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

sample208.0ms

Algorithm

intervals

Results

137.0ms	120×	body	1280	valid
42.0ms	64×	body	640	valid
8.0ms	19×	body	320	valid
6.0ms	46×	body	80	valid
2.0ms	7×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

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: 3.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`associate-l_binary64`
26×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`sqrt-prod_binary64`
14×	`unpow-prod-down_binary64`
11×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
8×	`distribute-lft-out_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-r_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `prod-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

18.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
3.0ms	(pow.f64 (sin.f64 ky) 2)
4.0ms	(pow.f64 (sin.f64 kx) 2)
24.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4961	1409
1	4961	1409

prune165.0ms

Filtered

75 candidates to 115 candidates (-53.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	12	116

Merged error: 2.2b

Counts

116 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`associate-r_binary64`
26×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`sqrt-prod_binary64`
14×	`unpow-prod-down_binary64`
11×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
8×	`distribute-lft-out_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `prod-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

19.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (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)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (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)
23.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify50.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4957	1309
1	4957	1309

prune123.0ms

Filtered

66 candidates to 115 candidates (-74.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	115	12	127

Merged error: 2.2b

Counts

127 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
1.1b	(log.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
1.3b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
16×	`log-prod_binary64`
15×	`sqrt-prod_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`unpow-prod-down_binary64`
8×	`exp-sum_binary64`
6×	`distribute-lft-out_binary64` `log-pow_binary64` `add-exp-log_binary64` `sqrt-div_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`exp-diff_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `pow-exp_binary64`

Counts

4 → 80

Calls

4 calls:

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

series72.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (sin.f64 kx) 2)
26.0ms	(log.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
22.0ms	(exp.f64 (log.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)))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4929	1060
1	4929	1060

prune111.0ms

Filtered

53 candidates to 92 candidates (-73.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	91	13	104

Merged error: 2.2b

Counts

104 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
1.1b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod_binary64`
87×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`
45×	`add-exp-log_binary64`
39×	`associate-l_binary64`
27×	`add-cbrt-cube_binary64`
20×	`prod-exp_binary64`
18×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
12×	`sqrt-div_binary64`
11×	`associate-/r*_binary64` `pow1_binary64` `div-exp_binary64`
10×	`cbrt-unprod_binary64`
6×	`cbrt-undiv_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `1-exp_binary64` `associate-r/_binary64` `rec-exp_binary64` `associate-/l_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 166

Calls

4 calls:

15.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
37.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
8.0ms	(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)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
52.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
25.0ms	(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)))

simplify83.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4947	3396
1	4947	3396

prune191.0ms

Filtered

101 candidates to 178 candidates (-76.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	8	9
Picked	1	0	1
Done	0	3	3
Total	178	13	191

Merged error: 2.2b

Counts

191 → 13

regimes749.0ms

Accuracy

0% (1.2b remaining)

Error of 3.7b against oracle of 2.5b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.1s	3760×	body	1280	valid
1.4s	2032×	body	640	valid
327.0ms	701×	body	320	valid
158.0ms	1229×	body	80	valid
84.0ms	278×	body	160	valid

Details

analyze1.3s

sample208.0ms

simplify68.0ms

prune3.0ms

localize14.0ms

rewrite36.0ms

series81.0ms

simplify68.0ms

prune165.0ms

localize14.0ms

rewrite37.0ms

series80.0ms

simplify50.0ms

prune123.0ms

localize18.0ms

rewrite35.0ms

series72.0ms

simplify41.0ms

prune111.0ms

localize19.0ms

rewrite77.0ms

series146.0ms

simplify83.0ms

prune191.0ms

regimes749.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling