Details

analyze2.4s (11.6%)

Algorithm

1×

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

sample99.0ms (0.5%)

Algorithm

1×

intervals

Results

41.0ms	401×	body	80	nan
24.0ms	256×	body	80	valid
4.0ms	36×	body	80	invalid

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5186	28

prune9.0ms (0%)

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: 34.6b

Counts

2 → 1

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.0b	(/.f64 (*.f64 l l) Om)
8.6b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
8.7b	(.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))))
20.3b	(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 (0.2%)

Algorithm

1×	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))))
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)))))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
5.0ms	(/.f64 (*.f64 l l) Om)

series3.2s (15.7%)

Counts

4 → 12

Calls

4 calls:

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)))))
426.0ms	(.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))))
134.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
4.0ms	(/.f64 (*.f64 l l) Om)

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5262	2536

prune243.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	11	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	11	110

Merged error: 22.1b

Counts

110 → 11

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.4b	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))
8.6b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
8.7b	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
20.3b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*)))))

rewrite54.0ms (0.3%)

Algorithm

1×	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:

16.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.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 Om l)))) (.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*))
9.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))

series3.3s (16%)

Counts

4 → 12

Calls

4 calls:

2.7s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*)))))
423.0ms	(.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))))
133.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
64.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5320	2775

prune274.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	125	11	136

Merged error: 21.2b

Counts

136 → 11

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

13.2b	(cbrt.f64 (/.f64 l Om))
13.2b	(cbrt.f64 (/.f64 l Om))
13.2b	(cbrt.f64 (/.f64 l Om))
20.3b	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.f64 (.f64 (.f64 n (pow.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) 2.0)) (pow.f64 (cbrt.f64 (/.f64 l Om)) 2.0)) (-.f64 U U*)))))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64`
27×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
14×	`pow1_binary64`
10×	`associate-*r/_binary64`
6×	`pow-prod-down_binary64` `sqrt-div_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `frac-sub_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64` `div-inv_binary64`
1×	`pow1/2_binary64` `sqrt-prod_binary64`

Counts

4 → 85

Calls

4 calls:

17.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.f64 (.f64 (.f64 n (pow.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) 2.0)) (pow.f64 (cbrt.f64 (/.f64 l Om)) 2.0)) (-.f64 U U*)))))
3.0ms	(cbrt.f64 (/.f64 l Om))
3.0ms	(cbrt.f64 (/.f64 l Om))
3.0ms	(cbrt.f64 (/.f64 l Om))

series2.7s (13.4%)

Counts

4 → 12

Calls

4 calls:

2.7s	(sqrt.f64 (.f64 (.f64 (.f64 2.0 n) U) (-.f64 (-.f64 t (.f64 2.0 (/.f64 l (/.f64 Om l)))) (.f64 (.f64 (.f64 n (pow.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) 2.0)) (pow.f64 (cbrt.f64 (/.f64 l Om)) 2.0)) (-.f64 U U*)))))
14.0ms	(cbrt.f64 (/.f64 l Om))
14.0ms	(cbrt.f64 (/.f64 l Om))
14.0ms	(cbrt.f64 (/.f64 l Om))

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5038	1760

prune197.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	97	11	108

Merged error: 21.2b

Counts

108 → 11

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.4b	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))
8.6b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
8.7b	(.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))))
20.3b	(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)))))

rewrite66.0ms (0.3%)

Algorithm

1×	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:

17.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))
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))))
14.0ms	(.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)))))

series3.3s (16.1%)

Counts

4 → 12

Calls

4 calls:

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)))))
427.0ms	(.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))))
137.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2.0)) (-.f64 U U*))
63.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2.0))

simplify49.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5364	2775

prune186.0ms (0.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	125	11	136

Merged error: 21.2b

Counts

136 → 11

regimes1.1s (5.4%)

Accuracy

Total 7.3b remaining (24.6%)

Threshold costs 0b (0%)

bsearch55.0ms (0.3%)

Steps

Iters	Range		Point
6	1.6541404280564278e-305	1.3341588840302468e-304	1.312713436382444e-304

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	584	74
1	584	74

end0.0ms (0%)

sample2.9s (14.2%)

Algorithm

1×

intervals

Results

1.3s	12807×	body	80	nan
795.0ms	8000×	body	80	valid
119.0ms	1143×	body	80	invalid

Details

analyze2.4s (11.6%)

sample99.0ms (0.5%)

simplify48.0ms (0.2%)

prune9.0ms (0%)

localize18.0ms (0.1%)

rewrite50.0ms (0.2%)

series3.2s (15.7%)

simplify42.0ms (0.2%)

prune243.0ms (1.2%)

localize18.0ms (0.1%)

rewrite54.0ms (0.3%)

series3.3s (16%)

simplify43.0ms (0.2%)

prune274.0ms (1.3%)

localize30.0ms (0.1%)

rewrite27.0ms (0.1%)

series2.7s (13.4%)

simplify37.0ms (0.2%)

prune197.0ms (1%)

localize18.0ms (0.1%)

rewrite66.0ms (0.3%)

series3.3s (16.1%)

simplify49.0ms (0.2%)

prune186.0ms (0.9%)

regimes1.1s (5.4%)

bsearch55.0ms (0.3%)

simplify16.0ms (0.1%)

end0.0ms (0%)

sample2.9s (14.2%)

Profiling