Details

analyze2.2s (6.1%)

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)

sample103.0ms (0.3%)

Algorithm

1×

intervals

Results

37.0ms	437×	body	128	nan
26.0ms	256×	body	128	valid
3.0ms	35×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify140.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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

Error

31.9b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

2.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.4b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.6b	(.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)))))))
20.2b	(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))))))))

rewrite265.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

22.7b

Rules

30×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
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×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `frac-times_binary64_429` `sub-neg_binary64_412`
3×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`
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))))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series4.4s (12.4%)

Error

20.3b

Counts

4 → 112

Calls

4 calls:

2.0s	(.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)))))))
1.1s	(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))))))))
864.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
328.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11567 to 8732 computations (24.5% saved)

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5050	8105

prune347.0ms (1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	224	19	243
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	226	19	245

Error

14.3b

Counts

245 → 19

Compiler

Compiled 8838 to 3250 computations (63.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
5.5b	(.f64 (-.f64 U U) (/.f64 l Om))
6.9b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
20.2b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))))

rewrite182.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

11.4b

Rules

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

Counts

4 → 107

Calls

4 calls:

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

Compiler

Compiled 4065 to 1666 computations (59% saved)

series3.7s (10.5%)

Error

13.6b

Counts

4 → 103

Calls

4 calls:

2.0s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
1.1s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))))
328.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
205.0ms	(.f64 (-.f64 U U) (/.f64 l Om))

Compiler

Compiled 10671 to 7915 computations (25.8% saved)

simplify106.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4970	6231
1	4970	6231

prune272.0ms (0.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	206	4	210
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	207	22	229

Error

11.4b

Counts

229 → 22

Compiler

Compiled 7546 to 2952 computations (60.9% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.6b	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))
20.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
20.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
20.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))

rewrite269.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

11.4b

Rules

43×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`sqrt-pow1_binary64_437`
8×	`associate-*r/_binary64_361`
6×	`sqrt-div_binary64_436` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458` `flip3-+_binary64_422` `flip-+_binary64_393`
3×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-r_binary64_359`
1×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360` `*-commutative_binary64_350`

Counts

4 → 70

Calls

4 calls:

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

Compiler

Compiled 7121 to 3019 computations (57.6% saved)

series5.9s (16.5%)

Error

11.4b

Counts

4 → 114

Calls

4 calls:

2.1s	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))
1.1s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
1.1s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
1.1s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))

Compiler

Compiled 32371 to 20045 computations (38.1% saved)

simplify133.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5114	8428

prune643.0ms (1.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	0	20	20
Picked	1	0	1
Done	0	1	1
Total	184	22	206

Error

11.4b

Counts

206 → 22

Compiler

Compiled 17802 to 7261 computations (59.2% saved)

localize45.0ms (0.1%)

Local error

Found 4 expressions with local error:

20.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2))))))
20.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2))))))
20.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
20.2b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))

rewrite362.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

11.4b

Rules

44×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
16×	`sqrt-pow1_binary64_437`
8×	`associate-*r/_binary64_361` `sqrt-div_binary64_436`
4×	`pow1/2_binary64_499` `add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435` `*-un-lft-identity_binary64_419`

Counts

4 → 60

Calls

4 calls:

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

Compiler

Compiled 9476 to 4081 computations (56.9% saved)

series5.4s (15.1%)

Error

11.4b

Counts

4 → 100

Calls

4 calls:

1.2s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
1.2s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
1.2s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2))))))
1.2s	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))) (*.f64 l -2))))))

Compiler

Compiled 46100 to 26244 computations (43.1% saved)

simplify100.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4990	6664
1	4990	6664

prune955.0ms (2.7%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	0	20	20
Picked	1	0	1
Done	0	1	1
Total	160	22	182

Error

11.4b

Counts

182 → 22

Compiler

Compiled 23384 to 9941 computations (57.5% saved)

regimes3.3s (9.2%)

Accuracy

Total 14.8b remaining (56.8%)

Threshold costs 0b (0%)

Compiler

Compiled 45642 to 30330 computations (33.5% saved)

bsearch11.0ms (0%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	1197	358
1	1197	358

end0.0ms (0%)

sample6.6s (18.5%)

Algorithm

1×

intervals

Results

1.4s	13339×	body	128	nan
719.0ms	8000×	body	128	valid
118.0ms	1226×	body	128	invalid

Compiler

Compiled 5956 to 3936 computations (33.9% saved)

Details

analyze2.2s (6.1%)

sample103.0ms (0.3%)

simplify140.0ms (0.4%)

prune5.0ms (0%)

localize17.0ms (0%)

rewrite265.0ms (0.7%)

series4.4s (12.4%)

simplify86.0ms (0.2%)

prune347.0ms (1%)

localize20.0ms (0.1%)

rewrite182.0ms (0.5%)

series3.7s (10.5%)

simplify106.0ms (0.3%)

prune272.0ms (0.8%)

localize27.0ms (0.1%)

rewrite269.0ms (0.8%)

series5.9s (16.5%)

simplify133.0ms (0.4%)

prune643.0ms (1.8%)

localize45.0ms (0.1%)

rewrite362.0ms (1%)

series5.4s (15.1%)

simplify100.0ms (0.3%)

prune955.0ms (2.7%)

regimes3.3s (9.2%)

bsearch11.0ms (0%)

simplify58.0ms (0.2%)

end0.0ms (0%)

sample6.6s (18.5%)

Profiling