Details

analyze2.2s (8.3%)

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)

sample93.0ms (0.3%)

Algorithm

1×

intervals

Results

36.0ms	409×	body	128	nan
23.0ms	256×	body	128	valid
3.0ms	29×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify140.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5178	39

prune8.0ms (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

35.1b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

11.7b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
0.8b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
0.0b	(.f64 n (-.f64 U U))
0.0b	(+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))
0.8b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
11.7b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
14.2b	(.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)))))))
19.3b	(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))))))))

rewrite58.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_465` `add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
29×	`add-sqr-sqrt_binary64_426`
27×	`associate-l_binary64_345`
24×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
19×	`times-frac_binary64_410`
18×	`distribute-lft-in_binary64_353` `distribute-rgt-in_binary64_354`
16×	`pow-prod-down_binary64_475`
14×	`prod-exp_binary64_453` `cbrt-unprod_binary64_437`
12×	`cancel-sign-sub-inv_binary64_370` `associate-*r/_binary64_346`
7×	`associate-r_binary64_344`
4×	`sqrt-pow1_binary64_422` `flip3-+_binary64_407` `add-log-exp_binary64_443` `frac-times_binary64_414` `flip-+_binary64_378` `sub-neg_binary64_397`
3×	`div-exp_binary64_455` `*-commutative_binary64_335` `cbrt-undiv_binary64_438`
2×	`associate-*l/_binary64_347` `div-inv_binary64_401` `sqrt-div_binary64_421` `unswap-sqr_binary64_372` `flip3--_binary64_408` `flip--_binary64_379`
1×	`pow1/2_binary64_484` `sqrt-prod_binary64_420`

Counts

4 → 131

Calls

8 calls:

15.0ms	(.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)))))
10.0ms	(.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)))))))
8.0ms	(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))))))))
0.0ms	(+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))

series4.4s (16.3%)

Counts

4 → 112

Calls

4 calls:

2.1s	(.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))))))))
857.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
315.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 7769 to 6376 computations (17.9% saved)

simplify119.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5072	7857

prune411.0ms (1.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	227	16	243
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	228	17	245

Error

15.0b

Counts

245 → 17

Compiler

Compiled 8434 to 3142 computations (62.7% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

7.9b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
7.3b	(*.f64 n (/.f64 l Om))
0.8b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))
0.0b	(+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))
7.3b	(*.f64 n (/.f64 l Om))
7.9b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
14.2b	(.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))))))
19.3b	(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

30×	`pow1_binary64_465`
27×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
23×	`add-sqr-sqrt_binary64_426`
21×	`associate-r_binary64_344`
18×	`*-un-lft-identity_binary64_404`
16×	`pow-prod-down_binary64_475` `add-cube-cbrt_binary64_439`
13×	`prod-exp_binary64_453` `cbrt-unprod_binary64_437`
10×	`associate-*r/_binary64_346` `times-frac_binary64_410`
6×	`cancel-sign-sub-inv_binary64_370`
5×	`associate-l_binary64_345` `distribute-lft-in_binary64_353` `distribute-rgt-in_binary64_354`
4×	`sqrt-pow1_binary64_422` `add-log-exp_binary64_443`
3×	`*-commutative_binary64_335`
2×	`div-exp_binary64_455` `sqrt-div_binary64_421` `unswap-sqr_binary64_372` `flip3-+_binary64_407` `flip3--_binary64_408` `frac-times_binary64_414` `flip-+_binary64_378` `sub-neg_binary64_397` `cbrt-undiv_binary64_438` `flip--_binary64_379`
1×	`associate-*l/_binary64_347` `pow1/2_binary64_484` `div-inv_binary64_401` `distribute-lft-out--_binary64_356` `difference-of-squares_binary64_373` `sqrt-prod_binary64_420`

Counts

4 → 107

Calls

8 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(*.f64 n (/.f64 l Om))
10.0ms	(.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	(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)))))))
0.0ms	(+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))

series3.6s (13.5%)

Counts

4 → 94

Calls

4 calls:

2.1s	(.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))))))
1.1s	(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)))))))
300.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
104.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 6843 to 5584 computations (18.4% saved)

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4996	6136
1	4996	6136

prune252.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	201	17	218

Error

15.0b

Counts

218 → 17

Compiler

Compiled 7021 to 2680 computations (61.8% saved)

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

7.3b	(*.f64 n (/.f64 l Om))
5.5b	(.f64 (.f64 n (/.f64 l Om)) U*)
0.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U*)))
0.0b	(+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U))
5.5b	(.f64 (.f64 n (/.f64 l Om)) U*)
7.3b	(*.f64 n (/.f64 l Om))
14.2b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U)))))
19.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U))))))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_465`
27×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
19×	`associate-r_binary64_344` `add-sqr-sqrt_binary64_426`
16×	`pow-prod-down_binary64_475`
14×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
13×	`prod-exp_binary64_453` `cbrt-unprod_binary64_437`
10×	`times-frac_binary64_410`
6×	`associate-*r/_binary64_346`
5×	`associate-l_binary64_345`
4×	`sqrt-pow1_binary64_422` `add-log-exp_binary64_443`
3×	`*-commutative_binary64_335`
2×	`div-exp_binary64_455` `sqrt-div_binary64_421` `unswap-sqr_binary64_372` `flip3-+_binary64_407` `flip-+_binary64_378` `cbrt-undiv_binary64_438`
1×	`associate-*l/_binary64_347` `pow1/2_binary64_484` `div-inv_binary64_401` `distribute-lft-in_binary64_353` `distribute-rgt-in_binary64_354` `sqrt-prod_binary64_420`

Counts

4 → 93

Calls

8 calls:

9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U)))))
8.0ms	(*.f64 n (/.f64 l Om))
7.0ms	(.f64 (.f64 n (/.f64 l Om)) 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)) U))))))
0.0ms	(+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U))

series2.5s (9.5%)

Counts

4 → 85

Calls

4 calls:

1.4s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U)))))
902.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) U))))))
175.0ms	(.f64 (.f64 n (/.f64 l Om)) U*)
103.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 5233 to 4391 computations (16.1% saved)

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4969	4745
1	4969	4745

prune223.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	169	9	178
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	177	18	195

Error

13.0b

Counts

195 → 18

Compiler

Compiled 5503 to 2431 computations (55.8% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

4.0b	(.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om)))))
0.1b	(*.f64 l (/.f64 l Om))
0.0b	(.f64 2 (.f64 l (/.f64 l Om)))
0.0b	(.f64 2 (.f64 U (.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om)))))))
0.1b	(*.f64 l (/.f64 l Om))
4.0b	(.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om)))))
8.7b	(.f64 U (.f64 n (-.f64 t (.f64 2 (.f64 l (/.f64 l Om))))))
13.8b	(sqrt.f64 (.f64 2 (.f64 U (.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om))))))))

rewrite38.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64_465`
22×	`add-sqr-sqrt_binary64_426`
17×	`associate-r_binary64_344`
16×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
15×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
13×	`associate-*r/_binary64_346`
11×	`pow-prod-down_binary64_475`
10×	`distribute-lft-in_binary64_353` `times-frac_binary64_410` `distribute-rgt-in_binary64_354`
9×	`associate-l_binary64_345`
6×	`cancel-sign-sub-inv_binary64_370` `sub-neg_binary64_397` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`
4×	`sqrt-pow1_binary64_422` `add-log-exp_binary64_443`
3×	`*-commutative_binary64_335` `unswap-sqr_binary64_372` `flip3--_binary64_408` `flip--_binary64_379`
2×	`sqrt-div_binary64_421`
1×	`div-exp_binary64_455` `pow1/2_binary64_484` `div-inv_binary64_401` `cbrt-undiv_binary64_438` `sqrt-prod_binary64_420`

Counts

4 → 99

Calls

8 calls:

8.0ms	(.f64 U (.f64 n (-.f64 t (.f64 2 (.f64 l (/.f64 l Om))))))
7.0ms	(sqrt.f64 (.f64 2 (.f64 U (.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om))))))))
7.0ms	(*.f64 l (/.f64 l Om))
6.0ms	(.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om)))))
0.0ms	(.f64 2 (.f64 U (.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om)))))))

series1.3s (4.9%)

Counts

4 → 73

Calls

4 calls:

472.0ms	(sqrt.f64 (.f64 2 (.f64 U (.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om))))))))
470.0ms	(.f64 U (.f64 n (-.f64 t (.f64 2 (.f64 l (/.f64 l Om))))))
301.0ms	(.f64 n (-.f64 t (.f64 2 (*.f64 l (/.f64 l Om)))))
67.0ms	(*.f64 l (/.f64 l Om))

Compiler

Compiled 2842 to 2687 computations (5.5% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5047	3189

prune174.0ms (0.7%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	166	6	172
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	168	22	190

Error

12.0b

Counts

190 → 22

Compiler

Compiled 3428 to 1707 computations (50.2% saved)

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5134	3487

regimes1.6s (5.9%)

Accuracy

Total 17.0b remaining (60.5%)

Threshold costs 0b (0%)

Compiler

Compiled 13818 to 10338 computations (25.2% saved)

bsearch136.0ms (0.5%)

Steps

Iters	Range	Point
9	6.357420482269927e+100	2.127434708613191e+108	1.1815522068552908e+108
3	-1.1773809507342139e-297	-9.850149359738927e-298	-1.0210835637414531e-297
2	-9.262385104630167e+189	-8.438280371225799e+189	-8.843543244185774e+189

Iters

Range

Point

6.357420482269927e+100

2.127434708613191e+108

1.1815522068552908e+108

-1.1773809507342139e-297

-9.850149359738927e-298

-1.0210835637414531e-297

-9.262385104630167e+189

-8.438280371225799e+189

-8.843543244185774e+189

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	176	159
1	176	159

end0.0ms (0%)

sample8.9s (33.4%)

Algorithm

1×

intervals

Results

1.2s	12938×	body	128	nan
748.0ms	8000×	body	128	valid
110.0ms	1180×	body	128	invalid

Compiler

Compiled 7142 to 5291 computations (25.9% saved)

Pareto

-0.06075218893175788

Details

analyze2.2s (8.3%)

sample93.0ms (0.3%)

simplify140.0ms (0.5%)

prune8.0ms (0%)

localize19.0ms (0.1%)

rewrite58.0ms (0.2%)

series4.4s (16.3%)

simplify119.0ms (0.4%)

prune411.0ms (1.5%)

localize17.0ms (0.1%)

rewrite51.0ms (0.2%)

series3.6s (13.5%)

simplify75.0ms (0.3%)

prune252.0ms (0.9%)

localize18.0ms (0.1%)

rewrite41.0ms (0.2%)

series2.5s (9.5%)

simplify109.0ms (0.4%)

prune223.0ms (0.8%)

localize14.0ms (0.1%)

rewrite38.0ms (0.1%)

series1.3s (4.9%)

simplify78.0ms (0.3%)

prune174.0ms (0.7%)

simplify109.0ms (0.4%)

regimes1.6s (5.9%)

bsearch136.0ms (0.5%)

simplify5.0ms (0%)

end0.0ms (0%)

sample8.9s (33.4%)

Profiling