Details

analyze2.5s (10.7%)

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)

sample417.0ms (1.8%)

Algorithm

1×

intervals

Results

148.0ms	45×	body	4096	invalid
70.0ms	123×	body	1024	valid
67.0ms	33×	body	2048	invalid
32.0ms	13×	body	4096	valid
27.0ms	29×	body	2048	valid
23.0ms	54×	body	512	valid
11.0ms	21×	body	1024	invalid
7.0ms	18×	body	512	invalid
4.0ms	18×	body	256	invalid
4.0ms	34×	body	128	invalid
3.0ms	13×	body	256	valid
3.0ms	24×	body	128	valid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify117.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5185	32

prune9.0ms (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

Error

39.3b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(/.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)))
1.2b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
14.0b	(/.f64 (pow.f64 t 3) (*.f64 l l))
27.4b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite89.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

405×	`add-exp-log_binary64_457`
237×	`prod-exp_binary64_468`
115×	`div-exp_binary64_470`
70×	`add-cbrt-cube_binary64_455`
56×	`pow-exp_binary64_487`
38×	`pow-to-exp_binary64_488`
35×	`cbrt-unprod_binary64_452`
24×	`times-frac_binary64_425`
21×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359` `add-sqr-sqrt_binary64_441`
19×	`unpow-prod-down_binary64_498`
15×	`associate-l/_binary64_362` `associate-/l_binary64_364`
14×	`cbrt-undiv_binary64_453`
9×	`pow1_binary64_480`
6×	`cube-prod_binary64_447` `tan-quot_binary64_578`
4×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `div-inv_binary64_416` `frac-times_binary64_429` `sqr-pow_binary64_391` `associate-*r/_binary64_361` `associate-/r/_binary64_365`
2×	`clear-num_binary64_418` `unpow3_binary64_485` `cube-mult_binary64_449` `-commutative_binary64_350` `associate-l_binary64_360` `frac-2neg_binary64_430` `associate-/r_binary64_363`
1×	`unpow2_binary64_484`

Counts

4 → 206

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))
20.0ms	(/.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)))
12.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series903.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

364.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
333.0ms	(/.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)))
178.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
28.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify108.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5120	5704

prune308.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	206	12	218
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	207	12	219

Error

16.4b

Counts

219 → 12

Compiler

Compiled 5649 to 2940 computations (48% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
1.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.2b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
17.3b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite74.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`add-exp-log_binary64_457`
183×	`prod-exp_binary64_468`
173×	`add-cbrt-cube_binary64_455`
87×	`cbrt-unprod_binary64_452`
82×	`div-exp_binary64_470`
46×	`cbrt-undiv_binary64_453`
23×	`add-sqr-sqrt_binary64_441`
20×	`times-frac_binary64_425`
17×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
15×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
9×	`associate-r_binary64_359` `pow1_binary64_480`
6×	`div-inv_binary64_416` `associate-/r*_binary64_363`
4×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `unswap-sqr_binary64_387` `associate-l_binary64_360` `associate-/l*_binary64_364`
3×	`pow-prod-down_binary64_490`
2×	`clear-num_binary64_418` `sqr-pow_binary64_391` `*-commutative_binary64_350` `frac-2neg_binary64_430` `unpow2_binary64_484`
1×	`associate-/r/_binary64_365`

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))))
14.0ms	(/.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))

series574.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

299.0ms	(/.f64 2 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k))))
169.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
64.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
42.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify117.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4978	5209
1	4978	5209

prune254.0ms (1.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	186	10	196
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	189	19	208

Error

10.0b

Counts

208 → 19

Compiler

Compiled 5042 to 2372 computations (53% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
1.1b	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
1.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
17.3b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite61.0ms (0.3%)

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:

15.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
14.0ms	(/.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)

series540.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

298.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
179.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
47.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
16.0ms	(pow.f64 (sin.f64 k) 2)

simplify110.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4983	4252
1	4983	4252

prune220.0ms (1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	159	7	166
Fresh	7	11	18
Picked	1	0	1
Done	0	0	0
Total	167	18	185

Error

9.0b

Counts

185 → 18

Compiler

Compiled 4409 to 2204 computations (50% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
1.5b	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.6b	(/.f64 (*.f64 l l) k)
10.3b	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))

rewrite60.0ms (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:

21.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
8.0ms	(/.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))
4.0ms	(/.f64 (*.f64 l l) k)

series396.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
125.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
46.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
15.0ms	(/.f64 (*.f64 l l) k)

simplify110.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4969	4787
1	4969	4787

prune236.0ms (1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	187	10	197
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	196	19	215

Error

2.5b

Counts

215 → 19

Compiler

Compiled 4941 to 2337 computations (52.7% saved)

regimes1.4s (5.9%)

Accuracy

Total 5.3b remaining (65%)

Threshold costs 0b (0%)

Compiler

Compiled 17845 to 13177 computations (26.2% saved)

bsearch176.0ms (0.8%)

Steps

Iters	Range		Point
7	5.695385680822188e+102	7.240011025557046e+104	2.9517580616168344e+103

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	32	76
1	32	76

end0.0ms (0%)

sample14.4s (62.1%)

Algorithm

1×

intervals

Results

3.9s	1214×	body	4096	invalid
2.1s	3766×	body	1024	valid
2.0s	993×	body	2048	invalid
1.2s	1061×	body	2048	valid
955.0ms	475×	body	4096	valid
558.0ms	1444×	body	512	valid
389.0ms	664×	body	1024	invalid
190.0ms	491×	body	512	invalid
142.0ms	1086×	body	128	invalid
119.0ms	809×	body	128	valid
119.0ms	445×	body	256	valid
76.0ms	294×	body	256	invalid

Compiler

Compiled 2672 to 1969 computations (26.3% saved)

Details

analyze2.5s (10.7%)

sample417.0ms (1.8%)

simplify117.0ms (0.5%)

prune9.0ms (0%)

localize16.0ms (0.1%)

rewrite89.0ms (0.4%)

series903.0ms (3.9%)

simplify108.0ms (0.5%)

prune308.0ms (1.3%)

localize14.0ms (0.1%)

rewrite74.0ms (0.3%)

series574.0ms (2.5%)

simplify117.0ms (0.5%)

prune254.0ms (1.1%)

localize14.0ms (0.1%)

rewrite61.0ms (0.3%)

series540.0ms (2.3%)

simplify110.0ms (0.5%)

prune220.0ms (1%)

localize14.0ms (0.1%)

rewrite60.0ms (0.3%)

series396.0ms (1.7%)

simplify110.0ms (0.5%)

prune236.0ms (1%)

regimes1.4s (5.9%)

bsearch176.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample14.4s (62.1%)

Profiling