Details

analyze2.3s (7.2%)

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

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample294.0ms (0.9%)

Algorithm

1×

intervals

Results

226.0ms	256×	body	128	valid
36.0ms	380×	body	128	nan
4.0ms	36×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5453	39

prune5.0ms (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: 31.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 (/.f64 l Om) (-.f64 U U))
5.1b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
7.8b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
23.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`pow-prod-down_binary64` `*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
10×	`times-frac_binary64`
9×	`associate-r_binary64`
6×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64` `frac-times_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

11.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series4.6s (14.2%)

Counts

4 → 12

Calls

4 calls:

3.5s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
787.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
200.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
108.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify77.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4961	2903
1	4961	2903

prune177.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 21.1b

Counts

123 → 10

Compiler

Compiled 4433 to 1941 computations (56.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 (/.f64 l Om) (-.f64 U U))
5.1b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
5.5b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
23.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `add-sqr-sqrt_binary64`
17×	`associate-r/_binary64` `associate-l*_binary64`
15×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
13×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`associate-r_binary64`
6×	`sub-neg_binary64`
5×	`sqrt-pow1_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `frac-times_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_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:

11.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

series4.6s (14.3%)

Counts

4 → 12

Calls

4 calls:

3.5s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
766.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
209.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
129.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify73.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5054	3001

prune164.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	123	12	135

Merged error: 17.6b

Counts

135 → 12

Compiler

Compiled 4577 to 2016 computations (56% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(*.f64 n (/.f64 l Om))
5.5b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
9.5b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
23.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

rewrite49.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64`
30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64` `add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
14×	`associate-*r/_binary64`
13×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`
5×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 105

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
8.0ms	(*.f64 n (/.f64 l Om))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

series4.7s (14.4%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
800.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
196.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
35.0ms	(*.f64 n (/.f64 l Om))

simplify72.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4956	2779
1	4956	2779

prune154.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	118	11	129

Merged error: 17.6b

Counts

129 → 11

Compiler

Compiled 4249 to 1870 computations (56% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.5b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
23.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
23.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
23.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`pow1_binary64`
27×	`pow-prod-down_binary64`
17×	`associate-*r/_binary64`
15×	`sqrt-pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
6×	`sqrt-div_binary64`
5×	`cbrt-unprod_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `frac-times_binary64`
1×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

series10.8s (33.4%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
3.5s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
3.5s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
213.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

simplify47.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5205	2610

prune260.0ms (0.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	89	11	100

Merged error: 17.6b

Counts

100 → 11

Compiler

Compiled 8110 to 3522 computations (56.6% saved)

regimes412.0ms (1.3%)

Compiler: Compiled 4066 to 2720 computations (33.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 28 to 23 computations (17.9% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	195	304
1	195	304

end0.0ms (0%)

sample3.3s (10.1%)

Algorithm

1×

intervals

Results

1.2s	12464×	body	128	nan
763.0ms	8000×	body	128	valid
117.0ms	1154×	body	128	invalid

Compiler

Compiled 702 to 437 computations (37.7% saved)

Details

analyze2.3s (7.2%)

sample294.0ms (0.9%)

simplify60.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite56.0ms (0.2%)

series4.6s (14.2%)

simplify77.0ms (0.2%)

prune177.0ms (0.5%)

localize17.0ms (0.1%)

rewrite56.0ms (0.2%)

series4.6s (14.3%)

simplify73.0ms (0.2%)

prune164.0ms (0.5%)

localize20.0ms (0.1%)

rewrite49.0ms (0.1%)

series4.7s (14.4%)

simplify72.0ms (0.2%)

prune154.0ms (0.5%)

localize28.0ms (0.1%)

rewrite53.0ms (0.2%)

series10.8s (33.4%)

simplify47.0ms (0.1%)

prune260.0ms (0.8%)

regimes412.0ms (1.3%)

bsearch2.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample3.3s (10.1%)

Profiling