Details

analyze4.9s (10.2%)

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)

sample687.0ms (1.4%)

Algorithm

1×

intervals

Results

141.0ms	116×	body	1024	valid
133.0ms	33×	body	4096	invalid
120.0ms	39×	body	2048	invalid
103.0ms	19×	body	4096	valid
67.0ms	32×	body	2048	valid
30.0ms	40×	body	512	valid
25.0ms	25×	body	1024	invalid
12.0ms	18×	body	512	invalid
11.0ms	21×	body	256	valid
7.0ms	28×	body	128	valid
6.0ms	26×	body	128	invalid
5.0ms	11×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify306.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5185	32

prune14.0ms (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: 41.9b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
1.1b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
14.2b	(/.f64 (pow.f64 t 3) (*.f64 l l))
30.6b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite172.0ms (0.4%)

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:

46.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
28.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
25.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
15.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series2.0s (4.3%)

Counts

4 → 12

Calls

4 calls:

1.1s	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
602.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
219.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
88.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify143.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5170	4255

prune531.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	188	11	199
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	11	200

Merged error: 15.6b

Counts

200 → 11

Compiler

Compiled 5271 to 2684 computations (49.1% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
1.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.1b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
20.8b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite104.0ms (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:

31.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
20.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
14.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.0ms	(pow.f64 (sin.f64 k) 2)

series952.0ms (2%)

Counts

4 → 12

Calls

4 calls:

554.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
215.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
137.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
46.0ms	(pow.f64 (sin.f64 k) 2)

simplify108.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5284	2583

prune232.0ms (0.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	134	13	147

Merged error: 12.5b

Counts

147 → 13

Compiler

Compiled 3337 to 1477 computations (55.7% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.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)
1.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
20.8b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite119.0ms (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:

31.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
25.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
12.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.0ms	(pow.f64 (sin.f64 k) 2)

series1.6s (3.3%)

Counts

4 → 12

Calls

4 calls:

941.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
452.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
143.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
46.0ms	(pow.f64 (sin.f64 k) 2)

simplify211.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4961	4249
1	4961	4249

prune423.0ms (0.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	158	8	166
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	162	17	179

Merged error: 11.6b

Counts

179 → 17

Compiler

Compiled 4407 to 2186 computations (50.4% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
1.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
8.5b	(/.f64 (*.f64 l l) k)
12.9b	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))

rewrite136.0ms (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:

39.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
19.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
14.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
9.0ms	(/.f64 (*.f64 l l) k)

series1.2s (2.4%)

Counts

4 → 12

Calls

4 calls:

596.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
397.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
136.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
42.0ms	(/.f64 (*.f64 l l) k)

simplify174.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4962	4787
1	4962	4787

prune453.0ms (0.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	188	9	197
Fresh	6	9	15
Picked	1	0	1
Done	0	1	1
Total	195	19	214

Merged error: 2.8b

Counts

214 → 19

Compiler

Compiled 4941 to 2337 computations (52.7% saved)

regimes3.6s (7.6%)

Compiler: Compiled 22496 to 16272 computations (27.7% saved)

bsearch16.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	79
1	33	79

end0.0ms (0%)

sample29.8s (62%)

Algorithm

1×

intervals

Results

7.4s	1207×	body	4096	invalid
4.7s	3884×	body	1024	valid
4.2s	1083×	body	2048	invalid
2.1s	495×	body	4096	valid
2.1s	1001×	body	2048	valid
1.1s	1379×	body	512	valid
672.0ms	637×	body	1024	invalid
360.0ms	508×	body	512	invalid
251.0ms	1026×	body	128	invalid
245.0ms	473×	body	256	valid
200.0ms	768×	body	128	valid
129.0ms	271×	body	256	invalid

Compiler

Compiled 3363 to 2429 computations (27.8% saved)

Details

analyze4.9s (10.2%)

sample687.0ms (1.4%)

simplify306.0ms (0.6%)

prune14.0ms (0%)

localize38.0ms (0.1%)

rewrite172.0ms (0.4%)

series2.0s (4.3%)

simplify143.0ms (0.3%)

prune531.0ms (1.1%)

localize33.0ms (0.1%)

rewrite104.0ms (0.2%)

series952.0ms (2%)

simplify108.0ms (0.2%)

prune232.0ms (0.5%)

localize32.0ms (0.1%)

rewrite119.0ms (0.2%)

series1.6s (3.3%)

simplify211.0ms (0.4%)

prune423.0ms (0.9%)

localize30.0ms (0.1%)

rewrite136.0ms (0.3%)

series1.2s (2.4%)

simplify174.0ms (0.4%)

prune453.0ms (0.9%)

regimes3.6s (7.6%)

bsearch16.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample29.8s (62%)

Profiling