Details

analyze2.8s (11.5%)

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)

sample428.0ms (1.8%)

Algorithm

1×

intervals

Results

106.0ms	17×	body	5120	invalid
80.0ms	29×	body	2560	invalid
79.0ms	100×	body	1280	valid
54.0ms	33×	body	2560	valid
31.0ms	58×	body	640	valid
20.0ms	4×	body	5120	valid
11.0ms	17×	body	1280	invalid
10.0ms	25×	body	320	valid
5.0ms	9×	body	640	invalid
4.0ms	28×	body	80	invalid
4.0ms	14×	body	160	valid
4.0ms	22×	body	80	valid
4.0ms	10×	body	320	invalid
2.0ms	6×	body	160	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify38.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5186	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: 41.2b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(.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))
16.9b	(/.f64 (pow.f64 t 3) (*.f64 l l))
27.8b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite71.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-exp-log_binary64`
139×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
51×	`div-exp_binary64`
37×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`pow-exp_binary64`
26×	`cbrt-unprod_binary64`
24×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
23×	`pow-to-exp_binary64` `unpow-prod-down_binary64`
18×	`associate-l_binary64`
12×	`associate-/l*_binary64`
11×	`pow1_binary64`
10×	`cube-prod_binary64` `associate-*l/_binary64`
8×	`cbrt-undiv_binary64`
5×	`sqr-pow_binary64` `unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `insert-posit16` `tan-quot_binary64`
3×	`div-inv_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
2×	`associate-*r/_binary64` `frac-times_binary64`
1×	`associate-/r*_binary64` `unpow2_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 191

Calls

4 calls:

24.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
15.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
12.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
8.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.1s (4.6%)

Counts

4 → 12

Calls

4 calls:

601.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
318.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
121.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
56.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5177	4347

prune299.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	189	14	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	14	204

Merged error: 16.2b

Counts

204 → 14

Compiler

Compiled 5461 to 2806 computations (48.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
2.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.2b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
23.2b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`add-exp-log_binary64`
102×	`prod-exp_binary64`
87×	`add-cbrt-cube_binary64`
48×	`cbrt-unprod_binary64`
27×	`div-exp_binary64`
15×	`cbrt-undiv_binary64` `add-sqr-sqrt_binary64`
10×	`pow-to-exp_binary64` `pow1_binary64` `pow-exp_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64`
2×	`*-commutative_binary64`
1×	`associate-/r_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 128

Calls

4 calls:

18.0ms	(/.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)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series490.0ms (2%)

Counts

4 → 12

Calls

4 calls:

275.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
106.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
81.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
28.0ms	(pow.f64 (sin.f64 k) 2)

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5473	2647

prune181.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	134	6	140
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	136	18	154

Merged error: 13.2b

Counts

154 → 18

Compiler

Compiled 3630 to 1653 computations (54.5% saved)

localize16.0ms (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)
2.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
23.2b	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite60.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-exp-log_binary64`
128×	`add-cbrt-cube_binary64`
111×	`prod-exp_binary64`
61×	`cbrt-unprod_binary64`
55×	`div-exp_binary64`
37×	`cbrt-undiv_binary64`
25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow-to-exp_binary64` `associate-r_binary64` `pow-exp_binary64`
7×	`unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `*-commutative_binary64`

Counts

4 → 158

Calls

4 calls:

18.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
17.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms	(pow.f64 (sin.f64 k) 2)

series860.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

474.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k))))
279.0ms	(/.f64 (.f64 k (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))) (.f64 (*.f64 l l) (cos.f64 k)))
75.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
32.0ms	(pow.f64 (sin.f64 k) 2)

simplify176.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4965	4330
1	4965	4330

prune232.0ms (1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	162	8	170
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	169	19	188

Merged error: 12.3b

Counts

188 → 19

Compiler

Compiled 4510 to 2260 computations (49.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
2.1b	(*.f64 t (pow.f64 (sin.f64 k) 2))
9.4b	(/.f64 (*.f64 l l) k)
14.5b	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`add-exp-log_binary64`
100×	`add-cbrt-cube_binary64`
73×	`times-frac_binary64`
60×	`prod-exp_binary64` `div-exp_binary64`
57×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
40×	`cbrt-undiv_binary64`
34×	`cbrt-unprod_binary64` `associate-r_binary64`
11×	`div-inv_binary64`
10×	`associate-/r_binary64` `associate-l*_binary64`
8×	`unswap-sqr_binary64`
6×	`pow1_binary64`
5×	`pow-to-exp_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64` `insert-posit16`
2×	`unpow2_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 189

Calls

4 calls:

26.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
10.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.0ms	(/.f64 (*.f64 l l) k)

series616.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(.f64 (/.f64 (.f64 l l) k) (/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))))
198.0ms	(/.f64 2 (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
79.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
25.0ms	(/.f64 (*.f64 l l) k)

simplify178.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4970	4862
1	4970	4862

prune246.0ms (1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	195	6	201
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	202	18	220

Merged error: 3.3b

Counts

220 → 18

Compiler

Compiled 5026 to 2376 computations (52.7% saved)

regimes237.0ms (1%)

Compiler: Compiled 1851 to 1409 computations (23.9% saved)

bsearch396.0ms (1.7%)

Steps

Iters	Range	Point
10	2.3582957204744294e-22	1.3089053343687802e-11	5.278128558933203e-22
9	-3.345552146308564e-42	-2.1115080601318553e-48	-2.894035770799735e-46
5	-9.723727345136073e+101	-4.441873384755086e+101	-7.007129757028244e+101

Iters

Range

Point

2.3582957204744294e-22

1.3089053343687802e-11

5.278128558933203e-22

-3.345552146308564e-42

-2.1115080601318553e-48

-2.894035770799735e-46

-9.723727345136073e+101

-4.441873384755086e+101

-7.007129757028244e+101

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	46	146
1	46	146

end0.0ms (0%)

sample15.2s (63.5%)

Algorithm

1×

intervals

Results

3.7s	761×	body	5120	invalid
3.1s	1224×	body	2560	invalid
2.7s	3325×	body	1280	valid
1.4s	960×	body	2560	valid
1.1s	1928×	body	640	valid
749.0ms	218×	body	5120	valid
595.0ms	721×	body	1280	invalid
276.0ms	561×	body	640	invalid
253.0ms	641×	body	320	valid
141.0ms	371×	body	320	invalid
115.0ms	882×	body	80	invalid
99.0ms	654×	body	80	valid
72.0ms	274×	body	160	valid
45.0ms	184×	body	160	invalid

Compiler

Compiled 542 to 392 computations (27.7% saved)

Details

analyze2.8s (11.5%)

sample428.0ms (1.8%)

simplify38.0ms (0.2%)

prune5.0ms (0%)

localize22.0ms (0.1%)

rewrite71.0ms (0.3%)

series1.1s (4.6%)

simplify107.0ms (0.4%)

prune299.0ms (1.2%)

localize16.0ms (0.1%)

rewrite47.0ms (0.2%)

series490.0ms (2%)

simplify86.0ms (0.4%)

prune181.0ms (0.8%)

localize16.0ms (0.1%)

rewrite60.0ms (0.2%)

series860.0ms (3.6%)

simplify176.0ms (0.7%)

prune232.0ms (1%)

localize16.0ms (0.1%)

rewrite61.0ms (0.3%)

series616.0ms (2.6%)

simplify178.0ms (0.7%)

prune246.0ms (1%)

regimes237.0ms (1%)

bsearch396.0ms (1.7%)

simplify7.0ms (0%)

end0.0ms (0%)

sample15.2s (63.5%)

Profiling