Details

analyze2.1s (14%)

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
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample109.0ms (0.7%)

Algorithm

1×

intervals

Results

54.0ms	79×	body	1024	valid
17.0ms	127×	body	128	valid
13.0ms	32×	body	512	valid
5.0ms	43×	body	128	invalid
5.0ms	18×	body	256	valid
2.0ms	6×	body	256	invalid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify219.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4928	35
1	4928	35

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: 33.5b

Counts

2 → 1

Compiler

Compiled 46 to 38 computations (17.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.8b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
4.6b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
13.0b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
16.5b	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite78.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-exp-log_binary64_449`
58×	`prod-exp_binary64_460`
52×	`add-cbrt-cube_binary64_447`
28×	`times-frac_binary64_420`
26×	`cbrt-unprod_binary64_444` `add-sqr-sqrt_binary64_435`
24×	`div-exp_binary64_462`
20×	`pow1_binary64_472`
19×	`*-un-lft-identity_binary64_414`
18×	`associate-l_binary64_357`
17×	`add-cube-cbrt_binary64_446`
16×	`associate-*l/_binary64_359`
12×	`associate-/l*_binary64_361`
10×	`cube-prod_binary64_439` `pow-prod-down_binary64_482` `unpow-prod-down_binary64_490` `associate-r_binary64_356` `frac-times_binary64_424`
8×	`cbrt-undiv_binary64_445` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `tan-quot_binary64_570`
6×	`associate-*r/_binary64_358`
5×	`unswap-sqr_binary64_382`
4×	`flip3-+_binary64_417` `sqr-pow_binary64_386` `add-log-exp_binary64_450` `flip-+_binary64_388`
3×	`cube-mult_binary64_441` `*-commutative_binary64_347` `unpow3_binary64_477`
2×	`div-inv_binary64_411`
1×	`distribute-lft-in_binary64_365` `clear-num_binary64_413` `distribute-rgt-in_binary64_366` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`

Counts

4 → 159

Calls

4 calls:

24.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
13.0ms	(.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))

series1.2s (8.2%)

Counts

4 → 12

Calls

4 calls:

728.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
339.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
124.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
44.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5586	3677

prune269.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Merged error: 13.6b

Counts

172 → 9

Compiler

Compiled 5001 to 2746 computations (45.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.8b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
3.5b	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
8.4b	(/.f64 (*.f64 t t) l)
13.0b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite77.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
65×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
44×	`associate-*l/_binary64_359`
34×	`frac-times_binary64_424`
29×	`pow1_binary64_472`
20×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
17×	`pow-prod-down_binary64_482`
16×	`tan-quot_binary64_570`
15×	`add-sqr-sqrt_binary64_435`
14×	`associate-*r/_binary64_358`
13×	`*-un-lft-identity_binary64_414`
11×	`add-cube-cbrt_binary64_446`
10×	`associate-r_binary64_356`
9×	`associate-l_binary64_357`
8×	`flip3-+_binary64_417` `flip-+_binary64_388`
7×	`times-frac_binary64_420`
4×	`add-log-exp_binary64_450`
3×	`-commutative_binary64_347` `associate-/r_binary64_360`
2×	`div-inv_binary64_411` `unswap-sqr_binary64_382`
1×	`distribute-lft-in_binary64_365` `clear-num_binary64_413` `distribute-rgt-in_binary64_366` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `associate-/l*_binary64_361`

Counts

4 → 151

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
15.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
8.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)

series1.2s (8%)

Counts

4 → 12

Calls

4 calls:

718.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
346.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
114.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
25.0ms	(/.f64 (*.f64 t t) l)

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5000	4012

prune245.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	154	9	163
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	160	12	172

Merged error: 9.1b

Counts

172 → 12

Compiler

Compiled 5011 to 2518 computations (49.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 l)
1.7b	(*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l)))
1.8b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (tan.f64 k))
13.0b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite128.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`add-exp-log_binary64_449`
247×	`add-cbrt-cube_binary64_447`
178×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
98×	`frac-times_binary64_424`
79×	`associate-*r/_binary64_358`
67×	`associate-*l/_binary64_359`
57×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
40×	`pow1_binary64_472`
32×	`tan-quot_binary64_570`
29×	`associate-r_binary64_356` `add-sqr-sqrt_binary64_435`
26×	`pow-prod-down_binary64_482`
23×	`*-un-lft-identity_binary64_414`
21×	`add-cube-cbrt_binary64_446`
20×	`times-frac_binary64_420`
16×	`flip3-+_binary64_417` `flip-+_binary64_388`
13×	`cbrt-prod_binary64_442`
5×	`associate-l_binary64_357`
4×	`add-log-exp_binary64_450`
3×	`*-commutative_binary64_347` `unswap-sqr_binary64_382`
1×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `div-inv_binary64_411` `distribute-lft-out_binary64_367` `pow1/3_binary64_493`

Counts

4 → 237

Calls

4 calls:

39.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
26.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (tan.f64 k))
14.0ms	(*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l)))
1.0ms	(cbrt.f64 l)

series1.5s (9.8%)

Counts

4 → 12

Calls

4 calls:

802.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
360.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (tan.f64 k))
176.0ms	(*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l)))
140.0ms	(cbrt.f64 l)

simplify141.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4998	8607
1	4998	8607

prune411.0ms (2.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	242	7	249
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	244	17	261

Merged error: 8.2b

Counts

261 → 17

Compiler

Compiled 9412 to 4162 computations (55.8% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))
3.0b	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))
3.0b	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))
13.0b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l)))) (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite169.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

542×	`associate-*r/_binary64_358`
513×	`frac-times_binary64_424`
294×	`associate-*l/_binary64_359`
291×	`cbrt-div_binary64_443`
153×	`add-exp-log_binary64_449`
117×	`add-cbrt-cube_binary64_447`
105×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
96×	`tan-quot_binary64_570`
64×	`flip3-+_binary64_417` `flip-+_binary64_388`
31×	`pow1_binary64_472`
22×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
21×	`pow-prod-down_binary64_482`
7×	`*-un-lft-identity_binary64_414`
5×	`add-cube-cbrt_binary64_446` `add-sqr-sqrt_binary64_435`
4×	`add-log-exp_binary64_450` `associate-r_binary64_356`
3×	`cbrt-prod_binary64_442` `pow1/3_binary64_493`
1×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `-commutative_binary64_347` `associate-l*_binary64_357` `distribute-lft-out_binary64_367`

Counts

4 → 286

Calls

4 calls:

55.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l)))) (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
6.0ms	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))
6.0ms	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))
6.0ms	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))

series1.6s (10.9%)

Counts

4 → 12

Calls

4 calls:

715.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l)))) (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))) (cbrt.f64 (.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
311.0ms	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))
306.0ms	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))
303.0ms	(cbrt.f64 (*.f64 (sin.f64 k) (/.f64 t (cbrt.f64 l))))

simplify227.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4984	19174
1	4984	19174

prune505.0ms (3.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	294	4	298
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	297	18	315

Merged error: 7.9b

Counts

315 → 18

Compiler

Compiled 15597 to 4086 computations (73.8% saved)

regimes259.0ms (1.7%)

Compiler: Compiled 2820 to 1836 computations (34.9% saved)

bsearch250.0ms (1.7%)

Steps

Iters	Range		Point
10	9.205622480800602e-215	4.613613901146152e-201	8.735486909965795e-203
10	-6.41732562053676e-124	-4.153556267865403e-141	-5.682272213353497e-132

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	67	248
1	67	248

end0.0ms (0%)

sample4.0s (26.9%)

Algorithm

1×

intervals

Results

1.7s	2651×	body	1024	valid
527.0ms	1271×	body	512	valid
475.0ms	3489×	body	128	valid
188.0ms	1461×	body	128	invalid
173.0ms	583×	body	256	valid
50.0ms	125×	body	512	invalid
38.0ms	140×	body	256	invalid
35.0ms	58×	body	1024	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 869 to 535 computations (38.4% saved)

Details

analyze2.1s (14%)

sample109.0ms (0.7%)

simplify219.0ms (1.5%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite78.0ms (0.5%)

series1.2s (8.2%)

simplify67.0ms (0.4%)

prune269.0ms (1.8%)

localize21.0ms (0.1%)

rewrite77.0ms (0.5%)

series1.2s (8%)

simplify106.0ms (0.7%)

prune245.0ms (1.6%)

localize23.0ms (0.2%)

rewrite128.0ms (0.8%)

series1.5s (9.8%)

simplify141.0ms (0.9%)

prune411.0ms (2.7%)

localize32.0ms (0.2%)

rewrite169.0ms (1.1%)

series1.6s (10.9%)

simplify227.0ms (1.5%)

prune505.0ms (3.3%)

regimes259.0ms (1.7%)

bsearch250.0ms (1.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.0s (26.9%)

Profiling