Details

analyze2.4s (11.5%)

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)

sample89.0ms (0.4%)

Algorithm

1×

intervals

Results

32.0ms	377×	body	128	nan
26.0ms	256×	body	128	valid
3.0ms	33×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify141.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5178	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: 27.4b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.1b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
12.1b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
16.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

rewrite52.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
19×	`times-frac_binary64_425`
18×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
16×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`associate-*r/_binary64_361` `cancel-sign-sub-inv_binary64_385`
7×	`associate-r_binary64_359`
4×	`flip3-+_binary64_422` `sub-neg_binary64_412` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip-+_binary64_393` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `div-inv_binary64_416` `unswap-sqr_binary64_387` `flip3--_binary64_423` `flip--_binary64_394`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

4 → 131

Calls

4 calls:

12.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

series2.7s (13.1%)

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
429.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
147.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
95.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5099	4107

prune198.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	10	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 17.2b

Counts

145 → 11

Compiler

Compiled 5346 to 2214 computations (58.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.3b	(*.f64 n (/.f64 l Om))
9.1b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
9.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
16.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`pow-prod-down_binary64_490` `add-cube-cbrt_binary64_454`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`times-frac_binary64_425` `associate-*r/_binary64_361`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 107

Calls

4 calls:

10.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
7.0ms	(*.f64 n (/.f64 l Om))
6.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

series2.6s (12.6%)

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
441.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
101.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
18.0ms	(*.f64 n (/.f64 l Om))

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5059	2829

prune155.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Merged error: 16.5b

Counts

130 → 10

Compiler

Compiled 4297 to 1867 computations (56.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.3b	(*.f64 n (/.f64 l Om))
7.5b	(.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)))))))
9.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
16.6b	(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))))))))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_480`
30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`add-sqr-sqrt_binary64_441`
20×	`pow-prod-down_binary64_490`
19×	`associate-r_binary64_359`
17×	`*-un-lft-identity_binary64_419`
15×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
14×	`associate-*r/_binary64_361`
10×	`times-frac_binary64_425`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`associate-l_binary64_360` `sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 111

Calls

4 calls:

13.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.0ms	(.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)))))))
7.0ms	(*.f64 n (/.f64 l Om))
6.0ms	(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))))))))

series2.6s (12.6%)

Counts

4 → 12

Calls

4 calls:

2.1s	(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))))))))
433.0ms	(.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)))))))
95.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
21.0ms	(*.f64 n (/.f64 l Om))

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5016	2927

prune163.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	121	12	133

Merged error: 14.7b

Counts

133 → 12

Compiler

Compiled 4412 to 1930 computations (56.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
16.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
16.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite51.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64_480`
22×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
18×	`pow-prod-down_binary64_490`
14×	`-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441` `associate-r/_binary64_361`
12×	`cancel-sign-sub-inv_binary64_385`
10×	`add-cube-cbrt_binary64_454` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `sqrt-pow1_binary64_437`
4×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394`
2×	`flip3-+_binary64_422` `associate-l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `-commutative_binary64_350` `associate-l_binary64_360` `flip-+_binary64_393` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 100

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
11.0ms	(.f64 (.f64 n (/.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 (.f64 n (/.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 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

series4.3s (20.9%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
95.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
89.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5112	2678

prune230.0ms (1.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	112	12	124

Merged error: 14.7b

Counts

124 → 12

Compiler

Compiled 6924 to 2914 computations (57.9% saved)

regimes882.0ms (4.3%)

Compiler: Compiled 10306 to 6776 computations (34.3% saved)

bsearch3.0ms (0%)

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

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	637	174
1	637	174

end0.0ms (0%)

sample3.6s (17.3%)

Algorithm

1×

intervals

Results

1.1s	12876×	body	128	nan
716.0ms	8000×	body	128	valid
106.0ms	1148×	body	128	invalid

Compiler

Compiled 1396 to 904 computations (35.2% saved)

Details

analyze2.4s (11.5%)

sample89.0ms (0.4%)

simplify141.0ms (0.7%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite52.0ms (0.3%)

series2.7s (13.1%)

simplify94.0ms (0.5%)

prune198.0ms (1%)

localize16.0ms (0.1%)

rewrite44.0ms (0.2%)

series2.6s (12.6%)

simplify77.0ms (0.4%)

prune155.0ms (0.7%)

localize16.0ms (0.1%)

rewrite47.0ms (0.2%)

series2.6s (12.6%)

simplify88.0ms (0.4%)

prune163.0ms (0.8%)

localize20.0ms (0.1%)

rewrite51.0ms (0.2%)

series4.3s (20.9%)

simplify51.0ms (0.2%)

prune230.0ms (1.1%)

regimes882.0ms (4.3%)

bsearch3.0ms (0%)

simplify21.0ms (0.1%)

end0.0ms (0%)

sample3.6s (17.3%)

Profiling