Details

analyze2.6s (9.6%)

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)

sample396.0ms (1.5%)

Algorithm

1×

intervals

Results

128.0ms	39×	body	4096	invalid
71.0ms	112×	body	1024	valid
45.0ms	32×	body	2048	invalid
36.0ms	31×	body	2048	valid
35.0ms	14×	body	4096	valid
31.0ms	65×	body	512	valid
18.0ms	26×	body	1024	invalid
4.0ms	10×	body	512	invalid
3.0ms	23×	body	128	valid
3.0ms	24×	body	128	invalid
3.0ms	11×	body	256	valid
2.0ms	8×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify174.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5185	32

prune8.0ms (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: 41.2b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
0.6b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
15.9b	(/.f64 (pow.f64 t 3) (*.f64 l l))
29.9b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite83.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-exp-log_binary64_457`
139×	`prod-exp_binary64_468`
52×	`add-cbrt-cube_binary64_455`
51×	`div-exp_binary64_470`
37×	`times-frac_binary64_425`
33×	`add-sqr-sqrt_binary64_441`
32×	`pow-exp_binary64_487`
26×	`cbrt-unprod_binary64_452`
24×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
23×	`unpow-prod-down_binary64_498` `pow-to-exp_binary64_488`
18×	`associate-l_binary64_360`
12×	`associate-/l*_binary64_364`
11×	`pow1_binary64_480`
10×	`associate-*l/_binary64_362` `cube-prod_binary64_447`
8×	`cbrt-undiv_binary64_453`
5×	`unswap-sqr_binary64_387` `sqr-pow_binary64_391`
4×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458` `tan-quot_binary64_578`
3×	`unpow3_binary64_485` `cube-mult_binary64_449` `div-inv_binary64_416` `*-commutative_binary64_350`
2×	`frac-times_binary64_429` `associate-*r/_binary64_361`
1×	`clear-num_binary64_418` `frac-2neg_binary64_430` `unpow2_binary64_484` `associate-/r*_binary64_363`

Counts

4 → 187

Calls

4 calls:

22.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
13.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
12.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
8.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.1s (4.2%)

Counts

4 → 12

Calls

4 calls:

627.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
328.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
117.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
43.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify74.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5170	4255

prune295.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	187	12	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	12	200

Merged error: 15.5b

Counts

200 → 12

Compiler

Compiled 5295 to 2709 computations (48.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
2.0b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.0b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
20.7b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite51.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`add-exp-log_binary64_457`
102×	`prod-exp_binary64_468`
87×	`add-cbrt-cube_binary64_455`
48×	`cbrt-unprod_binary64_452`
27×	`div-exp_binary64_470`
15×	`add-sqr-sqrt_binary64_441` `cbrt-undiv_binary64_453`
10×	`pow-exp_binary64_487` `pow-to-exp_binary64_488` `pow1_binary64_480`
9×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
7×	`unpow-prod-down_binary64_498`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `associate-l_binary64_360`
3×	`pow-prod-down_binary64_490` `sqr-pow_binary64_391` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`*-commutative_binary64_350`
1×	`clear-num_binary64_418` `times-frac_binary64_425` `div-inv_binary64_416` `frac-2neg_binary64_430` `pow-pow_binary64_491` `associate-/r_binary64_363` `associate-/l_binary64_364`

Counts

4 → 124

Calls

4 calls:

15.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
10.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series503.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

299.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
112.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
66.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
25.0ms	(pow.f64 (sin.f64 k) 2)

simplify57.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5284	2583

prune172.0ms (0.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	132	16	148

Merged error: 11.9b

Counts

148 → 16

Compiler

Compiled 3465 to 1564 computations (54.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
0.4b	(pow.f64 (sin.f64 k) 2)
2.0b	(*.f64 t (pow.f64 (sin.f64 k) 2))
20.7b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite63.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-exp-log_binary64_457`
128×	`add-cbrt-cube_binary64_455`
111×	`prod-exp_binary64_468`
61×	`cbrt-unprod_binary64_452`
55×	`div-exp_binary64_470`
37×	`cbrt-undiv_binary64_453`
25×	`add-sqr-sqrt_binary64_441`
20×	`times-frac_binary64_425`
19×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`associate-r_binary64_359` `pow-exp_binary64_487` `pow-to-exp_binary64_488`
7×	`unpow-prod-down_binary64_498`
6×	`div-inv_binary64_416` `associate-/r*_binary64_363`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `associate-/l*_binary64_364`
3×	`sqr-pow_binary64_391` `associate-l_binary64_360` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`associate-/r/_binary64_365` `*-commutative_binary64_350` `pow-pow_binary64_491`

Counts

4 → 154

Calls

4 calls:

16.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
15.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series906.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

512.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
296.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
73.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
24.0ms	(pow.f64 (sin.f64 k) 2)

simplify108.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4961	4249
1	4961	4249

prune228.0ms (0.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	157	9	166
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	161	21	182

Merged error: 10.7b

Counts

182 → 21

Compiler

Compiled 4584 to 2299 computations (49.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
2.0b	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.4b	(/.f64 (*.f64 l l) k)
12.5b	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))

rewrite70.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`add-exp-log_binary64_457`
100×	`add-cbrt-cube_binary64_455`
73×	`times-frac_binary64_425`
60×	`prod-exp_binary64_468` `div-exp_binary64_470`
57×	`add-sqr-sqrt_binary64_441`
41×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
40×	`cbrt-undiv_binary64_453`
34×	`associate-r_binary64_359` `cbrt-unprod_binary64_452`
11×	`div-inv_binary64_416`
10×	`associate-l_binary64_360` `associate-/r*_binary64_363`
8×	`unswap-sqr_binary64_387`
6×	`pow1_binary64_480`
5×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
4×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `associate-/l*_binary64_364`
2×	`clear-num_binary64_418` `sqr-pow_binary64_391` `associate-/r/_binary64_365` `*-commutative_binary64_350` `frac-2neg_binary64_430` `unpow2_binary64_484`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `frac-times_binary64_429` `associate-r/_binary64_361`

Counts

4 → 185

Calls

4 calls:

22.0ms	(.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)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.0ms	(/.f64 (*.f64 l l) k)

series633.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

323.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
216.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
69.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
25.0ms	(/.f64 (*.f64 l l) k)

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4962	4787
1	4962	4787

prune241.0ms (0.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	185	12	197
Fresh	13	7	20
Picked	1	0	1
Done	0	0	0
Total	199	19	218

Merged error: 3.0b

Counts

218 → 19

Compiler

Compiled 4941 to 2337 computations (52.7% saved)

regimes1.9s (7.1%)

Compiler: Compiled 20371 to 14783 computations (27.4% saved)

bsearch675.0ms (2.5%)

Steps

Iters	Range	Point
9	2.0616675390036656e+136	5.171088719507084e+142	3.7798603524990884e+136
6	6.317249117436057e-146	8.009067503212927e-145	7.457626896955295e-145
5	-4.1614543120264624e+114	-1.1193969752633512e+114	-1.4035772650202036e+114

Iters

Range

Point

2.0616675390036656e+136

5.171088719507084e+142

3.7798603524990884e+136

6.317249117436057e-146

8.009067503212927e-145

7.457626896955295e-145

-4.1614543120264624e+114

-1.1193969752633512e+114

-1.4035772650202036e+114

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	134
1	40	134

end0.0ms (0%)

sample16.2s (60.7%)

Algorithm

1×

intervals

Results

4.6s	1202×	body	4096	invalid
2.6s	3818×	body	1024	valid
2.0s	1034×	body	2048	invalid
1.1s	1002×	body	2048	valid
1.0s	432×	body	4096	valid
608.0ms	1440×	body	512	valid
375.0ms	645×	body	1024	invalid
181.0ms	475×	body	512	invalid
157.0ms	1093×	body	128	invalid
134.0ms	476×	body	256	valid
117.0ms	832×	body	128	valid
92.0ms	332×	body	256	invalid

Compiler

Compiled 3107 to 2244 computations (27.8% saved)

Details

analyze2.6s (9.6%)

sample396.0ms (1.5%)

simplify174.0ms (0.7%)

prune8.0ms (0%)

localize19.0ms (0.1%)

rewrite83.0ms (0.3%)

series1.1s (4.2%)

simplify74.0ms (0.3%)

prune295.0ms (1.1%)

localize16.0ms (0.1%)

rewrite51.0ms (0.2%)

series503.0ms (1.9%)

simplify57.0ms (0.2%)

prune172.0ms (0.6%)

localize17.0ms (0.1%)

rewrite63.0ms (0.2%)

series906.0ms (3.4%)

simplify108.0ms (0.4%)

prune228.0ms (0.9%)

localize16.0ms (0.1%)

rewrite70.0ms (0.3%)

series633.0ms (2.4%)

simplify89.0ms (0.3%)

prune241.0ms (0.9%)

regimes1.9s (7.1%)

bsearch675.0ms (2.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample16.2s (60.7%)

Profiling