Details

analyze2.4s (6.6%)

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)

sample107.0ms (0.3%)

Algorithm

1×

intervals

Results

42.0ms	436×	body	128	nan
23.0ms	256×	body	128	valid
3.0ms	32×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify51.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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

30.9b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize16.0ms (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)))))
7.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
8.6b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
22.5b	(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))))))))

rewrite271.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

23.9b

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

series4.2s (11.6%)

Error

18.0b

Counts

4 → 111

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)))))))
972.0ms	(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))))))))
804.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
327.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11350 to 8585 computations (24.4% saved)

simplify120.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5042	7717

prune364.0ms (1%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	214	28	242
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	215	29	244

Error

15.7b

Counts

244 → 29

Compiler

Compiled 8879 to 3448 computations (61.2% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

5.0b	(.f64 (-.f64 U U) (/.f64 n Om))
5.4b	(.f64 l (.f64 (-.f64 U* U) (/.f64 n Om)))
7.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om)))))))
22.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om))))))))

rewrite181.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

15.2b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
21×	`add-sqr-sqrt_binary64_441`
17×	`associate-r_binary64_359`
16×	`pow-prod-down_binary64_490` `*-un-lft-identity_binary64_419`
14×	`add-cube-cbrt_binary64_454`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`associate-*r/_binary64_361`
10×	`times-frac_binary64_425`
9×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `associate-*l/_binary64_362`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

Counts

4 → 103

Calls

4 calls:

10.0ms	(.f64 (-.f64 U U) (/.f64 n Om))
10.0ms	(.f64 l (.f64 (-.f64 U* U) (/.f64 n Om)))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om))))))))

Compiler

Compiled 3954 to 1619 computations (59.1% saved)

series3.7s (10.2%)

Error

14.2b

Counts

4 → 102

Calls

4 calls:

2.0s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om)))))))
1.0s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om))))))))
344.0ms	(.f64 l (.f64 (-.f64 U* U) (/.f64 n Om)))
217.0ms	(.f64 (-.f64 U U) (/.f64 n Om))

Compiler

Compiled 10454 to 7768 computations (25.7% saved)

simplify90.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4984	5926
1	4984	5926

prune275.0ms (0.8%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	199	6	205
Fresh	4	24	28
Picked	0	1	1
Done	0	0	0
Total	203	31	234

Error

15.2b

Counts

234 → 31

Compiler

Compiled 7521 to 3105 computations (58.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om)))))
5.0b	(.f64 (-.f64 U U) (/.f64 n Om))
5.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om))))))
22.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om)))))))

rewrite190.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

13.4b

Rules

33×	`pow1_binary64_480`
23×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `add-sqr-sqrt_binary64_441`
18×	`pow-prod-down_binary64_490`
17×	`associate-r_binary64_359`
16×	`*-un-lft-identity_binary64_419`
14×	`add-cube-cbrt_binary64_454`
11×	`associate-*r/_binary64_361` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`times-frac_binary64_425`
9×	`associate-l_binary64_360`
5×	`sqrt-pow1_binary64_437` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `*-commutative_binary64_350` `unswap-sqr_binary64_387`
2×	`sqrt-div_binary64_436` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `associate-*l/_binary64_362`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

Counts

4 → 104

Calls

4 calls:

10.0ms	(.f64 (-.f64 U U) (/.f64 n Om))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om))))))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om)))))))
6.0ms	(.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om)))))

Compiler

Compiled 3875 to 1667 computations (57% saved)

series4.9s (13.4%)

Error

13.7b

Counts

4 → 120

Calls

4 calls:

2.0s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om))))))
1.5s	(.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om)))))
999.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 l (.f64 (+.f64 -2 (.f64 (-.f64 U* U) (/.f64 n Om))) (/.f64 l Om)))))))
212.0ms	(.f64 (-.f64 U U) (/.f64 n Om))

Compiler

Compiled 12126 to 9288 computations (23.4% saved)

simplify118.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4988	7688
1	4988	7688

prune535.0ms (1.5%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	217	7	224
Fresh	6	23	29
Picked	1	0	1
Done	1	0	1
Total	225	30	255

Error

13.4b

Counts

255 → 30

Compiler

Compiled 8202 to 3177 computations (61.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.2b	(cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))
7.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (/.f64 l Om) (.f64 (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))) (cbrt.f64 (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))
8.6b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
22.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (/.f64 l Om) (.f64 (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))) (cbrt.f64 (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))))))

rewrite333.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

13.4b

Rules

28×	`pow1_binary64_480`
25×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
17×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
15×	`pow-prod-down_binary64_490`
14×	`associate-l_binary64_360`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cancel-sign-sub-inv_binary64_385`
10×	`associate-*r/_binary64_361`
9×	`times-frac_binary64_425`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `sub-neg_binary64_412` `associate-r_binary64_359`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `cbrt-prod_binary64_450`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `*-commutative_binary64_350` `cbrt-div_binary64_451`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `div-inv_binary64_416` `pow1/3_binary64_501`

Counts

4 → 106

Calls

4 calls:

12.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (/.f64 l Om) (.f64 (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))) (cbrt.f64 (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))
9.0ms	(cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (/.f64 l Om) (.f64 (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))) (cbrt.f64 (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))))))

Compiler

Compiled 8411 to 3185 computations (62.1% saved)

series5.8s (15.9%)

Error

11.9b

Counts

4 → 101

Calls

4 calls:

2.9s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (/.f64 l Om) (.f64 (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))) (cbrt.f64 (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U))))))))
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (/.f64 l Om) (.f64 (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) (cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))) (cbrt.f64 (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))))))
792.0ms	(cbrt.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))
359.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 17098 to 10982 computations (35.8% saved)

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4968	7171
1	4968	7171

prune401.0ms (1.1%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	2	27	29
Picked	0	1	1
Done	0	0	0
Total	206	31	237

Error

12.9b

Counts

237 → 31

Compiler

Compiled 11197 to 4172 computations (62.7% saved)

regimes4.5s (12.5%)

Accuracy

Total 16.9b remaining (61.8%)

Threshold costs 0b (0%)

Compiler

Compiled 51754 to 36898 computations (28.7% saved)

bsearch14.0ms (0%)

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

simplify69.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	1329	359
1	1329	359

end0.0ms (0%)

sample7.4s (20.5%)

Algorithm

1×

intervals

Results

1.2s	12801×	body	128	nan
754.0ms	8000×	body	128	valid
112.0ms	1205×	body	128	invalid

Compiler

Compiled 6721 to 4760 computations (29.2% saved)

Details

analyze2.4s (6.6%)

sample107.0ms (0.3%)

simplify51.0ms (0.1%)

prune5.0ms (0%)

localize16.0ms (0%)

rewrite271.0ms (0.8%)

series4.2s (11.6%)

simplify120.0ms (0.3%)

prune364.0ms (1%)

localize18.0ms (0%)

rewrite181.0ms (0.5%)

series3.7s (10.2%)

simplify90.0ms (0.2%)

prune275.0ms (0.8%)

localize18.0ms (0.1%)

rewrite190.0ms (0.5%)

series4.9s (13.4%)

simplify118.0ms (0.3%)

prune535.0ms (1.5%)

localize28.0ms (0.1%)

rewrite333.0ms (0.9%)

series5.8s (15.9%)

simplify108.0ms (0.3%)

prune401.0ms (1.1%)

regimes4.5s (12.5%)

bsearch14.0ms (0%)

simplify69.0ms (0.2%)

end0.0ms (0%)

sample7.4s (20.5%)

Profiling