Details

analyze2.4s (11.4%)

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)

sample413.0ms (2%)

Algorithm

1×

intervals

Results

174.0ms	46×	body	4096	invalid
60.0ms	119×	body	1024	valid
46.0ms	32×	body	2048	invalid
30.0ms	29×	body	2048	valid
22.0ms	12×	body	4096	valid
21.0ms	33×	body	1024	invalid
19.0ms	51×	body	512	valid
6.0ms	17×	body	512	invalid
5.0ms	41×	body	128	invalid
4.0ms	16×	body	256	valid
4.0ms	29×	body	128	valid
3.0ms	14×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify111.0ms (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

Merged error: 42.2b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(/.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)))
1.0b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
18.2b	(/.f64 (pow.f64 t 3) (*.f64 l l))
28.7b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite94.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

396×	`add-exp-log_binary64_457`
229×	`prod-exp_binary64_468`
115×	`div-exp_binary64_470`
65×	`add-cbrt-cube_binary64_455`
56×	`pow-exp_binary64_487`
40×	`times-frac_binary64_425`
38×	`pow-to-exp_binary64_488`
34×	`add-sqr-sqrt_binary64_441`
31×	`cbrt-unprod_binary64_452`
25×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
23×	`unpow-prod-down_binary64_498`
21×	`associate-r_binary64_359`
17×	`associate-l_binary64_360`
15×	`associate-/l*_binary64_364`
14×	`cbrt-undiv_binary64_453`
13×	`associate-*l/_binary64_362`
10×	`cube-prod_binary64_447`
6×	`pow1_binary64_480`
5×	`unswap-sqr_binary64_387` `sqr-pow_binary64_391`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416` `tan-quot_binary64_578`
3×	`unpow3_binary64_485` `cube-mult_binary64_449` `associate-/r/_binary64_365`
2×	`clear-num_binary64_418` `frac-times_binary64_429` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/r*_binary64_363`
1×	`pow-prod-down_binary64_490` `unpow2_binary64_484`

Counts

4 → 221

Calls

4 calls:

21.0ms	(.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)))
11.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
7.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series747.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
309.0ms	(/.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 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
24.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify108.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4993	5816
1	4993	5816

prune338.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	220	13	233
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	13	234

Merged error: 16.7b

Counts

234 → 13

Compiler

Compiled 6107 to 3149 computations (48.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.8b	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.2b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
20.5b	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

rewrite46.0ms (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 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))
9.0ms	(.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)

series287.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))
63.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
39.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
15.0ms	(pow.f64 (sin.f64 k) 2)

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4970	2537
1	4970	2537

prune163.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	131	18	149

Merged error: 9.5b

Counts

149 → 18

Compiler

Compiled 3419 to 1636 computations (52.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
0.4b	(pow.f64 (sin.f64 k) 2)
0.8b	(*.f64 t (pow.f64 (sin.f64 k) 2))
20.5b	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-exp-log_binary64_457`
65×	`add-cbrt-cube_binary64_455`
64×	`prod-exp_binary64_468`
34×	`cbrt-unprod_binary64_452`
18×	`div-exp_binary64_470`
16×	`add-sqr-sqrt_binary64_441`
12×	`cbrt-undiv_binary64_453`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`associate-r_binary64_359`
7×	`unpow-prod-down_binary64_498` `pow1_binary64_480`
6×	`pow-exp_binary64_487` `pow-to-exp_binary64_488` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387`
3×	`sqr-pow_binary64_391` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`*-commutative_binary64_350`
1×	`pow-prod-down_binary64_490` `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 → 107

Calls

4 calls:

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

series284.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))
55.0ms	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
38.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
15.0ms	(pow.f64 (sin.f64 k) 2)

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4997	2069
1	4997	2069

prune150.0ms (0.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	117	20	137

Merged error: 8.9b

Counts

137 → 20

Compiler

Compiled 3091 to 1561 computations (49.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.8b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.1b	(/.f64 (*.f64 l l) k)
13.5b	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-exp-log_binary64_457`
65×	`add-cbrt-cube_binary64_455`
52×	`prod-exp_binary64_468`
32×	`div-exp_binary64_470`
26×	`cbrt-unprod_binary64_452`
20×	`cbrt-undiv_binary64_453`
17×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`associate-r_binary64_359`
7×	`unpow-prod-down_binary64_498`
6×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
5×	`pow1_binary64_480`
4×	`times-frac_binary64_425` `add-log-exp_binary64_458` `unswap-sqr_binary64_387` `associate-/r*_binary64_363`
3×	`sqr-pow_binary64_391` `associate-l_binary64_360` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`clear-num_binary64_418` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-/l*_binary64_364`
1×	`associate-l/_binary64_362` `-commutative_binary64_350` `pow-pow_binary64_491` `associate-/l/_binary64_366`

Counts

4 → 112

Calls

4 calls:

13.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.0ms	(/.f64 (*.f64 l l) k)
3.0ms	(pow.f64 (sin.f64 k) 2)

series231.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))
40.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
14.0ms	(pow.f64 (sin.f64 k) 2)
13.0ms	(/.f64 (*.f64 l l) k)

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5011	2068

prune132.0ms (0.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	124	20	144

Merged error: 6.2b

Counts

144 → 20

Compiler

Compiled 2764 to 1176 computations (57.5% saved)

regimes1.2s (5.8%)

Compiler: Compiled 14947 to 11043 computations (26.1% saved)

bsearch291.0ms (1.4%)

Steps

Iters	Range		Point
10	-1.2700126822616206e-113	-2.74082351576932e-125	-1.2330902422552477e-113
8	-2.0898527739082499e-81	-9.894074786166198e-85	-1.0005272868091162e-84

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	44	78
1	44	78

end0.0ms (0%)

sample13.6s (64.9%)

Algorithm

1×

intervals

Results

3.7s	1228×	body	4096	invalid
2.0s	3849×	body	1024	valid
2.0s	1067×	body	2048	invalid
957.0ms	1021×	body	2048	valid
908.0ms	496×	body	4096	valid
501.0ms	1368×	body	512	valid
370.0ms	666×	body	1024	invalid
304.0ms	464×	body	256	valid
187.0ms	510×	body	512	invalid
133.0ms	1035×	body	128	invalid
106.0ms	802×	body	128	valid
80.0ms	311×	body	256	invalid

Compiler

Compiled 2257 to 1668 computations (26.1% saved)

Details

analyze2.4s (11.4%)

sample413.0ms (2%)

simplify111.0ms (0.5%)

prune5.0ms (0%)

localize21.0ms (0.1%)

rewrite94.0ms (0.4%)

series747.0ms (3.6%)

simplify108.0ms (0.5%)

prune338.0ms (1.6%)

localize16.0ms (0.1%)

rewrite46.0ms (0.2%)

series287.0ms (1.4%)

simplify72.0ms (0.3%)

prune163.0ms (0.8%)

localize13.0ms (0.1%)

rewrite41.0ms (0.2%)

series284.0ms (1.4%)

simplify68.0ms (0.3%)

prune150.0ms (0.7%)

localize16.0ms (0.1%)

rewrite39.0ms (0.2%)

series231.0ms (1.1%)

simplify68.0ms (0.3%)

prune132.0ms (0.6%)

regimes1.2s (5.8%)

bsearch291.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample13.6s (64.9%)

Profiling