Details

analyze2.6s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample107.0ms

Algorithm

intervals

Results

45.0ms	432×	body	80	nan
25.0ms	256×	body	80	valid
5.0ms	52×	body	80	invalid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5186	28

prune5.0ms

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: 31.2b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

7.3b	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))
7.4b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
8.4b	(/.f64 (*.f64 l l) Om)
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
25×	`pow1_binary64`
23×	`add-cbrt-cube_binary64`
22×	`associate-*r/_binary64`
16×	`prod-exp_binary64`
13×	`pow-prod-down_binary64`
11×	`flip3--_binary64` `flip--_binary64`
10×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
8×	`associate-r_binary64` `add-cube-cbrt_binary64` `frac-sub_binary64`
6×	`sub-neg_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64`
3×	`associate-/r*_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `associate-l_binary64` `pow-exp_binary64` `associate--l+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 97

Calls

4 calls:

15.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
5.0ms	(/.f64 (*.f64 l l) Om)
13.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

617.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))
100.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
4.0ms	(/.f64 (*.f64 l l) Om)
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4991	2467
1	4991	2467

prune200.0ms

Filtered

74 candidates to 109 candidates (-47.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	13	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	13	110

Merged error: 22.0b

Counts

110 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

4.5b	(-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*)))
7.3b	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))
7.4b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
26×	`associate-*r/_binary64`
25×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
16×	`flip3--_binary64` `flip--_binary64`
15×	`prod-exp_binary64`
13×	`pow-prod-down_binary64`
12×	`frac-sub_binary64`
10×	`sub-neg_binary64`
9×	`add-log-exp_binary64` `cbrt-unprod_binary64`
8×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64`
3×	`diff-log_binary64` `associate--l+_binary64`
2×	`associate--r+_binary64` `associate-l_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `associate--l-_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `sqrt-prod_binary64`

Counts

4 → 96

Calls

4 calls:

9.0ms	(-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*)))
15.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
14.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

269.0ms	(-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*)))
611.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))
98.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
1.6s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5093	3138

prune178.0ms

Filtered

76 candidates to 108 candidates (-42.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 20.7b

Counts

121 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

7.4b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
7.4b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
28×	`pow1_binary64`
24×	`associate-*r/_binary64`
18×	`prod-exp_binary64`
14×	`pow-prod-down_binary64` `add-cbrt-cube_binary64`
12×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-sqr-sqrt_binary64`
8×	`sqrt-pow1_binary64` `frac-sub_binary64`
6×	`cbrt-unprod_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
12.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
13.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

series3.2s

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
98.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4983	2448
1	4983	2448

prune230.0ms

Filtered

72 candidates to 102 candidates (-41.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 20.7b

Counts

114 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

7.4b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1_binary64`
32×	`associate-*r/_binary64`
19×	`pow-prod-down_binary64`
18×	`add-exp-log_binary64` `sqrt-div_binary64`
16×	`flip3--_binary64` `flip--_binary64`
12×	`sqrt-pow1_binary64` `frac-sub_binary64`
9×	`add-cbrt-cube_binary64` `prod-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
5×	`associate-r_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-prod_binary64`
2×	`sub-neg_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
12.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
13.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
12.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

series4.6s

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4983	2890
1	4983	2890

prune227.0ms

Filtered

72 candidates to 95 candidates (-31.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	95	12	107

Merged error: 20.7b

Counts

107 → 12

regimes743.0ms

Accuracy

6% (9.2b remaining)

Error of 31.6b against oracle of 22.4b and baseline of 32.2b

bsearch202.0ms

Steps

Iters	Range	Point
7	1.7611260343986184e+72	1.7841436293156583e+74	4.430527507132508e+72
8	2.335818691228601e-194	2.1123497032106298e-191	1.924388065751012e-191
8	-2.4821315226161346e-274	-5.577547737716691e-277	-5.655452501094331e-277

Iters

Range

Point

1.7611260343986184e+72

1.7841436293156583e+74

4.430527507132508e+72

2.335818691228601e-194

2.1123497032106298e-191

1.924388065751012e-191

-2.4821315226161346e-274

-5.577547737716691e-277

-5.655452501094331e-277

simplify17.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	655	129
1	655	129

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	12833×	body	80	nan
784.0ms	8000×	body	80	valid
129.0ms	1244×	body	80	invalid

Details

analyze2.6s

sample107.0ms

simplify51.0ms

prune5.0ms

localize20.0ms

rewrite50.0ms

series2.2s

simplify43.0ms

prune200.0ms

localize18.0ms

rewrite53.0ms

series2.5s

simplify60.0ms

prune178.0ms

localize24.0ms

rewrite52.0ms

series3.2s

simplify57.0ms

prune230.0ms

localize27.0ms

rewrite53.0ms

series4.6s

simplify38.0ms

prune227.0ms

regimes743.0ms

bsearch202.0ms

simplify17.0ms

end0.0ms

sample2.9s

Profiling