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

sample207.0ms

Algorithm

intervals

Results

131.0ms	118×	body	1280	valid
44.0ms	67×	body	640	valid
13.0ms	29×	body	320	valid
4.0ms	33×	body	80	valid
2.0ms	9×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	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: 4.2b

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) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
0.2b	(pow.f64 (sin.f64 ky) 2.0)
0.2b	(pow.f64 (sin.f64 kx) 2.0)
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

rewrite33.0ms

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` `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 → 100

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
3.0ms	(pow.f64 (sin.f64 ky) 2.0)
3.0ms	(pow.f64 (sin.f64 kx) 2.0)
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
18.0ms	(pow.f64 (sin.f64 ky) 2.0)
17.0ms	(pow.f64 (sin.f64 kx) 2.0)
23.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4925	1503
1	4925	1503

prune150.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 2.5b

Counts

113 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
3.9b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
45×	`sqrt-prod_binary64`
41×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
18×	`unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
10×	`pow1_binary64`
8×	`add-exp-log_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `unswap-sqr_binary64`
3×	`associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
20.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))

series88.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (sin.f64 ky) 2)
4.0ms	(pow.f64 (sin.f64 kx) 2)
46.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
34.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))

simplify54.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5041	1483

prune193.0ms

Filtered

73 candidates to 127 candidates (-74.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	127	10	137

Merged error: 2.5b

Counts

137 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) -1/2))
3.9b	(pow.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) -1/2)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64` `unpow-prod-down_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-exp-log_binary64`
9×	`pow-unpow_binary64` `associate-r_binary64`
7×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`
5×	`sqr-pow_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `pow-exp_binary64`
3×	`pow-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`unpow2_binary64`
1×	`cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
14.0ms	(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) -1/2))
9.0ms	(pow.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) -1/2)

series91.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (sin.f64 ky) 2)
4.0ms	(pow.f64 (sin.f64 kx) 2)
44.0ms	(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) -1/2))
39.0ms	(pow.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) -1/2)

simplify40.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4956	989
1	4956	989

prune121.0ms

Filtered

57 candidates to 94 candidates (-64.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Merged error: 2.2b

Counts

104 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (sin.f64 kx))
0.7b	(cbrt.f64 (sin.f64 kx))
0.7b	(cbrt.f64 (sin.f64 kx))
3.9b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (sin.f64 kx)) (cbrt.f64 (sin.f64 kx))) 2.0) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2.0)) (pow.f64 (sin.f64 ky) 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 48

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 kx))
2.0ms	(cbrt.f64 (sin.f64 kx))
2.0ms	(cbrt.f64 (sin.f64 kx))
10.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (sin.f64 kx)) (cbrt.f64 (sin.f64 kx))) 2.0) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2.0)) (pow.f64 (sin.f64 ky) 2.0)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 (sin.f64 kx))
17.0ms	(cbrt.f64 (sin.f64 kx))
19.0ms	(cbrt.f64 (sin.f64 kx))
24.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (sin.f64 kx)) (cbrt.f64 (sin.f64 kx))) 2.0) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2.0)) (pow.f64 (sin.f64 ky) 2.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4883	612
1	4883	612

prune65.0ms

Filtered

47 candidates to 60 candidates (-27.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	60	12	72

Merged error: 2.2b

Counts

72 → 12

regimes770.0ms

Accuracy

40.2% (1.5b remaining)

Error of 3.5b against oracle of 2.0b and baseline of 4.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	54
1	70	54

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.1s	3713×	body	1280	valid
1.4s	2009×	body	640	valid
348.0ms	756×	body	320	valid
170.0ms	1258×	body	80	valid
80.0ms	264×	body	160	valid

Details

analyze1.3s

sample207.0ms

simplify72.0ms

prune4.0ms

localize15.0ms

rewrite33.0ms

series104.0ms

simplify64.0ms

prune150.0ms

localize16.0ms

rewrite41.0ms

series88.0ms

simplify54.0ms

prune193.0ms

localize19.0ms

rewrite32.0ms

series91.0ms

simplify40.0ms

prune121.0ms

localize20.0ms

rewrite17.0ms

series77.0ms

simplify39.0ms

prune65.0ms

regimes770.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling