Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

sample54.0ms

Algorithm

intervals

Results

27.0ms	252×	body	80	valid
6.0ms	4×	body	640	invalid
2.0ms	3×	body	1280	invalid
1.0ms	2×	body	640	valid
1.0ms	2×	body	320	invalid
1.0ms	1×	body	1280	valid
0.0ms	5×	body	80	invalid
0.0ms	1×	body	160	invalid
0.0ms	1×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4986	28
1	4986	28

prune10.0ms

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: 15.2b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2.0)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)
33.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2.0) M))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64` `times-frac_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `cos-sum_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2.0)
9.0ms	(*.f64 K (+.f64 m n))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2.0) M))

series86.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2.0)
6.0ms	(*.f64 K (+.f64 m n))
48.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)
20.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2.0) M))

simplify79.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4930	822
1	4930	822

prune121.0ms

Filtered

62 candidates to 87 candidates (-40.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.8b

Counts

88 → 4

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0) l))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`diff-log_binary64` `add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `sqr-pow_binary64` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

2 → 36

Calls

2 calls:

18.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0) l))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0) l))
48.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4903	698
1	4903	698

prune57.0ms

Filtered

31 candidates to 42 candidates (-35.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Merged error: 0.8b

Counts

46 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)
0.0b	(/.f64 2.0 (+.f64 m n))
0.2b	(/.f64 K (/.f64 2.0 (+.f64 m n)))
33.1b	(cos.f64 (-.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))) M))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac_binary64`
100×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`
16×	`distribute-lft-out_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
6×	`unpow-prod-down_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `cos-sum_binary64` `distribute-lft-out--_binary64` `pow-exp_binary64`

Counts

4 → 152

Calls

4 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)
5.0ms	(/.f64 2.0 (+.f64 m n))
10.0ms	(/.f64 K (/.f64 2.0 (+.f64 m n)))
21.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))) M))

series93.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2.0) M) 2.0)
13.0ms	(/.f64 2.0 (+.f64 m n))
10.0ms	(/.f64 K (/.f64 2.0 (+.f64 m n)))
20.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4945	2005
1	4945	2005

prune194.0ms

Filtered

119 candidates to 164 candidates (-37.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	164	4	168

Merged error: 0.8b

Counts

168 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 K (/.f64 2.0 (+.f64 m n)))
0.2b	(/.f64 K (/.f64 2.0 (+.f64 m n)))
38.0b	(sin.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))))
38.5b	(cos.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
106×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`associate-/r*_binary64`
24×	`distribute-lft-out_binary64`
18×	`associate-/r/_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-inv_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
6×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 194

Calls

4 calls:

11.0ms	(/.f64 K (/.f64 2.0 (+.f64 m n)))
9.0ms	(/.f64 K (/.f64 2.0 (+.f64 m n)))
8.0ms	(sin.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))))
8.0ms	(cos.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 K (/.f64 2.0 (+.f64 m n)))
10.0ms	(/.f64 K (/.f64 2.0 (+.f64 m n)))
11.0ms	(sin.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))))
10.0ms	(cos.f64 (/.f64 K (/.f64 2.0 (+.f64 m n))))

simplify74.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5210	2730

prune276.0ms

Filtered

152 candidates to 206 candidates (-35.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	206	4	210

Merged error: 0.8b

Counts

210 → 4

regimes323.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	17
1	61	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

851.0ms	7832×	body	80	valid
39.0ms	66×	body	1280	invalid
35.0ms	81×	body	640	invalid
31.0ms	51×	body	1280	valid
30.0ms	68×	body	640	valid
24.0ms	76×	body	320	invalid
23.0ms	229×	body	80	invalid
11.0ms	35×	body	320	valid
5.0ms	26×	body	160	invalid
3.0ms	14×	body	160	valid
3.0ms	3×	body	2560	invalid

Details

analyze2.3s

sample54.0ms

simplify50.0ms

prune10.0ms

localize21.0ms

rewrite39.0ms

series86.0ms

simplify79.0ms

prune121.0ms

localize14.0ms

rewrite30.0ms

series99.0ms

simplify41.0ms

prune57.0ms

localize21.0ms

rewrite54.0ms

series93.0ms

simplify63.0ms

prune194.0ms

localize30.0ms

rewrite46.0ms

series41.0ms

simplify74.0ms

prune276.0ms

regimes323.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling