Details

analyze2.5s (7.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample109.0ms (0.3%)

Algorithm

1×

intervals

Results

39.0ms	410×	body	128	nan
29.0ms	256×	body	128	valid
3.0ms	31×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify53.0ms (0.2%)

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)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
8.5b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
9.6b	(.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)))))))
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))))))))

rewrite243.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

22.5b

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×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

4 → 131

Calls

4 calls:

12.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
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))))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series4.4s (12.9%)

Error

20.4b

Counts

4 → 114

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)))))))
1.1s	(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))))))))
839.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
316.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 12053 to 9083 computations (24.6% saved)

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4952	8179
1	4952	8179

prune339.0ms (1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	227	18	245
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	227	20	247

Error

15.4b

Counts

247 → 20

Compiler

Compiled 8818 to 3298 computations (62.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
4.9b	(/.f64 (.f64 l (-.f64 U U)) Om)
5.5b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
20.2b	(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)))))))

rewrite156.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

12.0b

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
9.0ms	(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)))))))
8.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
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 3313 to 1330 computations (59.9% saved)

series3.3s (9.7%)

Error

14.6b

Counts

4 → 105

Calls

4 calls:

1.5s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
1.1s	(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)))))))
310.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
221.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 10593 to 7780 computations (26.6% saved)

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4978	5624
1	4978	5624

prune261.0ms (0.8%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	1	17	18
Picked	1	0	1
Done	0	1	1
Total	188	25	213

Error

12.3b

Counts

213 → 25

Compiler

Compiled 7019 to 2860 computations (59.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
4.7b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))
11.0b	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))
20.2b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))

rewrite179.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

12.3b

Rules

36×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441` `associate-l_binary64_360`
21×	`*-un-lft-identity_binary64_419`
20×	`pow-prod-down_binary64_490`
15×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `times-frac_binary64_425`
10×	`associate-*r/_binary64_361`
5×	`sqrt-pow1_binary64_437` `associate-r_binary64_359` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`

Counts

4 → 105

Calls

4 calls:

12.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
11.0ms	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))

Compiler

Compiled 4245 to 1677 computations (60.5% saved)

series5.1s (14.9%)

Error

12.2b

Counts

4 → 126

Calls

4 calls:

2.0s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
1.5s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))
1.1s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))
326.0ms	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))

Compiler

Compiled 13219 to 10003 computations (24.3% saved)

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5195	8636

prune296.0ms (0.9%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	22	23
Picked	0	1	1
Done	0	1	1
Total	231	25	256

Error

12.3b

Counts

256 → 25

Compiler

Compiled 8780 to 3166 computations (63.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.6b	(.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)))))
9.6b	(.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)))))
20.2b	(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))))))
20.2b	(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

12.3b

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)))))
9.0ms	(.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)))))
9.0ms	(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 (19.6%)

Error

12.3b

Counts

4 → 132

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 26108 to 18046 computations (30.9% saved)

simplify117.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5326	10616

prune475.0ms (1.4%)

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	22	22
Picked	0	1	1
Done	0	2	2
Total	212	25	237

Error

12.3b

Counts

237 → 25

Compiler

Compiled 14210 to 5211 computations (63.3% saved)

regimes3.3s (9.5%)

Accuracy

Total 18.2b remaining (63.5%)

Threshold costs 0b (0%)

Compiler

Compiled 32906 to 25010 computations (24% saved)

bsearch122.0ms (0.4%)

Steps

Iters	Range		Point
9	2.2716978819603663e-204	1.658545335045418e-199	3.939700855501485e-203
5	-5.884798689140472e-214	-1.7725277171147971e-214	-2.709125090441015e-214

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	131
1	79	131

end0.0ms (0%)

sample6.0s (17.4%)

Algorithm

1×

intervals

Results

1.2s	12271×	body	128	nan
804.0ms	8000×	body	128	valid
116.0ms	1182×	body	128	invalid

Compiler

Compiled 4214 to 3188 computations (24.3% saved)

Details

analyze2.5s (7.3%)

sample109.0ms (0.3%)

simplify53.0ms (0.2%)

prune5.0ms (0%)

localize22.0ms (0.1%)

rewrite243.0ms (0.7%)

series4.4s (12.9%)

simplify108.0ms (0.3%)

prune339.0ms (1%)

localize18.0ms (0.1%)

rewrite156.0ms (0.5%)

series3.3s (9.7%)

simplify101.0ms (0.3%)

prune261.0ms (0.8%)

localize19.0ms (0.1%)

rewrite179.0ms (0.5%)

series5.1s (14.9%)

simplify92.0ms (0.3%)

prune296.0ms (0.9%)

localize22.0ms (0.1%)

rewrite223.0ms (0.7%)

series6.7s (19.6%)

simplify117.0ms (0.3%)

prune475.0ms (1.4%)

regimes3.3s (9.5%)

bsearch122.0ms (0.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.0s (17.4%)

Profiling