Details

analyze2.3s (0.7%)

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)

sample98.0ms (0%)

Algorithm

1×

intervals

Results

33.0ms	374×	body	128	nan
25.0ms	256×	body	128	valid
3.0ms	28×	body	128	invalid

Compiler

Compiled 60 to 62 computations (-3.3% saved)

simplify143.0ms (0%)

Algorithm

1×	egg-herbie

Counts

3 → 3

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5178	41

prune5.0ms (0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Kept	Total
New	3	3
Fresh	3	3
Picked	0	0
Done	0	0
Total	6	6

Error

30.5b

Counts

6 → 4

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

5.7b	(*.f64 n (pow.f64 (/.f64 l Om) 2))
3.5b	(-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))
0.3b	(pow.f64 (/.f64 l Om) 2)
0.0b	(.f64 2 (/.f64 (.f64 l l) Om))
6.5b	(/.f64 (*.f64 l l) Om)
8.2b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
10.1b	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
20.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

rewrite66.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_457`
25×	`pow1_binary64_480`
23×	`add-cbrt-cube_binary64_455`
22×	`associate-*r/_binary64_361`
16×	`prod-exp_binary64_468`
13×	`pow-prod-down_binary64_490`
12×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
11×	`flip3--_binary64_423` `flip--_binary64_394`
10×	`add-cube-cbrt_binary64_454` `cbrt-unprod_binary64_452` `cancel-sign-sub-inv_binary64_385`
8×	`distribute-rgt-in_binary64_369` `associate-r_binary64_359` `distribute-lft-in_binary64_368` `frac-sub_binary64_428`
6×	`sqrt-div_binary64_436` `sub-neg_binary64_412`
4×	`associate--l+_binary64_356` `add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
3×	`times-frac_binary64_425` `associate-/r*_binary64_363` `div-exp_binary64_470`
2×	`pow-exp_binary64_487` `-commutative_binary64_350` `associate-l*_binary64_360` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`

Counts

4 → 107

Calls

8 calls:

18.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
15.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
5.0ms	(/.f64 (*.f64 l l) Om)
0.0ms	(.f64 2 (/.f64 (.f64 l l) Om))

series3.8s (1.2%)

Counts

4 → 88

Calls

4 calls:

2.1s	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
1.2s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
380.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
73.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 6861 to 5664 computations (17.4% saved)

simplify84.0ms (0%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5356	7344

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
0.0b	(+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
0.0b	(+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))
0.0b	(.f64 n (-.f64 U U))
0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.7b	(.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)))))))
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))))))))

rewrite56.0ms (0%)

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

8 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))))))))
0.0ms	(.f64 n (-.f64 U U))

series4.5s (1.4%)

Counts

4 → 109

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)))))))
1.2s	(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))))))))
872.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
271.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 7771 to 6388 computations (17.8% saved)

simplify137.0ms (0%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4972	7835
1	4972	7835

prune3.6s (1.1%)

Pruning

169 alts after pruning (169 fresh and 0 done)

	Pruned	Kept	Total
New	268	167	435
Fresh	0	2	2
Picked	0	0	0
Done	2	0	2
Total	270	169	439

Error

16.1b

Counts

439 → 169

Compiler

Compiled 15432 to 8044 computations (47.9% saved)

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

4.8b	(*.f64 n (/.f64 l Om))
0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))
0.0b	(+.f64 t (.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)))
4.8b	(*.f64 n (/.f64 l Om))
7.5b	(.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))))))
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)))))))

rewrite48.0ms (0%)

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

8 calls:

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

series3.9s (1.2%)

Counts

4 → 91

Calls

4 calls:

2.4s	(.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)))))))
262.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
98.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 6845 to 5596 computations (18.2% saved)

simplify77.0ms (0%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5174	6084

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

19.7b	(sqrt.f64 (.f64 2 (.f64 t (*.f64 n U))))
4.5b	(.f64 t (.f64 n U))
0.0b	(.f64 2 (.f64 t (*.f64 n U)))
0.0b	(.f64 2 (.f64 t (*.f64 n U)))
4.5b	(.f64 t (.f64 n U))
19.7b	(sqrt.f64 (.f64 2 (.f64 t (*.f64 n U))))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64_480`
17×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
15×	`pow-prod-down_binary64_490`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`associate-l_binary64_360`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`sqrt-pow1_binary64_437`
3×	`add-log-exp_binary64_458`
2×	`associate-r_binary64_359` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

3 → 52

Calls

6 calls:

6.0ms	(.f64 2 (.f64 t (*.f64 n U)))
5.0ms	(sqrt.f64 (.f64 2 (.f64 t (*.f64 n U))))
5.0ms	(.f64 t (.f64 n U))
0.0ms	(.f64 2 (.f64 t (*.f64 n U)))
0.0ms	(sqrt.f64 (.f64 2 (.f64 t (*.f64 n U))))

series298.0ms (0.1%)

Counts

3 → 27

Calls

3 calls:

119.0ms	(.f64 2 (.f64 t (*.f64 n U)))
90.0ms	(.f64 t (.f64 n U))
88.0ms	(sqrt.f64 (.f64 2 (.f64 t (*.f64 n U))))

Compiler

Compiled 576 to 714 computations (-24% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5023	793

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 t (/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))))
0.0b	(.f64 n (-.f64 U U))
0.0b	(.f64 n (-.f64 U U))
0.0b	(.f64 n (-.f64 U U))
9.7b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.1b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))
20.3b	(/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
20.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))))))

rewrite77.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
28×	`pow1_binary64_480`
18×	`*-un-lft-identity_binary64_419`
17×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
16×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `add-sqr-sqrt_binary64_441`
15×	`pow-prod-down_binary64_490`
14×	`associate-r/_binary64_361` `associate-l*_binary64_360`
12×	`cancel-sign-sub-inv_binary64_385`
10×	`times-frac_binary64_425`
6×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
5×	`associate-r_binary64_359`
4×	`sub-neg_binary64_412` `add-log-exp_binary64_458` `flip3--_binary64_423` `sqrt-pow1_binary64_437` `flip--_binary64_394`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `div-inv_binary64_416` `frac-times_binary64_429` `associate-/r/_binary64_365` `*-commutative_binary64_350` `flip-+_binary64_393` `associate-/l/_binary64_366`
1×	`associate-l/_binary64_362` `clear-num_binary64_418` `pow1/2_binary64_499` `distribute-lft-out_binary64_370` `frac-2neg_binary64_430` `sqrt-prod_binary64_435` `associate-/r_binary64_363` `associate-/l*_binary64_364`

Counts

4 → 119

Calls

8 calls:

17.0ms	(/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
14.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
12.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))
10.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))))))
0.0ms	(.f64 n (-.f64 U U))

series18.7s (5.8%)

Counts

4 → 108

Calls

4 calls:

10.7s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))
5.2s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))))))
2.5s	(/.f64 (.f64 l (-.f64 (.f64 4 (.f64 l l)) (.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))) (.f64 Om (-.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
338.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 19324 to 11822 computations (38.8% saved)

simplify193.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4976	14858
1	4976	14858

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U U)) (sqrt.f64 (/.f64 l Om))))))
0.0b	(.f64 n (-.f64 U U))
0.0b	(+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U* U)) (sqrt.f64 (/.f64 l Om)))))
0.0b	(+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U U)) (sqrt.f64 (/.f64 l Om)))))))
5.0b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U* U)) (sqrt.f64 (/.f64 l Om))))))))
11.0b	(sqrt.f64 (/.f64 l Om))
11.0b	(sqrt.f64 (/.f64 l Om))
11.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U* U)) (sqrt.f64 (/.f64 l Om)))))))))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`sqrt-prod_binary64_435`
25×	`add-sqr-sqrt_binary64_441` `pow1_binary64_480`
20×	`times-frac_binary64_425`
19×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
12×	`pow-prod-down_binary64_490`
6×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sqrt-pow1_binary64_437`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `associate-*r/_binary64_361` `rem-sqrt-square_binary64_432`
3×	`pow1/2_binary64_499` `associate-r_binary64_359`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `flip-+_binary64_393`
1×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `-commutative_binary64_350` `associate-l*_binary64_360`

Counts

4 → 90

Calls

8 calls:

9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U* U)) (sqrt.f64 (/.f64 l Om))))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U* U)) (sqrt.f64 (/.f64 l Om)))))))))
3.0ms	(sqrt.f64 (/.f64 l Om))
3.0ms	(sqrt.f64 (/.f64 l Om))
0.0ms	(+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U U)) (sqrt.f64 (/.f64 l Om)))))))

series3.1s (1%)

Counts

4 → 73

Calls

4 calls:

2.0s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U* U)) (sqrt.f64 (/.f64 l Om))))))))
1.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (sqrt.f64 (/.f64 l Om)) (.f64 (.f64 n (-.f64 U* U)) (sqrt.f64 (/.f64 l Om)))))))))
40.0ms	(sqrt.f64 (/.f64 l Om))
38.0ms	(sqrt.f64 (/.f64 l Om))

Compiler

Compiled 6049 to 4950 computations (18.2% saved)

simplify103.0ms (0%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4993	5174
1	4993	5174

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))
0.0b	(.f64 n (-.f64 U U))
0.0b	(.f64 n (-.f64 U U))
0.0b	(.f64 n (-.f64 U U))
20.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))))
28.6b	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
28.6b	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
28.6b	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))

rewrite45.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

8 calls:

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

series4.1s (1.3%)

Counts

4 → 85

Calls

4 calls:

1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))) (cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))))
878.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
873.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))
873.0ms	(cbrt.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))

Compiler

Compiled 13489 to 8978 computations (33.4% saved)

simplify114.0ms (0%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4963	6173
1	4963	6173

prune22.2s (6.9%)

Pruning

367 alts after pruning (366 fresh and 1 done)

	Pruned	Kept	Total
New	562	247	809
Fresh	45	119	164
Picked	0	0	0
Done	4	1	5
Total	611	367	978

Error

15.8b

Counts

978 → 367

Compiler

Compiled 46812 to 21488 computations (54.1% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

4.8b	(*.f64 n (/.f64 l Om))
0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))
0.0b	(+.f64 t (.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)))
5.3b	(.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)))))))
5.5b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
7.5b	(.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))))))))

rewrite48.0ms (0%)

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

8 calls:

13.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.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))))))
0.0ms	(+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))

series5.1s (1.6%)

Counts

4 → 121

Calls

4 calls:

2.1s	(.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)))))))
1.6s	(.f64 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 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
254.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

Compiler

Compiled 8485 to 6984 computations (17.7% saved)

simplify90.0ms (0%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5235	8175

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

19.7b	(sqrt.f64 (.f64 2 (.f64 (*.f64 t n) U)))
5.7b	(.f64 (.f64 t n) U)
0.0b	(.f64 2 (.f64 (*.f64 t n) U))
0.0b	(.f64 2 (.f64 (*.f64 t n) U))
5.7b	(.f64 (.f64 t n) U)
19.7b	(sqrt.f64 (.f64 2 (.f64 (*.f64 t n) U)))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64_480`
17×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
15×	`pow-prod-down_binary64_490`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`associate-r_binary64_359` `associate-l_binary64_360` `sqrt-pow1_binary64_437`
3×	`add-log-exp_binary64_458`
2×	`*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

3 → 52

Calls

6 calls:

10.0ms	(.f64 2 (.f64 (*.f64 t n) U))
5.0ms	(.f64 (.f64 t n) U)
5.0ms	(sqrt.f64 (.f64 2 (.f64 (*.f64 t n) U)))
0.0ms	(.f64 2 (.f64 (*.f64 t n) U))
0.0ms	(sqrt.f64 (.f64 2 (.f64 (*.f64 t n) U)))

series293.0ms (0.1%)

Counts

3 → 27

Calls

3 calls:

114.0ms	(.f64 2 (.f64 (*.f64 t n) U))
94.0ms	(.f64 (.f64 t n) U)
85.0ms	(sqrt.f64 (.f64 2 (.f64 (*.f64 t n) U)))

Compiler

Compiled 576 to 714 computations (-24% saved)

simplify93.0ms (0%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5120	798

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

3.5b	(+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (*.f64 l -2)))
0.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (.f64 l -2))) (.f64 n U))))
0.1b	(.f64 (/.f64 l Om) (.f64 l -2))
0.0b	(.f64 n (-.f64 U U))
9.9b	(.f64 (.f64 l l) (.f64 n (-.f64 U U)))
10.6b	(.f64 (+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (.f64 l -2))) (.f64 n U))
18.9b	(/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U U))) (*.f64 Om Om))
26.2b	(sqrt.f64 (.f64 (+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (.f64 l -2))) (.f64 n U)))

rewrite80.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
32×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
27×	`pow1_binary64_480`
16×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
14×	`pow-prod-down_binary64_490`
12×	`cancel-sign-sub-inv_binary64_385`
10×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
8×	`associate-l/_binary64_362` `associate-r/_binary64_361`
4×	`sub-neg_binary64_412` `add-log-exp_binary64_458` `associate-l_binary64_360`
3×	`sqrt-div_binary64_436` `sqrt-pow1_binary64_437`
2×	`flip3-+_binary64_422` `frac-add_binary64_427` `associate-r_binary64_359` `flip3--_binary64_423` `*-commutative_binary64_350` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `times-frac_binary64_425` `pow1/2_binary64_499` `div-inv_binary64_416` `frac-2neg_binary64_430` `sqrt-prod_binary64_435` `associate-/r_binary64_363` `associate-/l_binary64_364`

Counts

4 → 111

Calls

8 calls:

18.0ms	(.f64 (+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (.f64 l -2))) (.f64 n U))
16.0ms	(sqrt.f64 (.f64 (+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (.f64 l -2))) (.f64 n U)))
15.0ms	(/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U U))) (*.f64 Om Om))
14.0ms	(.f64 (.f64 l l) (.f64 n (-.f64 U U)))
0.0ms	(.f64 n (-.f64 U U))

series2.6s (0.8%)

Counts

4 → 77

Calls

4 calls:

1.4s	(.f64 (+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (.f64 l -2))) (.f64 n U))
659.0ms	(sqrt.f64 (.f64 (+.f64 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (.f64 Om Om)) (.f64 (/.f64 l Om) (.f64 l -2))) (.f64 n U)))
383.0ms	(/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U U))) (*.f64 Om Om))
190.0ms	(.f64 (.f64 l l) (.f64 n (-.f64 U U)))

Compiler

Compiled 5010 to 4274 computations (14.7% saved)

simplify120.0ms (0%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5037	5161

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

4.5b	(.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (.f64 n U) t)))
4.5b	(.f64 t (.f64 n U))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (*.f64 n U))))
0.2b	(.f64 (sqrt.f64 2) (.f64 l l))
6.3b	(/.f64 (*.f64 n U) t)
6.5b	(/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om)
13.1b	(sqrt.f64 (/.f64 (*.f64 n U) t))
19.7b	(sqrt.f64 (.f64 t (.f64 n U)))

rewrite26.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
11×	`add-sqr-sqrt_binary64_441` `pow1_binary64_480`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`times-frac_binary64_425`
8×	`sqrt-prod_binary64_435`
6×	`associate-/r*_binary64_363`
5×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sqrt-pow1_binary64_437`
3×	`pow-prod-down_binary64_490` `div-inv_binary64_416`
2×	`clear-num_binary64_418` `pow1/2_binary64_499` `frac-2neg_binary64_430` `associate-/l*_binary64_364`
1×	`sqrt-div_binary64_436` `rem-sqrt-square_binary64_432`

Counts

4 → 74

Calls

8 calls:

8.0ms	(/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om)
4.0ms	(/.f64 (*.f64 n U) t)
4.0ms	(sqrt.f64 (.f64 t (.f64 n U)))
3.0ms	(sqrt.f64 (/.f64 (*.f64 n U) t))
0.0ms	(.f64 (sqrt.f64 2) (.f64 l l))

series355.0ms (0.1%)

Counts

4 → 33

Calls

4 calls:

102.0ms	(/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om)
101.0ms	(/.f64 (*.f64 n U) t)
78.0ms	(sqrt.f64 (.f64 t (.f64 n U)))
74.0ms	(sqrt.f64 (/.f64 (*.f64 n U) t))

Compiler

Compiled 1910 to 1662 computations (13% saved)

simplify71.0ms (0%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5059	1146

localize43.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 n (-.f64 U U))
0.0b	(.f64 n (-.f64 U U))
0.0b	(.f64 n (-.f64 U U))
0.0b	(.f64 2 (/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U*)))))
18.5b	(/.f64 (.f64 (.f64 U U) (.f64 (pow.f64 l 3) (.f64 n n))) (.f64 l (.f64 n (-.f64 U U*))))
21.1b	(/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U* (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U*))))
22.3b	(sqrt.f64 (.f64 n (.f64 U (-.f64 (.f64 2 (/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U))))) (+.f64 (/.f64 (.f64 (.f64 U U) (.f64 (pow.f64 l 3) (.f64 n n))) (.f64 l (.f64 n (-.f64 U U)))) (/.f64 (.f64 (.f64 n n) (.f64 (pow.f64 l 3) (.f64 U* U))) (.f64 l (.f64 n (-.f64 U U)))))))))
22.5b	(/.f64 (.f64 (.f64 n n) (.f64 (pow.f64 l 3) (.f64 U* U))) (.f64 l (.f64 n (-.f64 U U))))

rewrite192.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

649×	`add-exp-log_binary64_457`
435×	`prod-exp_binary64_468`
313×	`add-cbrt-cube_binary64_455`
189×	`cbrt-unprod_binary64_452`
120×	`div-exp_binary64_470`
60×	`cbrt-undiv_binary64_453`
30×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
25×	`associate-*r/_binary64_361`
10×	`pow1_binary64_480`
6×	`associate-/r/_binary64_365`
5×	`sqrt-div_binary64_436`
4×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `flip3--_binary64_423` `flip--_binary64_394`
3×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `times-frac_binary64_425` `div-inv_binary64_416` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r_binary64_363` `frac-sub_binary64_428` `associate-/l_binary64_364`
1×	`flip3-+_binary64_422` `frac-add_binary64_427` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-prod_binary64_435`

Counts

4 → 242

Calls

8 calls:

48.0ms	(sqrt.f64 (.f64 n (.f64 U (-.f64 (.f64 2 (/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U))))) (+.f64 (/.f64 (.f64 (.f64 U U) (.f64 (pow.f64 l 3) (.f64 n n))) (.f64 l (.f64 n (-.f64 U U)))) (/.f64 (.f64 (.f64 n n) (.f64 (pow.f64 l 3) (.f64 U* U))) (.f64 l (.f64 n (-.f64 U U)))))))))
24.0ms	(/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U* (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U*))))
21.0ms	(/.f64 (.f64 (.f64 n n) (.f64 (pow.f64 l 3) (.f64 U* U))) (.f64 l (.f64 n (-.f64 U U))))
20.0ms	(/.f64 (.f64 (.f64 U U) (.f64 (pow.f64 l 3) (.f64 n n))) (.f64 l (.f64 n (-.f64 U U*))))
0.0ms	(.f64 2 (/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U*)))))

series1.9s (0.6%)

Counts

4 → 72

Calls

4 calls:

982.0ms	(sqrt.f64 (.f64 n (.f64 U (-.f64 (.f64 2 (/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U))))) (+.f64 (/.f64 (.f64 (.f64 U U) (.f64 (pow.f64 l 3) (.f64 n n))) (.f64 l (.f64 n (-.f64 U U)))) (/.f64 (.f64 (.f64 n n) (.f64 (pow.f64 l 3) (.f64 U* U))) (.f64 l (.f64 n (-.f64 U U)))))))))
321.0ms	(/.f64 (.f64 (.f64 n n) (.f64 (pow.f64 l 3) (.f64 U* U))) (.f64 l (.f64 n (-.f64 U U))))
306.0ms	(/.f64 (.f64 U (.f64 (.f64 n n) (.f64 U* (pow.f64 l 3)))) (.f64 l (.f64 n (-.f64 U U*))))
302.0ms	(/.f64 (.f64 (.f64 U U) (.f64 (pow.f64 l 3) (.f64 n n))) (.f64 l (.f64 n (-.f64 U U*))))

Compiler

Compiled 7506 to 4911 computations (34.6% saved)

simplify140.0ms (0%)

Algorithm

1×	egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5053	11319

prune25.5s (7.9%)

Pruning

569 alts after pruning (565 fresh and 4 done)

	Pruned	Kept	Total
New	684	226	910
Fresh	22	339	361
Picked	0	0	0
Done	2	4	6
Total	708	569	1277

Error

11.2b

Counts

1277 → 569

Compiler

Compiled 46484 to 24082 computations (48.2% saved)

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

4.7b	(.f64 (.f64 n (/.f64 l Om)) (neg.f64 U))
0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (*.f64 n (/.f64 l Om)) (neg.f64 U)))))
0.0b	(+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (*.f64 n (/.f64 l Om)) (neg.f64 U))))))
0.0b	(+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U))))
5.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U))))))))
5.5b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U)))))))
5.5b	(.f64 (.f64 n (/.f64 l Om)) U*)
20.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U)))))))))

rewrite42.0ms (0%)

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`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`associate-*r/_binary64_361`
9×	`add-sqr-sqrt_binary64_441`
7×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `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`
1×	`associate-*l/_binary64_362` `pow1/2_binary64_499` `unswap-sqr_binary64_387` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 87

Calls

8 calls:

9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U))))))))
7.0ms	(.f64 (.f64 n (/.f64 l Om)) U*)
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U)))))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U)))))))
0.0ms	(+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U))))

series5.1s (1.6%)

Counts

4 → 115

Calls

4 calls:

2.1s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U))))))))
1.6s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U)))))))
1.2s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (+.f64 (.f64 (.f64 n (/.f64 l Om)) U) (.f64 (.f64 n (/.f64 l Om)) (neg.f64 U)))))))))
175.0ms	(.f64 (.f64 n (/.f64 l Om)) U*)

Compiler

Compiled 8343 to 6824 computations (18.2% saved)

simplify108.0ms (0%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4987	7721
1	4987	7721

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

19.7b	(sqrt.f64 (.f64 (+.f64 t t) (.f64 n U)))
4.5b	(.f64 (+.f64 t t) (.f64 n U))
4.5b	(.f64 (+.f64 t t) (.f64 n U))
19.7b	(sqrt.f64 (.f64 (+.f64 t t) (.f64 n U)))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64_480`
12×	`associate-l_binary64_360`
9×	`*-un-lft-identity_binary64_419`
7×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`pow-prod-down_binary64_490`
4×	`associate-*l/_binary64_362`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-lft-out_binary64_370` `sqrt-pow1_binary64_437` `distribute-rgt-out_binary64_372`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `add-log-exp_binary64_458` `flip-+_binary64_393`
1×	`pow1/2_binary64_499` `distribute-rgt1-in_binary64_375` `associate-r_binary64_359` `count-2_binary64_367` `*-commutative_binary64_350` `sqrt-prod_binary64_435` `distribute-lft1-in_binary64_374`

Counts

2 → 43

Calls

4 calls:

8.0ms	(.f64 (+.f64 t t) (.f64 n U))
6.0ms	(sqrt.f64 (.f64 (+.f64 t t) (.f64 n U)))
0.0ms	(.f64 (+.f64 t t) (.f64 n U))
0.0ms	(sqrt.f64 (.f64 (+.f64 t t) (.f64 n U)))

series199.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

112.0ms	(.f64 (+.f64 t t) (.f64 n U))
87.0ms	(sqrt.f64 (.f64 (+.f64 t t) (.f64 n U)))

Compiler

Compiled 432 to 516 computations (-19.4% saved)

simplify68.0ms (0%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4893	670
1	4893	670

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

7.3b	(.f64 (neg.f64 U) (.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))
6.4b	(.f64 (.f64 l l) U)
4.7b	(-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om)))
0.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (neg.f64 U) (.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om)))))))
16.6b	(/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om))
16.6b	(.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om))))
16.7b	(/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))
28.1b	(sqrt.f64 (.f64 (neg.f64 U) (.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))

rewrite71.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
21×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
19×	`pow1_binary64_480`
12×	`associate-*r/_binary64_361` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
10×	`add-sqr-sqrt_binary64_441` `cancel-sign-sub-inv_binary64_385`
9×	`*-un-lft-identity_binary64_419` `pow-prod-down_binary64_490`
7×	`add-cube-cbrt_binary64_454` `associate-r_binary64_359`
6×	`times-frac_binary64_425` `distribute-rgt-in_binary64_369` `div-inv_binary64_416` `distribute-lft-in_binary64_368`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
2×	`clear-num_binary64_418` `sub-neg_binary64_412` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `frac-2neg_binary64_430` `flip--_binary64_394` `associate-/r_binary64_363` `sub-div_binary64_426` `frac-sub_binary64_428` `associate-/l_binary64_364`
1×	`distribute-rgt-out--_binary64_373` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `unswap-sqr_binary64_387` `-commutative_binary64_350` `associate-l*_binary64_360` `sqrt-prod_binary64_435`

Counts

4 → 106

Calls

8 calls:

18.0ms	(.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om))))
17.0ms	(sqrt.f64 (.f64 (neg.f64 U) (.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))
12.0ms	(/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om))
9.0ms	(/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))
0.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (neg.f64 U) (.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om)))))))

series1.7s (0.5%)

Counts

4 → 51

Calls

4 calls:

753.0ms	(sqrt.f64 (.f64 (neg.f64 U) (.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))
614.0ms	(.f64 (.f64 n n) (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om))))
162.0ms	(/.f64 (.f64 (.f64 l l) U) (*.f64 Om Om))
161.0ms	(/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))

Compiler

Compiled 2948 to 2663 computations (9.7% saved)

simplify88.0ms (0%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5000	3431

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

1.2b	(exp.f64 (log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))
1.2b	(-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (exp.f64 (log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))))
0.3b	(pow.f64 (/.f64 l Om) 2)
0.0b	(.f64 2 (/.f64 (.f64 l l) Om))
6.5b	(/.f64 (*.f64 l l) Om)
8.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (exp.f64 (log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))))
8.2b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
25.5b	(log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))

rewrite59.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-exp-log_binary64_457`
19×	`prod-exp_binary64_468` `pow1_binary64_480`
14×	`associate-*r/_binary64_361` `add-cbrt-cube_binary64_455`
11×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
9×	`add-cube-cbrt_binary64_454`
8×	`pow-prod-down_binary64_490`
7×	`flip3--_binary64_423` `flip--_binary64_394`
6×	`sqrt-div_binary64_436` `rem-log-exp_binary64_460` `cancel-sign-sub-inv_binary64_385` `log-div_binary64_506`
5×	`associate-r_binary64_359`
4×	`exp-diff_binary64_467` `add-log-exp_binary64_458` `distribute-rgt-in_binary64_369` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `distribute-lft-in_binary64_368` `sqrt-pow1_binary64_437` `div-exp_binary64_470` `frac-sub_binary64_428`
3×	`times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`sub-neg_binary64_412` `log-pow_binary64_508` `pow-to-exp_binary64_488` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `log-prod_binary64_505` `distribute-lft-out--_binary64_371` `-commutative_binary64_350` `associate-l_binary64_360` `frac-2neg_binary64_430` `sqrt-prod_binary64_435` `associate-/l_binary64_364`

Counts

4 → 90

Calls

8 calls:

19.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (exp.f64 (log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
10.0ms	(log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))
5.0ms	(/.f64 (*.f64 l l) Om)
0.0ms	(.f64 2 (/.f64 (.f64 l l) Om))

series2.4s (0.7%)

Counts

4 → 65

Calls

4 calls:

1.3s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (exp.f64 (log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))))
546.0ms	(log.f64 (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))
481.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
74.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 5987 to 4909 computations (18% saved)

simplify76.0ms (0%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5158	4227

localize51.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(*.f64 l (sqrt.f64 2))
0.0b	(+.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (/.f64 (.f64 (.f64 n n) (.f64 U* U)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om))))))
0.0b	(+.f64 (/.f64 4 (.f64 Om (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (.f64 2 (/.f64 (.f64 U (.f64 U (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))))
0.0b	(.f64 2 (/.f64 (.f64 U (.f64 U (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om))))))
17.7b	(.f64 (.f64 n n) (.f64 U U*))
18.8b	(sqrt.f64 (.f64 (.f64 n U) (-.f64 (+.f64 (/.f64 4 (.f64 Om (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (.f64 2 (/.f64 (.f64 U (.f64 U (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))))) (+.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))))))
18.9b	(/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))
19.4b	(/.f64 (.f64 U (.f64 U* (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))

rewrite178.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`add-exp-log_binary64_457`
91×	`prod-exp_binary64_468`
89×	`add-cbrt-cube_binary64_455`
45×	`cbrt-unprod_binary64_452`
38×	`pow1_binary64_480`
36×	`div-exp_binary64_470`
22×	`associate-*r/_binary64_361`
18×	`cbrt-undiv_binary64_453`
17×	`pow-prod-down_binary64_490`
13×	`frac-sub_binary64_428`
11×	`sqrt-div_binary64_436`
9×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
8×	`flip3-+_binary64_422` `associate-/r/_binary64_365` `flip-+_binary64_393`
6×	`frac-add_binary64_427`
4×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `pow-plus_binary64_482` `pow-prod-up_binary64_489`
3×	`flip3--_binary64_423` `sqrt-pow1_binary64_437` `flip--_binary64_394`
2×	`clear-num_binary64_418` `times-frac_binary64_425` `div-inv_binary64_416` `frac-2neg_binary64_430` `pow-sqr_binary64_392` `associate-/r_binary64_363` `pow2_binary64_500` `associate-/l_binary64_364`
1×	`pow1/2_binary64_499` `associate-r_binary64_359` `unswap-sqr_binary64_387` `-commutative_binary64_350` `associate-l*_binary64_360` `sqrt-prod_binary64_435`

Counts

4 → 140

Calls

8 calls:

57.0ms	(sqrt.f64 (.f64 (.f64 n U) (-.f64 (+.f64 (/.f64 4 (.f64 Om (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (.f64 2 (/.f64 (.f64 U (.f64 U (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))))) (+.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))))))
30.0ms	(/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))
24.0ms	(/.f64 (.f64 U (.f64 U* (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))
9.0ms	(.f64 (.f64 n n) (.f64 U U*))
0.0ms	(.f64 2 (/.f64 (.f64 U (.f64 U (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om))))))

series2.8s (0.9%)

Counts

4 → 61

Calls

4 calls:

1.8s	(sqrt.f64 (.f64 (.f64 n U) (-.f64 (+.f64 (/.f64 4 (.f64 Om (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (.f64 2 (/.f64 (.f64 U (.f64 U (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))))) (+.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))))) (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))))))
479.0ms	(/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))
405.0ms	(/.f64 (.f64 U (.f64 U* (.f64 n n))) (.f64 (pow.f64 Om 3) (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U*) Om)))))
97.0ms	(.f64 (.f64 n n) (.f64 U U*))

Compiler

Compiled 13016 to 7672 computations (41.1% saved)

simplify133.0ms (0%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5592	14283

prune38.0s (11.8%)

Pruning

756 alts after pruning (750 fresh and 6 done)

	Pruned	Kept	Total
New	548	228	776
Fresh	38	522	560
Picked	0	0	0
Done	3	6	9
Total	589	756	1345

Error

10.9b

Counts

1345 → 756

Compiler

Compiled 25222 to 9166 computations (63.7% saved)

simplify1.5s (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	7632	109772

regimes1.1min (20.4%)

Compiler: Compiled 576315 to 342384 computations (40.6% saved)

bsearch144.0ms (0%)

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

regimes25.8s (8%)

Compiler: Compiled 182368 to 130670 computations (28.3% saved)

bsearch55.0ms (0%)

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

regimes8.0s (2.5%)

Compiler: Compiled 72867 to 53740 computations (26.2% saved)

bsearch23.0ms (0%)

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

regimes4.9s (1.5%)

Compiler: Compiled 46218 to 33690 computations (27.1% saved)

bsearch79.0ms (0%)

Steps

Iters	Range		Point
5	7.549125585187788e+196	2.6122514552897932e+197	9.375455422571545e+196

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes3.8s (1.2%)

Compiler: Compiled 41844 to 29694 computations (29% saved)

bsearch222.0ms (0.1%)

Steps

Iters

Range

Point

5.314998492537324e-159

1.0386801479305895e-157

1.0265641528632078e-157

-1.562152382386771e+29

-9.196686888035334e+23

-7.37744113393698e+27

-1.5806317560535012e+175

-1.7048811473384043e+172

-2.288091003434274e+174

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes1.5s (0.5%)

Compiler: Compiled 8964 to 8304 computations (7.4% saved)

bsearch213.0ms (0.1%)

Steps

Iters

Range

Point

5.314998492537324e-159

1.0386801479305895e-157

1.1066923262746806e-158

-1.562152382386771e+29

-9.196686888035334e+23

-3.801842269998187e+27

-1.5806317560535012e+175

-1.7048811473384043e+172

-4.2577670731976007e+173

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes757.0ms (0.2%)

Compiler: Compiled 5568 to 5634 computations (-1.2% saved)

bsearch109.0ms (0%)

Steps

Iters	Range		Point
8	2.632898751177867e-199	7.664679565108635e-197	9.254280005184624e-198
6	-1.2035000031874361e-306	-1.567804441649184e-307	-8.939592240728657e-307

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes945.0ms (0.3%)

Compiler: Compiled 5136 to 5286 computations (-2.9% saved)

bsearch222.0ms (0.1%)

Steps

Iters

Range

Point

5.314998492537324e-159

1.0386801479305895e-157

4.897470277910266e-158

-1.2944937791330396e+36

-4.3338310691358135e+30

-3.198428286253744e+31

-1.5806317560535012e+175

-1.7048811473384043e+172

-8.006058640161498e+174

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes835.0ms (0.3%)

Compiler: Compiled 4992 to 5166 computations (-3.5% saved)

bsearch279.0ms (0.1%)

Steps

Iters	Range		Point
9	5.512787748032907e+103	8.130694421228446e+108	2.3947496780133307e+104
9	1.3626531886083067e-182	1.4008803498197553e-174	2.2782929962950365e-176
9	-1.2944937791330396e+36	-4.3338310691358135e+30	-7.7637127646784e+34
5	-1.7017763473082286e+214	-4.3034527690552585e+213	-6.389588186975487e+213

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes749.0ms (0.2%)

Compiler: Compiled 4728 to 4956 computations (-4.8% saved)

bsearch168.0ms (0.1%)

Steps

Iters	Range		Point
10	5.342961503254379e-65	8.373634271790417e-50	5.523615901209126e-50
9	-2.9294693018248504e+31	-1.9629679090509684e+26	-1.436021515694449e+29

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes270.0ms (0.1%)

Compiler: Compiled 1494 to 2052 computations (-37.3% saved)

bsearch80.0ms (0%)

Steps

Iters	Range		Point
6	3.131712232669721e+172	2.146236408257953e+173	4.512649071113925e+172

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes402.0ms (0.1%)

Compiler: Compiled 1398 to 1956 computations (-39.9% saved)

bsearch315.0ms (0.1%)

Steps

Iters	Range		Point
8	5.1576833932883234e+196	1.8304258416211185e+201	1.2202590128081094e+201
7	2.362967354053797e-141	1.4348757857415762e-139	3.13126537796642e-141
6	-1.9881294728072662e-252	-3.9405101400083607e-253	-7.593430322271435e-253
8	-2.4575217870830303e-156	-1.882826120591935e-160	-1.8628278213737705e-156
6	-2.483376131794177e-103	-6.078448364892855e-104	-1.3874823129819738e-103

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes351.0ms (0.1%)

Compiler: Compiled 1326 to 1878 computations (-41.6% saved)

bsearch38.0ms (0%)

Steps

Iters	Range		Point
5	8.488511314084413e-173	2.4783870706833654e-172	1.8625196802125445e-172

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes159.0ms (0%)

Compiler: Compiled 540 to 864 computations (-60% saved)

bsearch132.0ms (0%)

Steps

Iters	Range		Point
7	-5.502615558928749e-298	-3.980418865678054e-300	-7.128042310595049e-300
10	-1.1277153361358248e-24	-2.7380464933244435e-42	-2.0030237459866915e-25

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes62.0ms (0%)

Compiler: Compiled 108 to 282 computations (-161.1% saved)

bsearch0.0ms (0%)

regimes56.0ms (0%)

Accuracy

Total 17.8b remaining (66.6%)

Threshold costs 0b (0%)

Compiler

Compiled 60 to 216 computations (-260% saved)

bsearch43.0ms (0%)

Compiler: Compiled 1173 to 734 computations (37.4% saved)

simplify82.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	2340	1568
1	2340	1568

end0.0ms (0%)

sample47.8s (14.9%)

Algorithm

1×

intervals

Results

1.2s	13099×	body	128	nan
746.0ms	8000×	body	128	valid
111.0ms	1167×	body	128	invalid

Compiler

Compiled 73992 to 44047 computations (40.5% saved)

Pareto

0.6179769461986966