Details

analyze2.3s (8.5%)

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)

sample95.0ms (0.4%)

Algorithm

1×

intervals

Results

36.0ms	396×	body	128	nan
24.0ms	256×	body	128	valid
6.0ms	30×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify147.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5178	39

prune6.0ms (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

31.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.5b	(.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)))))))
10.4b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
20.5b	(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))))))))

rewrite53.0ms (0.2%)

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)))))
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)))))))
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))))))))

series4.2s (15.8%)

Counts

4 → 110

Calls

4 calls:

1.9s	(.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)))))))
1.2s	(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))))))))
840.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
266.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 8104 to 6618 computations (18.3% saved)

simplify122.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5005	8096

prune354.0ms (1.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	223	18	241
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	225	18	243

Error

15.1b

Counts

243 → 18

Compiler

Compiled 8758 to 3244 computations (63% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(*.f64 n (/.f64 l Om))
9.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.5b	(.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))))))
20.5b	(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)))))))

rewrite47.0ms (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:

11.0ms	(.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))
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)))))))

series3.5s (12.9%)

Counts

4 → 92

Calls

4 calls:

1.9s	(.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))))))
1.2s	(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)))))))
252.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
109.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 7178 to 5826 computations (18.8% saved)

simplify73.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5470	6345

prune254.0ms (0.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	199	18	217

Error

15.1b

Counts

217 → 18

Compiler

Compiled 7310 to 2776 computations (62% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
7.2b	(.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)))))))
9.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.5b	(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))))))))

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
20×	`pow-prod-down_binary64_490`
15×	`associate-*r/_binary64_361`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
13×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419`
9×	`distribute-rgt-in_binary64_369` `add-cube-cbrt_binary64_454` `associate-r_binary64_359` `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×	`flip3-+_binary64_422` `*-commutative_binary64_350` `flip-+_binary64_393`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `unswap-sqr_binary64_387` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 101

Calls

4 calls:

11.0ms	(.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	(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))))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))

series4.9s (18.4%)

Counts

4 → 122

Calls

4 calls:

2.0s	(.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)))))))
1.5s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
1.2s	(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))))))))
259.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

Compiler

Compiled 8818 to 7214 computations (18.2% saved)

simplify87.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5494	8436

prune304.0ms (1.1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	218	5	223
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	221	20	241

Error

11.1b

Counts

241 → 20

Compiler

Compiled 8283 to 2901 computations (65% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.7b	(.f64 (/.f64 l Om) (.f64 n U*))
9.0b	(.f64 (/.f64 l Om) (.f64 n (neg.f64 U)))
9.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (/.f64 l Om) (.f64 n U)) (.f64 (/.f64 l Om) (.f64 n (neg.f64 U))))))))
20.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (/.f64 l Om) (.f64 n U)) (.f64 (/.f64 l Om) (.f64 n (neg.f64 U)))))))))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
33×	`pow1_binary64_480`
27×	`associate-l_binary64_360`
19×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
18×	`pow-prod-down_binary64_490` `times-frac_binary64_425` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `associate-*r/_binary64_361` `sqrt-pow1_binary64_437` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `sqrt-div_binary64_436` `div-inv_binary64_416` `distribute-rgt-neg-out_binary64_379` `flip-+_binary64_393`
1×	`distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `distribute-lft-in_binary64_368` `sqrt-prod_binary64_435`

Counts

4 → 107

Calls

4 calls:

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

series3.6s (13.4%)

Counts

4 → 89

Calls

4 calls:

2.0s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (/.f64 l Om) (.f64 n U)) (.f64 (/.f64 l Om) (.f64 n (neg.f64 U))))))))
1.2s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (/.f64 l Om) (.f64 n U)) (.f64 (/.f64 l Om) (.f64 n (neg.f64 U)))))))))
191.0ms	(.f64 (/.f64 l Om) (.f64 n U*))
190.0ms	(.f64 (/.f64 l Om) (.f64 n (neg.f64 U)))

Compiler

Compiled 7384 to 5888 computations (20.3% saved)

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5242	6340

prune227.0ms (0.8%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	18	18
Picked	0	1	1
Done	0	1	1
Total	195	21	216

Error

11.1b

Counts

216 → 21

Compiler

Compiled 7412 to 2364 computations (68.1% saved)

regimes1.8s (6.8%)

Accuracy

Total 15.8b remaining (57.8%)

Threshold costs 0b (0%)

Compiler

Compiled 18634 to 13090 computations (29.8% saved)

bsearch7.0ms (0%)

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

simplify33.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	860	301
1	860	301

end0.0ms (0%)

sample4.5s (16.7%)

Algorithm

1×

intervals

Results

1.2s	13192×	body	128	nan
757.0ms	8000×	body	128	valid
115.0ms	1220×	body	128	invalid

Compiler

Compiled 2542 to 1755 computations (31% saved)

Details

analyze2.3s (8.5%)

sample95.0ms (0.4%)

simplify147.0ms (0.5%)

prune6.0ms (0%)

localize21.0ms (0.1%)

rewrite53.0ms (0.2%)

series4.2s (15.8%)

simplify122.0ms (0.5%)

prune354.0ms (1.3%)

localize17.0ms (0.1%)

rewrite47.0ms (0.2%)

series3.5s (12.9%)

simplify73.0ms (0.3%)

prune254.0ms (0.9%)

localize17.0ms (0.1%)

rewrite43.0ms (0.2%)

series4.9s (18.4%)

simplify87.0ms (0.3%)

prune304.0ms (1.1%)

localize24.0ms (0.1%)

rewrite46.0ms (0.2%)

series3.6s (13.4%)

simplify76.0ms (0.3%)

prune227.0ms (0.8%)

regimes1.8s (6.8%)

bsearch7.0ms (0%)

simplify33.0ms (0.1%)

end0.0ms (0%)

sample4.5s (16.7%)

Profiling