Details

analyze2.3s

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

sample108.0ms

Algorithm

intervals

Results

44.0ms	473×	body	80	nan
28.0ms	256×	body	80	valid
4.0ms	39×	body	80	invalid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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: 35.1b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

6.5b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
8.0b	(/.f64 (*.f64 l l) Om)
10.1b	(.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))))
19.2b	(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)))))

rewrite47.0ms

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:

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

series3.3s

Counts

4 → 12

Calls

4 calls:

142.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
4.0ms	(/.f64 (*.f64 l l) Om)
432.0ms	(.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))))
2.7s	(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)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5262	2536

prune200.0ms

Filtered

74 candidates to 109 candidates (-47.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	97	12	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Merged error: 21.6b

Counts

110 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))
6.5b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
10.1b	(.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))))
19.2b	(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

35×	`add-exp-log_binary64`
25×	`pow1_binary64` `associate-r_binary64` `add-sqr-sqrt_binary64`
22×	`associate-*r/_binary64`
20×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
13×	`pow-prod-down_binary64`
11×	`flip3--_binary64` `flip--_binary64`
10×	`cbrt-unprod_binary64` `times-frac_binary64`
8×	`frac-sub_binary64`
6×	`sub-neg_binary64` `sqrt-div_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
3×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `sqr-pow_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 113

Calls

4 calls:

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

series3.3s

Counts

4 → 12

Calls

4 calls:

67.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))
140.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
441.0ms	(.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))))
2.7s	(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)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5364	2775

prune203.0ms

Filtered

87 candidates to 125 candidates (-43.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	126	11	137

Merged error: 20.2b

Counts

137 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

5.2b	(*.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2)))
6.5b	(.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U))
10.1b	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U*))))
19.2b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U*)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log_binary64`
67×	`prod-exp_binary64`
25×	`pow1_binary64` `associate-r_binary64` `add-sqr-sqrt_binary64`
24×	`add-cbrt-cube_binary64`
22×	`associate-*r/_binary64`
20×	`pow-exp_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
13×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
11×	`flip3--_binary64` `flip--_binary64`
10×	`pow-to-exp_binary64` `times-frac_binary64` `div-exp_binary64`
8×	`frac-sub_binary64`
6×	`sub-neg_binary64` `sqrt-div_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64`
3×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `*-commutative_binary64`
2×	`sqr-pow_binary64` `associate--l+_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 130

Calls

4 calls:

9.0ms	(*.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2)))
19.0ms	(.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U))
17.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.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 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U*)))))

series3.4s

Counts

4 → 12

Calls

4 calls:

72.0ms	(*.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2)))
136.0ms	(.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U))
432.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U*))))
2.7s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (pow.f64 (/.f64 l Om) (/.f64 2.0 2))) (-.f64 U U*)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5734	3448

prune213.0ms

Filtered

88 candidates to 142 candidates (-61.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	142	11	153

Merged error: 20.2b

Counts

153 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

12.7b	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
12.7b	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
12.7b	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
19.2b	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2.0 n) U) (.f64 (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))) (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))) (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

984×	`associate-*r/_binary64`
900×	`cbrt-div_binary64`
750×	`flip3--_binary64` `flip--_binary64`
600×	`frac-sub_binary64`
540×	`frac-times_binary64`
342×	`sqrt-div_binary64`
90×	`associate-*l/_binary64`
34×	`pow1_binary64`
22×	`pow-prod-down_binary64`
9×	`cbrt-prod_binary64`
8×	`sqrt-pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
1×	`pow1/2_binary64` `sqrt-prod_binary64`

Counts

4 → 410

Calls

4 calls:

8.0ms	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
8.0ms	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
11.0ms	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
59.0ms	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2.0 n) U) (.f64 (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))) (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))) (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))))

series3.8s

Counts

4 → 12

Calls

4 calls:

372.0ms	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
373.0ms	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
372.0ms	(cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
2.7s	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2.0 n) U) (.f64 (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))) (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U)))))) (cbrt.f64 (-.f64 (-.f64 t (.f64 2.0 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U))))))

simplify360.0ms

Algorithm

egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5330	76272

prune2.9s

Filtered

263 candidates to 422 candidates (-60.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	421	1	422
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	421	12	433

Merged error: 20.2b

Counts

433 → 12

regimes1.2s

Accuracy

36.5% (5.8b remaining)

Error of 27.7b against oracle of 21.9b and baseline of 31.1b

bsearch1.0ms

simplify20.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	791	155
1	791	155

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	12970×	body	80	nan
772.0ms	8000×	body	80	valid
115.0ms	1151×	body	80	invalid

Details

analyze2.3s

sample108.0ms

simplify48.0ms

prune5.0ms

localize22.0ms

rewrite47.0ms

series3.3s

simplify42.0ms

prune200.0ms

localize18.0ms

rewrite53.0ms

series3.3s

simplify47.0ms

prune203.0ms

localize19.0ms

rewrite65.0ms

series3.4s

simplify53.0ms

prune213.0ms

localize29.0ms

rewrite175.0ms

series3.8s

simplify360.0ms

prune2.9s

regimes1.2s

bsearch1.0ms

simplify20.0ms

end0.0ms

sample2.9s

Profiling