Details

analyze2.7s

Algorithm

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

sample522.0ms

Algorithm

intervals

Results

133.0ms	48×	body	2560	invalid
131.0ms	26×	body	5120	invalid
91.0ms	105×	body	1280	valid
40.0ms	28×	body	2560	valid
34.0ms	61×	body	640	valid
30.0ms	37×	body	1280	invalid
11.0ms	4×	body	5120	valid
9.0ms	17×	body	640	invalid
6.0ms	15×	body	320	valid
6.0ms	15×	body	320	invalid
4.0ms	30×	body	80	valid
4.0ms	30×	body	80	invalid
4.0ms	13×	body	160	valid
1.0ms	2×	body	160	invalid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4842	21
1	4842	21

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 38.9b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(.f64 (/.f64 (pow.f64 t 3.0) (.f64 l l)) (sin.f64 k))
1.5b	(.f64 (.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
17.0b	(/.f64 (pow.f64 t 3.0) (*.f64 l l))
27.1b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3.0) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

228×	`add-exp-log_binary64`
139×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
51×	`div-exp_binary64`
32×	`pow-exp_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`cbrt-unprod_binary64` `times-frac_binary64`
23×	`pow-to-exp_binary64` `associate-r_binary64` `unpow-prod-down_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`associate-l_binary64`
11×	`pow1_binary64`
10×	`associate-*l/_binary64`
8×	`cbrt-undiv_binary64`
7×	`associate-/l*_binary64`
5×	`sqr-pow_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `tan-quot_binary64`
3×	`div-inv_binary64` `*-commutative_binary64`
2×	`associate-*r/_binary64` `frac-times_binary64`
1×	`associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 170

Calls

4 calls:

10.0ms	(.f64 (/.f64 (pow.f64 t 3.0) (.f64 l l)) (sin.f64 k))
15.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
7.0ms	(/.f64 (pow.f64 t 3.0) (*.f64 l l))
20.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3.0) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(.f64 (/.f64 (pow.f64 t 3.0) (.f64 l l)) (sin.f64 k))
93.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
51.0ms	(/.f64 (pow.f64 t 3.0) (*.f64 l l))
134.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3.0) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5423	2715

prune225.0ms

Filtered

99 candidates to 182 candidates (-83.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	169	13	182
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	13	183

Merged error: 16.0b

Counts

183 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2.0 (.f64 (pow.f64 (.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))))
6.9b	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))
7.7b	(*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))
14.3b	(.f64 (pow.f64 (.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

1042×	`add-exp-log_binary64`
654×	`prod-exp_binary64`
401×	`pow-exp_binary64`
346×	`div-exp_binary64`
221×	`pow-to-exp_binary64`
49×	`add-cbrt-cube_binary64`
33×	`add-sqr-sqrt_binary64`
22×	`unpow-prod-down_binary64`
19×	`associate-r_binary64` `times-frac_binary64`
18×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64`
14×	`cbrt-undiv_binary64`
13×	`sqr-pow_binary64`
12×	`associate-l_binary64`
11×	`unswap-sqr_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`unpow2_binary64` `div-inv_binary64`
2×	`associate-/r_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/r/_binary64`

Counts

4 → 376

Calls

4 calls:

19.0ms	(/.f64 2.0 (.f64 (pow.f64 (.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))))
10.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))
7.0ms	(*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))
19.0ms	(.f64 (pow.f64 (.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 2.0 (.f64 (pow.f64 (.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))))
22.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))
138.0ms	(*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))
131.0ms	(.f64 (pow.f64 (.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k))))

simplify77.0ms

Algorithm

egg-herbie

Counts

388 → 388

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5814	8058

prune262.0ms

Filtered

101 candidates to 388 candidates (-284.2%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	377	11	388
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	380	21	401

Merged error: 14.1b

Counts

401 → 21

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 k) 2)
0.4b	(/.f64 2.0 (.f64 (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (*.f64 l l) (cos.f64 k)))))
6.9b	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))
14.3b	(.f64 (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (*.f64 l l) (cos.f64 k))))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

3231×	`add-exp-log_binary64`
2403×	`prod-exp_binary64`
1382×	`pow-exp_binary64`
934×	`div-exp_binary64`
782×	`pow-to-exp_binary64`
47×	`add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64` `times-frac_binary64`
17×	`cbrt-unprod_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
14×	`cbrt-undiv_binary64`
13×	`unpow-prod-down_binary64`
12×	`associate-r_binary64`
11×	`associate-/l*_binary64`
6×	`sqr-pow_binary64`
5×	`pow1_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `unpow2_binary64`
3×	`pow-unpow_binary64` `div-inv_binary64`
2×	`associate-/r_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `*-commutative_binary64`

Counts

4 → 773

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 k) 2)
34.0ms	(/.f64 2.0 (.f64 (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (*.f64 l l) (cos.f64 k)))))
10.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))
22.0ms	(.f64 (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (*.f64 l l) (cos.f64 k))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (sin.f64 k) 2)
221.0ms	(/.f64 2.0 (.f64 (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (*.f64 l l) (cos.f64 k)))))
20.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (.f64 l l) (cos.f64 k)))
140.0ms	(.f64 (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))) 1.0) (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (*.f64 l l) (cos.f64 k))))

simplify142.0ms

Algorithm

egg-herbie

Counts

785 → 785

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4992	17244
1	4992	17244

prune220.0ms

Filtered

80 candidates to 785 candidates (-881.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	778	7	785
Fresh	6	13	19
Picked	1	0	1
Done	1	0	1
Total	786	20	806

Merged error: 12.7b

Counts

806 → 20

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2.0 (.f64 (pow.f64 (pow.f64 k (/.f64 2.0 2)) 1.0) (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0))))
3.2b	(.f64 (pow.f64 (pow.f64 k (/.f64 2.0 2)) 1.0) (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0)))
6.9b	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l)))
11.6b	(.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

6211×	`add-exp-log_binary64`
4717×	`prod-exp_binary64`
3127×	`pow-exp_binary64`
1803×	`div-exp_binary64`
1653×	`pow-to-exp_binary64`
74×	`add-cbrt-cube_binary64`
34×	`cbrt-unprod_binary64`
23×	`associate-l_binary64`
20×	`unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`cbrt-undiv_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`associate-/l*_binary64`
7×	`sqr-pow_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`unpow2_binary64` `div-inv_binary64` `associate-*l/_binary64`
2×	`associate-/r_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/r/_binary64`

Counts

4 → 1452

Calls

4 calls:

55.0ms	(/.f64 2.0 (.f64 (pow.f64 (pow.f64 k (/.f64 2.0 2)) 1.0) (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0))))
32.0ms	(.f64 (pow.f64 (pow.f64 k (/.f64 2.0 2)) 1.0) (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0)))
10.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l)))
17.0ms	(.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0))

series389.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/.f64 2.0 (.f64 (pow.f64 (pow.f64 k (/.f64 2.0 2)) 1.0) (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0))))
109.0ms	(.f64 (pow.f64 (pow.f64 k (/.f64 2.0 2)) 1.0) (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0)))
20.0ms	(/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l)))
108.0ms	(.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (.f64 (cos.f64 k) (.f64 l l))) (pow.f64 (.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)) 1.0))

simplify290.0ms

Algorithm

egg-herbie

Counts

1464 → 1464

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6100	45966

prune219.0ms

Filtered

94 candidates to 1464 candidates (-1457.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	1460	4	1464
Fresh	7	12	19
Picked	1	0	1
Done	0	0	0
Total	1468	16	1484

Merged error: 12.5b

Counts

1484 → 16

regimes483.0ms

Accuracy

32.3% (4.5b remaining)

Error of 16.1b against oracle of 11.6b and baseline of 18.3b

bsearch625.0ms

Steps

Iters	Range		Point
12	8.454760535194243e+135	4.198301172383795e+174	1.348002792593927e+154
6	-5.258480599691555e+162	-4.660031886579687e+161	-4.780421029131753e+161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	73
1	53	73

end0.0ms

sample15.3s

Algorithm

intervals

Results

3.5s	737×	body	5120	invalid
3.4s	1276×	body	2560	invalid
3.0s	3292×	body	1280	valid
1.3s	906×	body	2560	valid
1.2s	2000×	body	640	valid
677.0ms	750×	body	1280	invalid
614.0ms	190×	body	5120	valid
284.0ms	666×	body	320	valid
275.0ms	523×	body	640	invalid
151.0ms	386×	body	320	invalid
144.0ms	918×	body	80	invalid
101.0ms	706×	body	80	valid
67.0ms	240×	body	160	valid
52.0ms	202×	body	160	invalid

Details

analyze2.7s

sample522.0ms

simplify47.0ms

prune9.0ms

localize18.0ms

rewrite61.0ms

series345.0ms

simplify46.0ms

prune225.0ms

localize20.0ms

rewrite94.0ms

series512.0ms

simplify77.0ms

prune262.0ms

localize22.0ms

rewrite173.0ms

series385.0ms

simplify142.0ms

prune220.0ms

localize23.0ms

rewrite331.0ms

series389.0ms

simplify290.0ms

prune219.0ms

regimes483.0ms

bsearch625.0ms

simplify2.0ms

end0.0ms

sample15.3s

Profiling