Details

analyze2.6s (3.5%)

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 (0.1%)

Algorithm

1×

intervals

Results

42.0ms	415×	body	128	nan
24.0ms	256×	body	128	valid
4.0ms	40×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5178	39

prune7.0ms (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

31.4b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.9b	(.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)))))))
11.0b	(.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))))))))

rewrite412.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

21.9b

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:

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 4884 to 1897 computations (61.2% saved)

series7.1s (9.8%)

Error

18.7b

Counts

4 → 113

Calls

4 calls:

3.3s	(.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)))))))
1.9s	(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))))))))
1.4s	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
476.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 9777 to 7632 computations (21.9% saved)

simplify122.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4992	8014
1	4992	8014

prune369.0ms (0.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	221	23	244
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	223	23	246

Error

14.3b

Counts

246 → 23

Compiler

Compiled 5623 to 2398 computations (57.4% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

5.2b	(*.f64 n (/.f64 l Om))
6.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.9b	(.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))))))
19.8b	(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)))))))

rewrite307.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

14.3b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`add-cube-cbrt_binary64_454` `pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`associate-*r/_binary64_361` `times-frac_binary64_425`
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` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `sub-neg_binary64_412` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

Counts

4 → 107

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.0ms	(.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))))))
7.0ms	(*.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)))))))

Compiler

Compiled 3759 to 1527 computations (59.4% saved)

series5.9s (8%)

Error

13.6b

Counts

4 → 95

Calls

4 calls:

3.3s	(.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))))))
1.9s	(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)))))))
477.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
148.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 8591 to 6699 computations (22% saved)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5020	6293

prune313.0ms (0.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	194	8	202
Fresh	8	14	22
Picked	1	0	1
Done	0	0	0
Total	203	22	225

Error

14.3b

Counts

225 → 22

Compiler

Compiled 4615 to 2036 computations (55.9% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

5.0b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))
7.0b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
7.0b	(.f64 (-.f64 U U) (/.f64 l Om))
19.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))))

rewrite292.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

11.4b

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` `unswap-sqr_binary64_387` `*-commutative_binary64_350`
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:

11.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
11.0ms	(.f64 (-.f64 U U) (/.f64 l Om))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))

Compiler

Compiled 3803 to 1545 computations (59.4% saved)

series8.1s (11.1%)

Error

13.6b

Counts

4 → 122

Calls

4 calls:

3.3s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
2.5s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))
1.8s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))))
307.0ms	(.f64 (-.f64 U U) (/.f64 l Om))

Compiler

Compiled 10371 to 8189 computations (21% saved)

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4984	8231
1	4984	8231

prune325.0ms (0.4%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	214	12	226
Fresh	7	14	21
Picked	1	0	1
Done	0	0	0
Total	222	26	248

Error

11.4b

Counts

248 → 26

Compiler

Compiled 5210 to 2257 computations (56.7% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

6.0b	(.f64 (.f64 2 n) (.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))
6.5b	(.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))
7.0b	(.f64 (-.f64 U U) (/.f64 l Om))
19.8b	(sqrt.f64 (+.f64 (.f64 2 (.f64 t (.f64 U n))) (.f64 (.f64 2 n) (.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))))

rewrite434.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

10.7b

Rules

50×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
33×	`pow1_binary64_480`
29×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
22×	`add-sqr-sqrt_binary64_441`
20×	`associate-*r/_binary64_361`
19×	`pow-prod-down_binary64_490`
16×	`*-un-lft-identity_binary64_419` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
15×	`associate-r_binary64_359`
14×	`add-cube-cbrt_binary64_454`
10×	`times-frac_binary64_425`
9×	`associate-l_binary64_360`
6×	`frac-times_binary64_429`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-*l/_binary64_362`
3×	`sqrt-prod_binary64_435` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

Counts

4 → 127

Calls

4 calls:

24.0ms	(.f64 (.f64 2 n) (.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))
18.0ms	(.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))
11.0ms	(.f64 (-.f64 U U) (/.f64 l Om))
8.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 t (.f64 U n))) (.f64 (.f64 2 n) (.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))))

Compiler

Compiled 5588 to 2160 computations (61.3% saved)

series5.4s (7.4%)

Error

10.8b

Counts

4 → 94

Calls

4 calls:

2.1s	(.f64 (.f64 2 n) (.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))
1.7s	(.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))
1.2s	(sqrt.f64 (+.f64 (.f64 2 (.f64 t (.f64 U n))) (.f64 (.f64 2 n) (.f64 U (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))) (*.f64 l -2)))))))
315.0ms	(.f64 (-.f64 U U) (/.f64 l Om))

Compiler

Compiled 8753 to 6732 computations (23.1% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5292	7362

prune331.0ms (0.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	209	12	221
Fresh	9	16	25
Picked	1	0	1
Done	0	0	0
Total	219	28	247

Error

9.8b

Counts

247 → 28

Compiler

Compiled 4762 to 1769 computations (62.9% saved)

regimes36.4s (50%)

Accuracy

Total 16.2b remaining (62.3%)

Threshold costs 0b (0%)

Compiler

Compiled 244686 to 169444 computations (30.8% saved)

bsearch63.0ms (0.1%)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	246	329
1	246	329

end8.0ms (0%)

Compiler: Compiled 217 to 115 computations (47% saved)

sample3.9s (5.4%)

Algorithm

1×

intervals

Results

1.2s	12963×	body	128	nan
772.0ms	8000×	body	128	valid
110.0ms	1166×	body	128	invalid

Compiler

Compiled 1245 to 844 computations (32.2% saved)

Details

analyze2.6s (3.5%)

sample109.0ms (0.1%)

simplify50.0ms (0.1%)

prune7.0ms (0%)

localize21.0ms (0%)

rewrite412.0ms (0.6%)

series7.1s (9.8%)

simplify122.0ms (0.2%)

prune369.0ms (0.5%)

localize18.0ms (0%)

rewrite307.0ms (0.4%)

series5.9s (8%)

simplify71.0ms (0.1%)

prune313.0ms (0.4%)

localize18.0ms (0%)

rewrite292.0ms (0.4%)

series8.1s (11.1%)

simplify102.0ms (0.1%)

prune325.0ms (0.4%)

localize26.0ms (0%)

rewrite434.0ms (0.6%)

series5.4s (7.4%)

simplify79.0ms (0.1%)

prune331.0ms (0.5%)

regimes36.4s (50%)

bsearch63.0ms (0.1%)

simplify7.0ms (0%)

end8.0ms (0%)

sample3.9s (5.4%)

Profiling