Details

analyze4.3s (5.5%)

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)

sample191.0ms (0.2%)

Algorithm

1×

intervals

Results

70.0ms	432×	body	128	nan
49.0ms	256×	body	128	valid
5.0ms	33×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify269.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5178	39

prune16.0ms (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

31.6b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

1.4b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
8.7b	(.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)))))))
11.8b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
21.9b	(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))))))))

rewrite487.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

23.6b

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:

25.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
19.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
18.0ms	(.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)))))))
13.0ms	(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)

series9.1s (11.7%)

Error

18.3b

Counts

4 → 114

Calls

4 calls:

3.6s	(.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)))))))
3.1s	(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))))))))
1.4s	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
509.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 13523 to 10179 computations (24.7% saved)

simplify284.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4983	9119
1	4983	9119

prune700.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	228	17	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	17	247

Error

15.1b

Counts

247 → 17

Compiler

Compiled 9301 to 3342 computations (64.1% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

5.9b	(*.f64 n (/.f64 l Om))
8.7b	(.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))))))
9.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
21.9b	(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)))))))

rewrite366.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

14.8b

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:

27.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.0ms	(.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))))))
17.0ms	(*.f64 n (/.f64 l Om))
15.0ms	(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 4070 to 1665 computations (59.1% saved)

series8.1s (10.4%)

Error

14.8b

Counts

4 → 97

Calls

4 calls:

3.7s	(.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))))))
3.4s	(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)))))))
517.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
199.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 12083 to 9026 computations (25.3% saved)

simplify242.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4946	7122
1	4946	7122

prune521.0ms (0.7%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	202	19	221

Error

14.8b

Counts

221 → 19

Compiler

Compiled 7804 to 2908 computations (62.7% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.7b	(.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)))))
8.7b	(.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)))))
21.9b	(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))))))
21.9b	(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))))))

rewrite446.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

14.8b

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:

18.0ms	(.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)))))
18.0ms	(.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)))))
13.0ms	(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))))))
13.0ms	(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 5946 to 2493 computations (58.1% saved)

series14.8s (18.9%)

Error

14.8b

Counts

4 → 140

Calls

4 calls:

3.7s	(.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)))))
3.7s	(.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)))))
3.2s	(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))))))
3.1s	(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 30114 to 20632 computations (31.5% saved)

simplify263.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4974	12000
1	4974	12000

prune1.1s (1.4%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	17	17
Picked	0	1	1
Done	0	1	1
Total	220	19	239

Error

14.8b

Counts

239 → 19

Compiler

Compiled 15879 to 5925 computations (62.7% saved)

localize65.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.7b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))
10.7b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))
10.7b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
21.9b	(sqrt.f64 (.f64 (.f64 (.f64 U (.f64 2 n)) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

rewrite662.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

14.8b

Rules

60×	`cbrt-div_binary64_451`
34×	`pow1_binary64_480`
32×	`associate-*r/_binary64_361`
30×	`flip3-+_binary64_422` `flip-+_binary64_393`
28×	`frac-times_binary64_429`
26×	`sqrt-div_binary64_436`
22×	`pow-prod-down_binary64_490`
14×	`associate-*l/_binary64_362`
9×	`cbrt-prod_binary64_450`
8×	`sqrt-pow1_binary64_437`
7×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
3×	`pow1/3_binary64_501`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

4 → 82

Calls

4 calls:

42.0ms	(sqrt.f64 (.f64 (.f64 (.f64 U (.f64 2 n)) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
6.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
5.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))
5.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))

Compiler

Compiled 9824 to 3513 computations (64.2% saved)

series14.9s (19.1%)

Error

14.6b

Counts

4 → 129

Calls

4 calls:

3.8s	(sqrt.f64 (.f64 (.f64 (.f64 U (.f64 2 n)) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
3.4s	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
3.3s	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))
3.3s	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))

Compiler

Compiled 40510 to 27528 computations (32% saved)

simplify349.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4974	17753
1	4974	17753

prune1.5s (1.9%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	2	14	16
Picked	0	1	1
Done	0	2	2
Total	211	19	230

Error

14.8b

Counts

230 → 19

Compiler

Compiled 19516 to 6604 computations (66.2% saved)

regimes6.9s (8.8%)

Accuracy

Total 14.4b remaining (50.8%)

Threshold costs 0b (0%)

Compiler

Compiled 36650 to 25586 computations (30.2% saved)

bsearch21.0ms (0%)

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

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	1152	221
1	1152	221

end0.0ms (0%)

sample12.3s (15.7%)

Algorithm

1×

intervals

Results

2.1s	12895×	body	128	nan
1.3s	8000×	body	128	valid
206.0ms	1194×	body	128	invalid

Compiler

Compiled 4741 to 3297 computations (30.5% saved)

Details

analyze4.3s (5.5%)

sample191.0ms (0.2%)

simplify269.0ms (0.3%)

prune16.0ms (0%)

localize37.0ms (0%)

rewrite487.0ms (0.6%)

series9.1s (11.7%)

simplify284.0ms (0.4%)

prune700.0ms (0.9%)

localize38.0ms (0%)

rewrite366.0ms (0.5%)

series8.1s (10.4%)

simplify242.0ms (0.3%)

prune521.0ms (0.7%)

localize47.0ms (0.1%)

rewrite446.0ms (0.6%)

series14.8s (18.9%)

simplify263.0ms (0.3%)

prune1.1s (1.4%)

localize65.0ms (0.1%)

rewrite662.0ms (0.8%)

series14.9s (19.1%)

simplify349.0ms (0.4%)

prune1.5s (1.9%)

regimes6.9s (8.8%)

bsearch21.0ms (0%)

simplify76.0ms (0.1%)

end0.0ms (0%)

sample12.3s (15.7%)

Profiling