Details

analyze1.3s

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
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

sample205.0ms

Algorithm

intervals

Results

126.0ms	115×	body	1280	valid
50.0ms	75×	body	640	valid
10.0ms	19×	body	320	valid
5.0ms	37×	body	80	valid
3.0ms	10×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5114	16

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.9b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
16×	`unpow-prod-down_binary64`
10×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 102

Calls

4 calls:

13.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)
13.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)
25.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify39.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5455	1421

prune155.0ms

Filtered

67 candidates to 114 candidates (-70.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 2.7b

Counts

115 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac_binary64`
150×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
65×	`sqrt-prod_binary64`
32×	`unpow-prod-down_binary64`
28×	`associate-/r*_binary64`
26×	`distribute-lft-out_binary64`
17×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`div-exp_binary64`
6×	`pow-unpow_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rec-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 189

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)
24.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify76.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5002	3463

prune173.0ms

Filtered

91 candidates to 201 candidates (-120.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	202	10	212

Merged error: 2.7b

Counts

212 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
0.3b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b	(pow.f64 (sin.f64 ky) 2)
4.6b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64` `times-frac_binary64`
45×	`sqrt-prod_binary64`
36×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
23×	`unpow-prod-down_binary64`
20×	`distribute-lft-out_binary64`
11×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`inv-pow_binary64` `div-exp_binary64` `pow-flip_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

10.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
21.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
49.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.0ms	(pow.f64 (sin.f64 ky) 2)
37.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

simplify53.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4967	1985
1	4967	1985

prune148.0ms

Filtered

81 candidates to 150 candidates (-85.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	150	10	160

Merged error: 2.7b

Counts

160 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 kx))
0.6b	(cbrt.f64 (sin.f64 kx))
0.8b	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.5b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`cbrt-prod_binary64`
6×	`pow1_binary64` `unpow-prod-down_binary64`
5×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `pow1/3_binary64` `sqrt-prod_binary64`
2×	`pow-pow_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 kx))
2.0ms	(cbrt.f64 (sin.f64 kx))
4.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
13.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt.f64 (sin.f64 kx))
18.0ms	(cbrt.f64 (sin.f64 kx))
29.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
24.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

simplify72.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4898	535
1	4898	535

prune72.0ms

Filtered

54 candidates to 70 candidates (-29.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	70	10	80

Merged error: 2.6b

Counts

80 → 10

regimes567.0ms

Accuracy

-33.9% (2.3b remaining)

Error of 5.2b against oracle of 2.9b and baseline of 4.6b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	39
1	68	39

end0.0ms

sample6.2s

Algorithm

intervals

Results

4.0s	3713×	body	1280	valid
1.3s	1985×	body	640	valid
364.0ms	750×	body	320	valid
160.0ms	1276×	body	80	valid
77.0ms	276×	body	160	valid

Details

analyze1.3s

sample205.0ms

simplify71.0ms

prune4.0ms

localize15.0ms

rewrite36.0ms

series82.0ms

simplify39.0ms

prune155.0ms

localize16.0ms

rewrite41.0ms

series76.0ms

simplify76.0ms

prune173.0ms

localize16.0ms

rewrite52.0ms

series116.0ms

simplify53.0ms

prune148.0ms

localize18.0ms

rewrite21.0ms

series91.0ms

simplify72.0ms

prune72.0ms

regimes567.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample6.2s

Profiling