4988	4249

prune177.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	166	17	183

Merged error: 11.1b

Counts

183 → 17

Compiler

Compiled 4429 to 2203 computations (50.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
1.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
9.6b	(/.f64 (*.f64 l l) k)
12.6b	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`add-exp-log_binary64`
100×	`add-cbrt-cube_binary64`
73×	`times-frac_binary64`
60×	`prod-exp_binary64` `div-exp_binary64`
57×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
40×	`cbrt-undiv_binary64`
34×	`cbrt-unprod_binary64` `associate-r_binary64`
11×	`div-inv_binary64`
10×	`associate-/r_binary64` `associate-l*_binary64`
8×	`unswap-sqr_binary64`
6×	`pow1_binary64`
5×	`pow-to-exp_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 185

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
9.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.0ms	(/.f64 (*.f64 l l) k)

series78.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
23.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
10.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(/.f64 (*.f64 l l) k)

simplify110.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5140	4789

prune171.0ms (0.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	187	10	197
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	195	19	214

Merged error: 3.8b

Counts

214 → 19

Compiler

Compiled 4942 to 2393 computations (51.6% saved)

regimes350.0ms (1.5%)

Compiler: Compiled 1897 to 1402 computations (26.1% saved)

bsearch1.7s (7.5%)

Steps

Iters	Range		Point
10	3.979017513352507e-128	5.92874269549338e-114	4.5629687678940777e-128
11	-2.2527838284796687e-155	-1.87757270749326e-180	-6.210609360145837e-162

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	50	124
1	50	124

end0.0ms (0%)

sample15.8s (68.3%)

Algorithm

1×

intervals

Results

3.5s	725×	body	5120	invalid
3.1s	1220×	body	2560	invalid
2.7s	3290×	body	1280	valid
1.4s	945×	body	2560	valid
1.1s	1998×	body	640	valid
688.0ms	732×	body	1280	invalid
610.0ms	190×	body	5120	valid
263.0ms	543×	body	640	invalid
238.0ms	604×	body	320	valid
126.0ms	945×	body	80	invalid
126.0ms	346×	body	320	invalid
94.0ms	699×	body	80	valid
72.0ms	274×	body	160	valid
47.0ms	193×	body	160	invalid

Compiler

Compiled 544 to 391 computations (28.1% saved)

Details

analyze2.6s (11.3%)

sample482.0ms (2.1%)

simplify68.0ms (0.3%)

prune11.0ms (0%)

localize18.0ms (0.1%)

rewrite74.0ms (0.3%)

series166.0ms (0.7%)

simplify121.0ms (0.5%)

prune280.0ms (1.2%)

localize16.0ms (0.1%)

rewrite60.0ms (0.3%)

series122.0ms (0.5%)

simplify136.0ms (0.6%)

prune198.0ms (0.9%)

localize16.0ms (0.1%)

rewrite47.0ms (0.2%)

series113.0ms (0.5%)

simplify106.0ms (0.5%)

prune177.0ms (0.8%)

localize16.0ms (0.1%)

rewrite50.0ms (0.2%)

series78.0ms (0.3%)

simplify110.0ms (0.5%)

prune171.0ms (0.7%)

regimes350.0ms (1.5%)

bsearch1.7s (7.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample15.8s (68.3%)

Profiling