Details

analyze2.5s (8.3%)

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)

sample394.0ms (1.3%)

Algorithm

1×

intervals

Results

126.0ms	47×	body	4096	invalid
73.0ms	123×	body	1024	valid
61.0ms	34×	body	2048	invalid
31.0ms	19×	body	4096	valid
30.0ms	30×	body	2048	valid
18.0ms	45×	body	512	valid
12.0ms	23×	body	1024	invalid
7.0ms	19×	body	512	invalid
5.0ms	37×	body	128	invalid
5.0ms	19×	body	256	valid
3.0ms	20×	body	128	valid
1.0ms	5×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify103.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5185	32

prune7.0ms (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

38.9b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.0b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
0.5b	(/.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)))
0.2b	(pow.f64 (/.f64 k t) 2)
0.1b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
0.5b	(/.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))
14.5b	(/.f64 (pow.f64 t 3) (*.f64 l l))
28.4b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite91.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

396×	`add-exp-log_binary64_442`
229×	`prod-exp_binary64_453`
115×	`div-exp_binary64_455`
65×	`add-cbrt-cube_binary64_440`
56×	`pow-exp_binary64_472`
40×	`times-frac_binary64_410`
38×	`pow-to-exp_binary64_473`
34×	`add-sqr-sqrt_binary64_426`
31×	`cbrt-unprod_binary64_437`
25×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
23×	`unpow-prod-down_binary64_483`
21×	`associate-r_binary64_344`
17×	`associate-l_binary64_345`
15×	`associate-/l*_binary64_349`
14×	`cbrt-undiv_binary64_438`
13×	`associate-*l/_binary64_347`
10×	`cube-prod_binary64_432`
6×	`pow1_binary64_465`
5×	`sqr-pow_binary64_376` `unswap-sqr_binary64_372`
4×	`div-inv_binary64_401` `tan-quot_binary64_563` `add-log-exp_binary64_443`
3×	`unpow3_binary64_470` `associate-/r/_binary64_350` `cube-mult_binary64_434`
2×	`-commutative_binary64_335` `frac-2neg_binary64_415` `associate-/r_binary64_348` `associate-*r/_binary64_346` `clear-num_binary64_403` `frac-times_binary64_414`
1×	`pow-prod-down_binary64_475` `unpow2_binary64_469`

Counts

4 → 221

Calls

8 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))
19.0ms	(/.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))
0.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))

series1.5s (5%)

Counts

4 → 35

Calls

4 calls:

667.0ms	(/.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)))
487.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
239.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
106.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

Compiler

Compiled 1397 to 1220 computations (12.7% saved)

simplify110.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5185	6256

prune687.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	243	13	256
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	244	13	257

Error

16.4b

Counts

257 → 13

Compiler

Compiled 6536 to 3333 computations (49% saved)

localize15.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
0.4b	(pow.f64 (sin.f64 k) 2)
0.1b	(.f64 (.f64 l l) (cos.f64 k))
0.0b	(.f64 2 (/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2)))))
0.4b	(pow.f64 (sin.f64 k) 2)
1.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.0b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
21.0b	(/.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_442`
102×	`prod-exp_binary64_453`
87×	`add-cbrt-cube_binary64_440`
48×	`cbrt-unprod_binary64_437`
27×	`div-exp_binary64_455`
15×	`cbrt-undiv_binary64_438` `add-sqr-sqrt_binary64_426`
10×	`pow-to-exp_binary64_473` `pow1_binary64_465` `pow-exp_binary64_472`
9×	`associate-r_binary64_344` `*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
7×	`unpow-prod-down_binary64_483`
4×	`associate-l_binary64_345` `unswap-sqr_binary64_372` `add-log-exp_binary64_443`
3×	`pow-prod-down_binary64_475` `unpow2_binary64_469` `sqr-pow_binary64_376` `pow-unpow_binary64_481`
2×	`*-commutative_binary64_335`
1×	`frac-2neg_binary64_415` `div-inv_binary64_401` `associate-/r_binary64_348` `times-frac_binary64_410` `clear-num_binary64_403` `associate-/l_binary64_349` `pow-pow_binary64_476`

Counts

4 → 124

Calls

8 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)
0.0ms	(.f64 2 (/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2)))))

series721.0ms (2.4%)

Counts

4 → 25

Calls

4 calls:

477.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))
131.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
91.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
22.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 947 to 796 computations (15.9% saved)

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4989	2748
1	4989	2748

prune228.0ms (0.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	140	9	149
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	142	20	162

Error

10.6b

Counts

162 → 20

Compiler

Compiled 3687 to 1741 computations (52.8% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
0.1b	(.f64 (.f64 l l) (cos.f64 k))
0.1b	(.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))
0.0b	(.f64 2 (/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))))
0.2b	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
0.4b	(pow.f64 (sin.f64 k) 2)
1.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
21.0b	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

rewrite39.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-exp-log_binary64_442`
65×	`add-cbrt-cube_binary64_440`
64×	`prod-exp_binary64_453`
34×	`cbrt-unprod_binary64_437`
18×	`div-exp_binary64_455`
16×	`add-sqr-sqrt_binary64_426`
12×	`cbrt-undiv_binary64_438`
10×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
9×	`associate-r_binary64_344`
7×	`pow1_binary64_465` `unpow-prod-down_binary64_483`
6×	`pow-to-exp_binary64_473` `associate-l_binary64_345` `pow-exp_binary64_472`
4×	`unswap-sqr_binary64_372` `add-log-exp_binary64_443`
3×	`unpow2_binary64_469` `sqr-pow_binary64_376` `pow-unpow_binary64_481`
2×	`*-commutative_binary64_335`
1×	`pow-prod-down_binary64_475` `frac-2neg_binary64_415` `div-inv_binary64_401` `associate-/r_binary64_348` `times-frac_binary64_410` `clear-num_binary64_403` `associate-/l_binary64_349` `pow-pow_binary64_476`

Counts

4 → 107

Calls

8 calls:

13.0ms	(/.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)
0.0ms	(.f64 2 (/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))))

series719.0ms (2.4%)

Counts

4 → 25

Calls

4 calls:

491.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))
124.0ms	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
86.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
18.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 951 to 788 computations (17.1% saved)

simplify87.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4974	2280
1	4974	2280

prune181.0ms (0.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	4	15	19
Picked	1	0	1
Done	0	0	0
Total	132	20	152

Error

10.1b

Counts

152 → 20

Compiler

Compiled 3366 to 1665 computations (50.5% saved)

localize15.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.2b	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
0.1b	(.f64 (/.f64 (.f64 l l) k) (cos.f64 k))
0.0b	(.f64 2 (/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))
0.4b	(pow.f64 (sin.f64 k) 2)
1.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
8.5b	(/.f64 (*.f64 l l) k)
12.8b	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))

rewrite38.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-exp-log_binary64_442`
65×	`add-cbrt-cube_binary64_440`
52×	`prod-exp_binary64_453`
32×	`div-exp_binary64_455`
26×	`cbrt-unprod_binary64_437`
20×	`cbrt-undiv_binary64_438`
17×	`add-sqr-sqrt_binary64_426`
11×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
8×	`associate-r_binary64_344`
7×	`unpow-prod-down_binary64_483`
6×	`pow-to-exp_binary64_473` `pow-exp_binary64_472`
5×	`pow1_binary64_465`
4×	`associate-/r*_binary64_348` `unswap-sqr_binary64_372` `times-frac_binary64_410` `add-log-exp_binary64_443`
3×	`associate-l_binary64_345` `unpow2_binary64_469` `sqr-pow_binary64_376` `pow-unpow_binary64_481`
2×	`frac-2neg_binary64_415` `div-inv_binary64_401` `clear-num_binary64_403` `associate-/l*_binary64_349`
1×	`associate-/l/_binary64_351` `associate-l/_binary64_347` `-commutative_binary64_335` `pow-pow_binary64_476`

Counts

4 → 112

Calls

8 calls:

13.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(/.f64 (*.f64 l l) k)
3.0ms	(pow.f64 (sin.f64 k) 2)
0.0ms	(.f64 2 (/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

series676.0ms (2.3%)

Counts

4 → 25

Calls

4 calls:

507.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))
85.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
63.0ms	(/.f64 (*.f64 l l) k)
21.0ms	(pow.f64 (sin.f64 k) 2)

Compiler

Compiled 949 to 798 computations (15.9% saved)

simplify70.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4984	2264
1	4984	2264

prune171.0ms (0.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	7	12	19
Picked	1	0	1
Done	0	0	0
Total	140	17	157

Error

6.6b

Counts

157 → 17

Compiler

Compiled 2989 to 1223 computations (59.1% saved)

simplify45.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	666	3437
1	666	3437

regimes906.0ms (3%)

Accuracy

Total 7.1b remaining (52.7%)

Threshold costs 0b (0%)

Compiler

Compiled 10525 to 7806 computations (25.8% saved)

bsearch723.0ms (2.4%)

Steps

Iters	Range		Point
7	1.0369835531132589e-113	9.523924445698534e-112	1.3396666814857636e-113
8	-5.337804635612075e-156	-3.5574957000412326e-159	-1.937105691112254e-158

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	41	105
1	41	105

end0.0ms (0%)

sample19.6s (65.8%)

Algorithm

1×

intervals

Results

4.1s	1265×	body	4096	invalid
2.1s	3836×	body	1024	valid
2.1s	1084×	body	2048	invalid
1.0s	499×	body	4096	valid
975.0ms	1010×	body	2048	valid
528.0ms	1374×	body	512	valid
358.0ms	646×	body	1024	invalid
199.0ms	514×	body	512	invalid
144.0ms	1075×	body	128	invalid
127.0ms	479×	body	256	valid
112.0ms	802×	body	128	valid
83.0ms	284×	body	256	invalid

Compiler

Compiled 6764 to 4997 computations (26.1% saved)

Pareto

0.2672765667359609

Details

analyze2.5s (8.3%)

sample394.0ms (1.3%)

simplify103.0ms (0.3%)

prune7.0ms (0%)

localize20.0ms (0.1%)

rewrite91.0ms (0.3%)

series1.5s (5%)

simplify110.0ms (0.4%)

prune687.0ms (2.3%)

localize15.0ms (0.1%)

rewrite46.0ms (0.2%)

series721.0ms (2.4%)

simplify76.0ms (0.3%)

prune228.0ms (0.8%)

localize16.0ms (0.1%)

rewrite39.0ms (0.1%)

series719.0ms (2.4%)

simplify87.0ms (0.3%)

prune181.0ms (0.6%)

localize15.0ms (0.1%)

rewrite38.0ms (0.1%)

series676.0ms (2.3%)

simplify70.0ms (0.2%)

prune171.0ms (0.6%)

simplify45.0ms (0.2%)

regimes906.0ms (3%)

bsearch723.0ms (2.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample19.6s (65.8%)

Profiling