Details

analyze3.0s (0.5%)

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)

sample143.0ms (0%)

Algorithm

1×

intervals

Results

62.0ms	436×	body	128	nan
34.0ms	256×	body	128	valid
5.0ms	34×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify156.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5178	39

prune9.0ms (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

Merged error: 32.7b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.3b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
11.4b	(.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)))))))
20.2b	(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))))))))

rewrite70.0ms (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

4 calls:

15.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
14.0ms	(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))))))))
12.0ms	(.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)))))))
12.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))

series3.9s (0.7%)

Counts

4 → 12

Calls

4 calls:

3.0s	(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))))))))
623.0ms	(.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)))))))
181.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
151.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify102.0ms (0%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5099	4107

prune1.1s (0.2%)

Pruning

61 alts after pruning (61 fresh and 0 done)

	Pruned	Kept	Total
New	83	60	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	61	145

Merged error: 24.3b

Counts

145 → 61

Compiler

Compiled 7498 to 3567 computations (52.4% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
6.8b	(*.f64 n (/.f64 l Om))
11.4b	(.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))))))
20.2b	(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)))))))

rewrite64.0ms (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

4 calls:

17.0ms	(.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))))))
14.0ms	(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)))))))
11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
8.0ms	(*.f64 n (/.f64 l Om))

series3.5s (0.6%)

Counts

4 → 12

Calls

4 calls:

2.7s	(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)))))))
622.0ms	(.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))))))
148.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
30.0ms	(*.f64 n (/.f64 l Om))

simplify109.0ms (0%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5059	2829

prune1.5s (0.2%)

Pruning

87 alts after pruning (86 fresh and 1 done)

	Pruned	Kept	Total
New	77	42	119
Fresh	16	44	60
Picked	0	1	1
Done	0	0	0
Total	93	87	180

Merged error: 22.8b

Counts

180 → 87

Compiler

Compiled 7522 to 3896 computations (48.2% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
6.8b	(*.f64 n (/.f64 l Om))
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)))))))
20.2b	(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))))))))

rewrite72.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_480`
30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`add-sqr-sqrt_binary64_441`
20×	`pow-prod-down_binary64_490`
19×	`associate-r_binary64_359`
17×	`*-un-lft-identity_binary64_419`
15×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
14×	`associate-*r/_binary64_361`
10×	`times-frac_binary64_425`
8×	`distribute-rgt-in_binary64_369` `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×	`*-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 → 111

Calls

4 calls:

23.0ms	(.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)))))))
8.0ms	(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))))))))
7.0ms	(*.f64 n (/.f64 l Om))

series4.0s (0.7%)

Counts

4 → 12

Calls

4 calls:

3.1s	(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))))))))
684.0ms	(.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)))))))
132.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
23.0ms	(*.f64 n (/.f64 l Om))

simplify142.0ms (0%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5016	2927

prune1.6s (0.3%)

Pruning

108 alts after pruning (106 fresh and 2 done)

	Pruned	Kept	Total
New	90	33	123
Fresh	12	73	85
Picked	0	1	1
Done	0	1	1
Total	102	108	210

Merged error: 19.8b

Counts

210 → 108

Compiler

Compiled 8585 to 4503 computations (47.5% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
6.8b	(*.f64 n (/.f64 l Om))
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)))))))
20.2b	(pow.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))))))) 1/2)

rewrite76.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-exp-log_binary64_457`
36×	`pow1_binary64_480`
30×	`add-cbrt-cube_binary64_455`
23×	`prod-exp_binary64_468` `add-sqr-sqrt_binary64_441`
20×	`pow-prod-down_binary64_490`
19×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`add-cube-cbrt_binary64_454`
15×	`cbrt-unprod_binary64_452`
10×	`times-frac_binary64_425` `associate-*r/_binary64_361`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`pow-exp_binary64_487` `associate-l_binary64_360` `pow-pow_binary64_491`
4×	`add-log-exp_binary64_458`
3×	`*-commutative_binary64_350` `pow-unpow_binary64_496`
2×	`sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `difference-of-squares_binary64_388` `unpow-prod-down_binary64_498` `div-inv_binary64_416` `sqr-pow_binary64_391` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `flip-+_binary64_393` `unpow1/2_binary64_483`

Counts

4 → 119

Calls

4 calls:

19.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
14.0ms	(*.f64 n (/.f64 l Om))
10.0ms	(pow.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))))))) 1/2)
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)))))))

series1.9s (0.3%)

Counts

4 → 12

Calls

4 calls:

1.1s	(pow.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))))))) 1/2)
667.0ms	(.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)))))))
118.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
27.0ms	(*.f64 n (/.f64 l Om))

simplify103.0ms (0%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4961	3141
1	4961	3141

prune2.5s (0.4%)

Pruning

130 alts after pruning (128 fresh and 2 done)

	Pruned	Kept	Total
New	95	36	131
Fresh	13	92	105
Picked	1	0	1
Done	0	2	2
Total	109	130	239

Merged error: 19.8b

Counts

239 → 130

Compiler

Compiled 4268 to 1843 computations (56.8% saved)

regimes13.6s (2.3%)

Compiler: Compiled 84044 to 57418 computations (31.7% saved)

bsearch9.4min (93.7%)

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

Details

analyze3.0s (0.5%)

sample143.0ms (0%)

simplify156.0ms (0%)

prune9.0ms (0%)

localize19.0ms (0%)

rewrite70.0ms (0%)

series3.9s (0.7%)

simplify102.0ms (0%)

prune1.1s (0.2%)

localize36.0ms (0%)

rewrite64.0ms (0%)

series3.5s (0.6%)

simplify109.0ms (0%)

prune1.5s (0.2%)

localize18.0ms (0%)

rewrite72.0ms (0%)

series4.0s (0.7%)

simplify142.0ms (0%)

prune1.6s (0.3%)

localize29.0ms (0%)

rewrite76.0ms (0%)

series1.9s (0.3%)

simplify103.0ms (0%)

prune2.5s (0.4%)

regimes13.6s (2.3%)

bsearch9.4min (93.7%)

Profiling