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

sample452.0ms

Algorithm

intervals

Results

119.0ms	23×	body	5120	invalid
87.0ms	36×	body	2560	invalid
83.0ms	106×	body	1280	valid
46.0ms	33×	body	2560	valid
32.0ms	60×	body	640	valid
27.0ms	29×	body	1280	invalid
10.0ms	20×	body	640	invalid
7.0ms	19×	body	320	valid
6.0ms	3×	body	5120	valid
5.0ms	41×	body	80	invalid
5.0ms	14×	body	320	invalid
4.0ms	28×	body	80	valid
2.0ms	8×	body	160	invalid
2.0ms	7×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5186	32

prune5.0ms

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: 40.4b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.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))
15.6b	(/.f64 (pow.f64 t 3) (*.f64 l l))
28.8b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

396×	`add-exp-log_binary64`
229×	`prod-exp_binary64`
115×	`div-exp_binary64`
65×	`add-cbrt-cube_binary64`
56×	`pow-exp_binary64`
40×	`times-frac_binary64`
38×	`pow-to-exp_binary64`
34×	`add-sqr-sqrt_binary64`
31×	`cbrt-unprod_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
23×	`unpow-prod-down_binary64`
21×	`associate-r_binary64`
17×	`associate-l_binary64`
15×	`associate-/l*_binary64`
14×	`cbrt-undiv_binary64`
13×	`associate-*l/_binary64`
10×	`cube-prod_binary64`
6×	`pow1_binary64`
5×	`sqr-pow_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `tan-quot_binary64`
3×	`associate-/r/_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`associate-/r_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `unpow2_binary64`

Counts

4 → 221

Calls

4 calls:

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))
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))

series737.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(/.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)))
70.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
26.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))
335.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

simplify124.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5216	5826

prune188.0ms

Filtered

106 candidates to 233 candidates (-119.8%)

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: 15.9b

Counts

234 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.7b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
19.9b	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

rewrite39.0ms

Algorithm

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`
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 → 124

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 k) 2)
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
9.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
14.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow.f64 (sin.f64 k) 2)
43.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
59.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
170.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

simplify107.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4979	2537
1	4979	2537

prune103.0ms

Filtered

58 candidates to 136 candidates (-134.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	130	19	149

Merged error: 11.2b

Counts

149 → 19

localize16.0ms

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)
0.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
19.9b	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-exp-log_binary64`
65×	`add-cbrt-cube_binary64`
64×	`prod-exp_binary64`
34×	`cbrt-unprod_binary64`
18×	`div-exp_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`cbrt-undiv_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64`
6×	`pow-to-exp_binary64` `associate-l_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64`
2×	`*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 107

Calls

4 calls:

7.0ms	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
3.0ms	(pow.f64 (sin.f64 k) 2)
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
14.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(.f64 k (.f64 t (pow.f64 (sin.f64 k) 2)))
15.0ms	(pow.f64 (sin.f64 k) 2)
47.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
168.0ms	(/.f64 (.f64 (.f64 l l) (cos.f64 k)) (.f64 k (.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

simplify105.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4964	2069
1	4964	2069

prune103.0ms

Filtered

58 candidates to 119 candidates (-105.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	119	19	138

Merged error: 10.2b

Counts

138 → 19

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.9b	(*.f64 t (pow.f64 (sin.f64 k) 2))
7.8b	(/.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))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-exp-log_binary64`
65×	`add-cbrt-cube_binary64`
52×	`prod-exp_binary64`
32×	`div-exp_binary64`
26×	`cbrt-unprod_binary64`
20×	`cbrt-undiv_binary64`
17×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-r_binary64`
7×	`unpow-prod-down_binary64`
6×	`pow-to-exp_binary64` `pow-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `times-frac_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`associate-/l/_binary64` `pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 k) 2)
6.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.0ms	(/.f64 (*.f64 l l) k)
15.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (sin.f64 k) 2)
43.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
13.0ms	(/.f64 (*.f64 l l) k)
172.0ms	(/.f64 (.f64 (/.f64 (.f64 l l) k) (cos.f64 k)) (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))))

simplify101.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5006	2068

prune80.0ms

Filtered

62 candidates to 124 candidates (-100.0%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	3	15	18
Picked	0	1	1
Done	0	0	0
Total	121	22	143

Merged error: 7.7b

Counts

143 → 22

regimes221.0ms

Accuracy

2.5% (6.9b remaining)

Error of 13.8b against oracle of 6.9b and baseline of 14.0b

bsearch352.0ms

Steps

Iters	Range		Point
7	7.685451128416463e-15	1.7944653218779994e-13	1.0962257049040088e-13
10	8.080012539086253e-84	8.65422330629162e-73	4.842177147515977e-74

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	111
1	48	111

end0.0ms

sample15.3s

Algorithm

intervals

Results

3.9s	799×	body	5120	invalid
3.3s	1281×	body	2560	invalid
2.8s	3340×	body	1280	valid
1.5s	1003×	body	2560	valid
1.1s	1881×	body	640	valid
677.0ms	783×	body	1280	invalid
650.0ms	195×	body	5120	valid
275.0ms	657×	body	320	valid
270.0ms	532×	body	640	invalid
143.0ms	356×	body	320	invalid
129.0ms	933×	body	80	invalid
90.0ms	647×	body	80	valid
74.0ms	277×	body	160	valid
48.0ms	189×	body	160	invalid

Details

analyze2.7s

sample452.0ms

simplify28.0ms

prune5.0ms

localize23.0ms

rewrite73.0ms

series737.0ms

simplify124.0ms

prune188.0ms

localize16.0ms

rewrite39.0ms

series289.0ms

simplify107.0ms

prune103.0ms

localize16.0ms

rewrite37.0ms

series279.0ms

simplify105.0ms

prune103.0ms

localize16.0ms

rewrite34.0ms

series243.0ms

simplify101.0ms

prune80.0ms

regimes221.0ms

bsearch352.0ms

simplify3.0ms

end0.0ms

sample15.3s

Profiling