Details

analyze2.4s (5.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5820	672
0	6	6
1	6	6

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)

sample92.0ms (0.2%)

Algorithm

1×

intervals

Results

31.0ms	369×	body	128	nan
23.0ms	256×	body	128	valid
3.0ms	34×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify53.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

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

31.7b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.1b	(.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)))))))
15.4b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
19.4b	(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))))))))

rewrite479.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

22.2b

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×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `*-commutative_binary64_350`
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)))
11.0ms	(.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))))))))

Compiler

Compiled 4884 to 1897 computations (61.2% saved)

series7.0s (15.7%)

Error

19.6b

Counts

4 → 112

Calls

4 calls:

3.3s	(.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)))))))
1.7s	(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))))))))
1.4s	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
476.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 9605 to 7534 computations (21.6% saved)

simplify121.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4965	7874
1	4965	7874

prune362.0ms (0.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	223	20	243
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	225	20	245

Error

15.7b

Counts

245 → 20

Compiler

Compiled 5289 to 2251 computations (57.4% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

6.1b	(*.f64 n (/.f64 l Om))
8.7b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.1b	(.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))))))
19.4b	(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)))))))

rewrite296.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

15.1b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`add-cube-cbrt_binary64_454` `pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`associate-*r/_binary64_361` `times-frac_binary64_425`
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` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `sub-neg_binary64_412` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

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))))))
8.0ms	(*.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)))))))

Compiler

Compiled 3759 to 1527 computations (59.4% saved)

series5.8s (13%)

Error

15.7b

Counts

4 → 94

Calls

4 calls:

3.3s	(.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))))))
1.7s	(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)))))))
487.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
145.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 8419 to 6601 computations (21.6% saved)

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5156	6123

prune261.0ms (0.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	197	4	201
Fresh	4	15	19
Picked	0	1	1
Done	0	0	0
Total	201	20	221

Error

15.1b

Counts

221 → 20

Compiler

Compiled 4340 to 1910 computations (56% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.1b	(.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)))))
10.1b	(.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)))))
19.4b	(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))))))
19.4b	(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))))))

rewrite302.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

15.1b

Rules

42×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
22×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`sqrt-pow1_binary64_437` `associate-*r/_binary64_361`
6×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `-un-lft-identity_binary64_419` `associate-r*_binary64_359`
4×	`add-log-exp_binary64_458` `flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393`
2×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360` `*-commutative_binary64_350`

Counts

4 → 80

Calls

4 calls:

10.0ms	(.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)))))
10.0ms	(.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)))))
8.0ms	(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 5256 to 2187 computations (58.4% saved)

series10.8s (24.2%)

Error

15.1b

Counts

4 → 130

Calls

4 calls:

3.4s	(.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)))))
3.4s	(.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)))))
1.9s	(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))))))
1.9s	(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 21596 to 15208 computations (29.6% saved)

simplify122.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5016	9850

prune407.0ms (0.9%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	18	18
Picked	0	1	1
Done	0	1	1
Total	210	20	230

Error

15.1b

Counts

230 → 20

Compiler

Compiled 8290 to 3461 computations (58.3% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

5.9b	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
7.2b	(.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))))))
7.5b	(.f64 (-.f64 U U) (/.f64 l Om))
19.4b	(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)))))))

rewrite291.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

12.7b

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` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `associate-*l/_binary64_362` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
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:

11.0ms	(.f64 (-.f64 U U) (/.f64 l Om))
10.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
9.0ms	(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)))))))
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))))))

Compiler

Compiled 3669 to 1491 computations (59.4% saved)

series5.9s (13.1%)

Error

15.1b

Counts

4 → 97

Calls

4 calls:

3.4s	(.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))))))
1.7s	(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)))))))
399.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
242.0ms	(.f64 (-.f64 U U) (/.f64 l Om))

Compiler

Compiled 8737 to 6810 computations (22.1% saved)

simplify87.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4995	6238
1	4995	6238

prune265.0ms (0.6%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	1	16	17
Picked	1	0	1
Done	0	2	2
Total	202	22	224

Error

13.2b

Counts

224 → 22

Compiler

Compiled 3852 to 1546 computations (59.9% saved)

regimes5.6s (12.6%)

Accuracy

Total 14.3b remaining (54.3%)

Threshold costs 0b (0%)

Compiler

Compiled 56414 to 40724 computations (27.8% saved)

bsearch16.0ms (0%)

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

simplify31.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	1125	326
1	1125	326

end8.0ms (0%)

Compiler: Compiled 215 to 119 computations (44.7% saved)

sample3.7s (8.3%)

Algorithm

1×

intervals

Results

1.2s	12801×	body	128	nan
734.0ms	8000×	body	128	valid
110.0ms	1183×	body	128	invalid

Compiler

Compiled 972 to 680 computations (30% saved)

Details

analyze2.4s (5.5%)

sample92.0ms (0.2%)

simplify53.0ms (0.1%)

prune6.0ms (0%)

localize17.0ms (0%)

rewrite479.0ms (1.1%)

series7.0s (15.7%)

simplify121.0ms (0.3%)

prune362.0ms (0.8%)

localize21.0ms (0%)

rewrite296.0ms (0.7%)

series5.8s (13%)

simplify71.0ms (0.2%)

prune261.0ms (0.6%)

localize23.0ms (0.1%)

rewrite302.0ms (0.7%)

series10.8s (24.2%)

simplify122.0ms (0.3%)

prune407.0ms (0.9%)

localize18.0ms (0%)

rewrite291.0ms (0.7%)

series5.9s (13.1%)

simplify87.0ms (0.2%)

prune265.0ms (0.6%)

regimes5.6s (12.6%)

bsearch16.0ms (0%)

simplify31.0ms (0.1%)

end8.0ms (0%)

sample3.7s (8.3%)

Profiling