Details

analyze1.8s

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
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

sample103.0ms

Algorithm

intervals

Results

45.0ms	53×	body	1280	valid
21.0ms	38×	body	640	valid
16.0ms	137×	body	80	valid
7.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4872	37
1	4872	37

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 17.7b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
16×	`*-un-lft-identity_binary64`
15×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64` `prod-exp_binary64`
9×	`cbrt-unprod_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`pow-prod-down_binary64` `times-frac_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
16.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
113.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
168.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
159.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify82.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4969	2554
1	4969	2554

prune138.0ms

Filtered

67 candidates to 103 candidates (-53.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 13.2b

Counts

104 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.4b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log_binary64`
25×	`add-cbrt-cube_binary64`
18×	`pow1_binary64`
14×	`prod-exp_binary64`
12×	`*-un-lft-identity_binary64`
11×	`cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
8×	`pow-prod-down_binary64`
7×	`unpow-prod-down_binary64`
6×	`times-frac_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

7.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
15.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
115.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
171.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
155.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5166	2466

prune127.0ms

Filtered

63 candidates to 100 candidates (-58.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	100	10	110

Merged error: 13.2b

Counts

110 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`
6×	`pow1/2_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series881.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
289.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
149.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
149.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify80.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4957	2368
1	4957	2368

prune175.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	88	10	98

Merged error: 13.2b

Counts

98 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

1.7b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.9b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
15.0b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.0b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `associate-l_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

9.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

297.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
192.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
297.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
295.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify115.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4957	2721
1	4957	2721

prune164.0ms

Filtered

60 candidates to 82 candidates (-36.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	81	11	92

Merged error: 13.2b

Counts

92 → 11

regimes229.0ms

Accuracy

84.3% (0.9b remaining)

Error of 13.6b against oracle of 12.8b and baseline of 18.3b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	152
1	47	152

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	1484×	body	1280	valid
727.0ms	1265×	body	640	valid
498.0ms	4311×	body	80	valid
249.0ms	604×	body	320	valid
91.0ms	336×	body	160	valid
1.0ms	1×	body	1280	invalid
1.0ms	1×	body	640	invalid
0.0ms	1×	body	80	invalid

Details

analyze1.8s

sample103.0ms

simplify123.0ms

prune3.0ms

localize16.0ms

rewrite42.0ms

series524.0ms

simplify82.0ms

prune138.0ms

localize16.0ms

rewrite40.0ms

series522.0ms

simplify59.0ms

prune127.0ms

localize18.0ms

rewrite38.0ms

series881.0ms

simplify80.0ms

prune175.0ms

localize23.0ms

rewrite34.0ms

series1.1s

simplify115.0ms

prune164.0ms

regimes229.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample3.0s

Profiling