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

sample203.0ms

Algorithm

intervals

Results

128.0ms	116×	body	1280	valid
47.0ms	70×	body	640	valid
9.0ms	21×	body	320	valid
5.0ms	43×	body	80	valid
2.0ms	6×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5114	16

prune3.0ms

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: 4.7b

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 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite31.0ms

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.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 ky) 2)
4.0ms	(pow.f64 (sin.f64 kx) 2)
27.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify37.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5455	1421

prune112.0ms

Filtered

67 candidates to 114 candidates (-70.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	104	10	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	10	115

Merged error: 3.0b

Counts

115 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

4.4b	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`unpow2_binary64` `pow1/3_binary64` `sqr-pow_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 → 63

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

series83.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
20.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
20.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
22.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

simplify59.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4887	648
1	4887	648

prune77.0ms

Filtered

52 candidates to 75 candidates (-44.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 3.0b

Counts

85 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

62×	`sqrt-prod_binary64`
56×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
15×	`unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
11×	`associate-/r*_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`

Counts

4 → 113

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 kx) 2)
14.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (sin.f64 kx) 2)
49.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
20.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
21.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4991	1945
1	4991	1945

prune117.0ms

Filtered

72 candidates to 125 candidates (-73.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	125	10	135

Merged error: 3.0b

Counts

135 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
8×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 70

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 kx) 2)
21.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
21.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify64.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4927	722
1	4927	722

prune61.0ms

Filtered

50 candidates to 82 candidates (-64.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	82	10	92

Merged error: 3.0b

Counts

92 → 10

regimes367.0ms

Accuracy

0% (1.5b remaining)

Error of 4.1b against oracle of 2.6b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	29
1	19	29

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.1s	3721×	body	1280	valid
1.3s	1980×	body	640	valid
340.0ms	713×	body	320	valid
182.0ms	1275×	body	80	valid
88.0ms	311×	body	160	valid

Details

analyze1.3s

sample203.0ms

simplify69.0ms

prune3.0ms

localize15.0ms

rewrite31.0ms

series73.0ms

simplify37.0ms

prune112.0ms

localize18.0ms

rewrite26.0ms

series83.0ms

simplify59.0ms

prune77.0ms

localize17.0ms

rewrite41.0ms

series94.0ms

simplify57.0ms

prune117.0ms

localize18.0ms

rewrite28.0ms

series49.0ms

simplify64.0ms

prune61.0ms

regimes367.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling