Details

analyze2.2s (6.7%)

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)

sample109.0ms (0.3%)

Algorithm

1×

intervals

Results

41.0ms	483×	body	128	nan
26.0ms	256×	body	128	valid
3.0ms	36×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify143.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5178	39

prune5.0ms (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

31.3b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.6b	(.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)))))))
12.0b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
19.8b	(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))))))))

rewrite248.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

24.3b

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:

13.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series4.3s (13%)

Error

19.1b

Counts

4 → 112

Calls

4 calls:

1.9s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
1.0s	(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))))))))
824.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
326.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11564 to 8738 computations (24.4% saved)

simplify125.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4974	7813
1	4974	7813

prune342.0ms (1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	226	17	243
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	227	18	245

Error

16.4b

Counts

245 → 18

Compiler

Compiled 8626 to 3203 computations (62.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
6.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
6.4b	(/.f64 (.f64 l (-.f64 U U)) Om)
19.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

rewrite158.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

12.9b

Rules

31×	`pow1_binary64_480`
23×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
17×	`pow-prod-down_binary64_490`
12×	`associate-*r/_binary64_361`
10×	`add-sqr-sqrt_binary64_441` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
5×	`sqrt-pow1_binary64_437` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458` `associate-l_binary64_360` `associate-r_binary64_359`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364` `unswap-sqr_binary64_387`

Counts

4 → 89

Calls

4 calls:

9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
8.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))

Compiler

Compiled 3633 to 1482 computations (59.2% saved)

series4.8s (14.5%)

Error

16.1b

Counts

4 → 117

Calls

4 calls:

2.0s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
1.4s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
1.0s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
152.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 12164 to 9315 computations (23.4% saved)

simplify120.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4974	7689
1	4974	7689

prune272.0ms (0.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	199	7	206
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	203	21	224

Error

12.5b

Counts

224 → 21

Compiler

Compiled 7677 to 2752 computations (64.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.6b	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
10.6b	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
19.8b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
19.8b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

rewrite223.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

12.5b

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

Compiler

Compiled 5946 to 2494 computations (58.1% saved)

series6.7s (20.3%)

Error

12.5b

Counts

4 → 130

Calls

4 calls:

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

Compiler

Compiled 25592 to 17678 computations (30.9% saved)

simplify153.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4991	9892
1	4991	9892

prune675.0ms (2%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	19	19
Picked	0	1	1
Done	0	1	1
Total	210	21	231

Error

12.5b

Counts

231 → 21

Compiler

Compiled 14335 to 5513 computations (61.5% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

4.0b	(.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om))))
6.3b	(.f64 (.f64 2 n) (.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om)))))
8.9b	(/.f64 (*.f64 l l) Om)
15.7b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om))))))

rewrite151.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

12.5b

Rules

31×	`pow1_binary64_480`
23×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
17×	`pow-prod-down_binary64_490`
10×	`add-sqr-sqrt_binary64_441` `associate-*r/_binary64_361` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
8×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
6×	`sub-neg_binary64_412` `cancel-sign-sub-inv_binary64_385`
5×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `associate-l_binary64_360` `associate-r_binary64_359`
3×	`flip3--_binary64_423` `flip--_binary64_394` `times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l*_binary64_364` `unswap-sqr_binary64_387`

Counts

4 → 93

Calls

4 calls:

10.0ms	(.f64 (.f64 2 n) (.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om)))))
10.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om))))))
6.0ms	(.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om))))
5.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 2365 to 1224 computations (48.2% saved)

series1.4s (4.1%)

Error

12.4b

Counts

4 → 72

Calls

4 calls:

513.0ms	(.f64 (.f64 2 n) (.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om)))))
409.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om))))))
295.0ms	(.f64 U (-.f64 t (.f64 2 (/.f64 (*.f64 l l) Om))))
67.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 3907 to 3324 computations (14.9% saved)

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5365	3209

prune162.0ms (0.5%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	155	10	165
Fresh	4	14	18
Picked	1	0	1
Done	0	2	2
Total	160	26	186

Error

12.4b

Counts

186 → 26

Compiler

Compiled 3179 to 1585 computations (50.1% saved)

regimes4.0s (12.1%)

Accuracy

Total 18.0b remaining (62.5%)

Threshold costs 0b (0%)

Compiler

Compiled 40498 to 30418 computations (24.9% saved)

bsearch180.0ms (0.5%)

Steps

Iters	Range		Point
10	2.9089825744938623e+60	1.3623543189394292e+71	7.872510036920366e+64
4	8.631074684961277e-191	1.5218987040325567e-190	1.3211102329035494e-190
6	9.317417404514546e-300	5.389367161167212e-299	9.437245162500533e-300

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	163
1	131	163

end0.0ms (0%)

sample6.5s (19.6%)

Algorithm

1×

intervals

Results

1.2s	13383×	body	128	nan
741.0ms	8000×	body	128	valid
118.0ms	1268×	body	128	invalid

Compiler

Compiled 5184 to 3878 computations (25.2% saved)

Details

analyze2.2s (6.7%)

sample109.0ms (0.3%)

simplify143.0ms (0.4%)

prune5.0ms (0%)

localize16.0ms (0%)

rewrite248.0ms (0.8%)

series4.3s (13%)

simplify125.0ms (0.4%)

prune342.0ms (1%)

localize18.0ms (0.1%)

rewrite158.0ms (0.5%)

series4.8s (14.5%)

simplify120.0ms (0.4%)

prune272.0ms (0.8%)

localize22.0ms (0.1%)

rewrite223.0ms (0.7%)

series6.7s (20.3%)

simplify153.0ms (0.5%)

prune675.0ms (2%)

localize12.0ms (0%)

rewrite151.0ms (0.5%)

series1.4s (4.1%)

simplify62.0ms (0.2%)

prune162.0ms (0.5%)

regimes4.0s (12.1%)

bsearch180.0ms (0.5%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.5s (19.6%)

Profiling