Details

analyze2.5s (10.9%)

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)

sample344.0ms (1.5%)

Algorithm

1×

intervals

Results

116.0ms	43×	body	4096	invalid
62.0ms	127×	body	1024	valid
53.0ms	27×	body	2048	invalid
36.0ms	39×	body	2048	valid
18.0ms	43×	body	512	valid
12.0ms	23×	body	1024	invalid
11.0ms	9×	body	4096	valid
5.0ms	16×	body	512	invalid
4.0ms	31×	body	128	invalid
3.0ms	13×	body	256	valid
3.0ms	25×	body	128	valid
3.0ms	12×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify114.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5185	32

prune5.0ms (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

38.8b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
0.8b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
15.8b	(/.f64 (pow.f64 t 3) (*.f64 l l))
26.3b	(.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

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:

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))
12.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
11.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.3s (5.6%)

Counts

4 → 37

Calls

4 calls:

490.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
450.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
245.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
108.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

Compiler

Compiled 1577 to 1362 computations (13.6% saved)

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5205	4760

prune297.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	213	11	224
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	214	11	225

Error

13.8b

Counts

225 → 11

Compiler

Compiled 5766 to 2924 computations (49.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
1.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.4b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
17.7b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite49.0ms (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:

14.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
11.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series725.0ms (3.1%)

Counts

4 → 32

Calls

4 calls:

439.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
151.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
105.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
30.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 1208 to 1002 computations (17.1% saved)

simplify62.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5608	2945

prune172.0ms (0.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	147	9	156
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	150	17	167

Error

9.0b

Counts

167 → 17

Compiler

Compiled 3848 to 1720 computations (55.3% saved)

localize14.0ms (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)
1.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
17.7b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite59.0ms (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:

17.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
13.0ms	(/.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)

series1.1s (4.8%)

Counts

4 → 35

Calls

4 calls:

553.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
427.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
102.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
29.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 1326 to 1122 computations (15.4% saved)

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5009	4764

prune240.0ms (1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	187	19	206

Error

8.3b

Counts

206 → 19

Compiler

Compiled 4898 to 2427 computations (50.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
1.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.6b	(/.f64 k (*.f64 l l))
12.4b	(.f64 (/.f64 k (.f64 l l)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-exp-log_binary64_457`
47×	`add-cbrt-cube_binary64_455`
45×	`prod-exp_binary64_468`
23×	`cbrt-unprod_binary64_452`
19×	`add-sqr-sqrt_binary64_441`
13×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
12×	`div-exp_binary64_470`
10×	`associate-l_binary64_360` `pow1_binary64_480`
9×	`associate-r_binary64_359`
8×	`cbrt-undiv_binary64_453`
7×	`unpow-prod-down_binary64_498`
6×	`times-frac_binary64_425`
5×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387`
3×	`pow-prod-down_binary64_490` `sqr-pow_binary64_391` `pow-unpow_binary64_496` `unpow2_binary64_484` `associate-/l*_binary64_364`
2×	`div-inv_binary64_416` `*-commutative_binary64_350`
1×	`associate-l/_binary64_362` `clear-num_binary64_418` `frac-2neg_binary64_430` `pow-pow_binary64_491` `associate-/r_binary64_363`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f64 (/.f64 k (.f64 l l)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(/.f64 k (*.f64 l l))
3.0ms	(pow.f64 (sin.f64 k) 2)

series507.0ms (2.2%)

Counts

4 → 30

Calls

4 calls:

307.0ms	(.f64 (/.f64 k (.f64 l l)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))
106.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
65.0ms	(/.f64 k (*.f64 l l))
29.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 1154 to 958 computations (17% saved)

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4996	2034
1	4996	2034

prune136.0ms (0.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	136	22	158

Error

2.3b

Counts

158 → 22

Compiler

Compiled 3095 to 1400 computations (54.8% saved)

regimes1.1s (4.9%)

Accuracy

Total 3.8b remaining (48.6%)

Threshold costs 0b (0%)

Compiler

Compiled 15139 to 11131 computations (26.5% saved)

bsearch484.0ms (2.1%)

Steps

Iters	Range		Point
8	1.9610200612956055e+168	8.0807268625446e+170	4.21563689246568e+170
8	1.9864934737780638e-154	1.8298179057417934e-150	2.0248506160887325e-154

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	42	89
1	42	89

end0.0ms (0%)

sample13.4s (58.1%)

Algorithm

1×

intervals

Results

3.7s	1158×	body	4096	invalid
2.1s	1107×	body	2048	invalid
2.1s	4012×	body	1024	valid
972.0ms	1005×	body	2048	valid
836.0ms	459×	body	4096	valid
471.0ms	1278×	body	512	valid
366.0ms	679×	body	1024	invalid
169.0ms	487×	body	512	invalid
124.0ms	1004×	body	128	invalid
114.0ms	463×	body	256	valid
103.0ms	783×	body	128	valid
83.0ms	336×	body	256	invalid

Compiler

Compiled 2294 to 1687 computations (26.5% saved)

Details

analyze2.5s (10.9%)

sample344.0ms (1.5%)

simplify114.0ms (0.5%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite74.0ms (0.3%)

series1.3s (5.6%)

simplify96.0ms (0.4%)

prune297.0ms (1.3%)

localize14.0ms (0.1%)

rewrite49.0ms (0.2%)

series725.0ms (3.1%)

simplify62.0ms (0.3%)

prune172.0ms (0.7%)

localize14.0ms (0.1%)

rewrite59.0ms (0.3%)

series1.1s (4.8%)

simplify96.0ms (0.4%)

prune240.0ms (1%)

localize14.0ms (0.1%)

rewrite36.0ms (0.2%)

series507.0ms (2.2%)

simplify66.0ms (0.3%)

prune136.0ms (0.6%)

regimes1.1s (4.9%)

bsearch484.0ms (2.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample13.4s (58.1%)

Profiling