Details

analyze2.3s (6.6%)

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)

sample103.0ms (0.3%)

Algorithm

1×

intervals

Results

45.0ms	431×	body	128	nan
25.0ms	256×	body	128	valid
4.0ms	40×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify212.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5453	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

Merged error: 30.0b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize222.0ms (0.6%)

Local error

Found 4 expressions with local error:

5.4b	(.f64 (/.f64 l Om) (-.f64 U U))
6.2b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.6b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
17.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite57.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_472`
27×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
21×	`add-sqr-sqrt_binary64_435`
17×	`associate-l_binary64_357`
16×	`pow-prod-down_binary64_482` `*-un-lft-identity_binary64_414`
14×	`add-cube-cbrt_binary64_446`
13×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444` `associate-*r/_binary64_358`
10×	`times-frac_binary64_420`
9×	`associate-r_binary64_356`
6×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `sub-neg_binary64_407`
4×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `add-log-exp_binary64_450` `flip--_binary64_389` `frac-times_binary64_424`
3×	`*-commutative_binary64_347`
2×	`sqrt-div_binary64_430` `associate-*l/_binary64_359` `flip3-+_binary64_417` `cbrt-undiv_binary64_445` `flip-+_binary64_388` `unswap-sqr_binary64_382` `div-exp_binary64_462`
1×	`distribute-lft-out--_binary64_368` `difference-of-squares_binary64_383` `div-inv_binary64_411` `sqrt-prod_binary64_429` `pow1/2_binary64_491`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
11.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
9.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series4.7s (13.2%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
794.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
208.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
122.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	2903
1	4961	2903

prune194.0ms (0.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	11	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	111	12	123

Merged error: 19.3b

Counts

123 → 12

Compiler

Compiled 4604 to 2018 computations (56.2% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

12.6b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
12.6b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
12.6b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
17.1b	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))))

rewrite65.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-div_binary64_443`
34×	`pow1_binary64_472`
32×	`associate-*r/_binary64_358`
30×	`flip3-+_binary64_417` `flip-+_binary64_388`
28×	`frac-times_binary64_424`
26×	`sqrt-div_binary64_430`
22×	`pow-prod-down_binary64_482`
14×	`associate-*l/_binary64_359`
9×	`cbrt-prod_binary64_442`
8×	`sqrt-pow1_binary64_431`
7×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
4×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
3×	`pow1/3_binary64_493`
1×	`sqrt-prod_binary64_429` `pow1/2_binary64_491`

Counts

4 → 82

Calls

4 calls:

24.0ms	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))))
3.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
3.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
3.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))

series5.9s (16.7%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U))))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))))
784.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
763.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
750.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5165	8429

prune314.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	92	14	106

Merged error: 19.3b

Counts

106 → 14

Compiler

Compiled 9585 to 3733 computations (61.1% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

17.1b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
18.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
18.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
18.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite67.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`associate-*r/_binary64_358`
60×	`cbrt-div_binary64_443`
30×	`flip3-+_binary64_417` `flip-+_binary64_388`
28×	`frac-times_binary64_424`
26×	`sqrt-div_binary64_430`
24×	`pow1_binary64_472`
15×	`sqrt-pow1_binary64_431`
14×	`associate-*l/_binary64_359`
12×	`pow1/3_binary64_493`
9×	`pow-prod-up_binary64_481`
6×	`pow-plus_binary64_474`
5×	`pow-prod-down_binary64_482`
4×	`add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450` `add-sqr-sqrt_binary64_435`
3×	`cbrt-prod_binary64_442` `pow-sqr_binary64_387`
2×	`pow2_binary64_492`
1×	`sqrt-prod_binary64_429` `pow3_binary64_494` `pow1/2_binary64_491`

Counts

4 → 83

Calls

4 calls:

16.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series8.9s (25.1%)

Counts

4 → 12

Calls

4 calls:

3.5s	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
1.8s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.8s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.8s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4978	8663
1	4978	8663

prune333.0ms (0.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	95	14	109

Merged error: 19.3b

Counts

109 → 14

Compiler

Compiled 9813 to 4079 computations (58.4% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

18.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
18.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
18.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
18.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite51.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-div_binary64_443` `associate-*r/_binary64_358`
4×	`pow1_binary64_472` `flip3-+_binary64_417` `add-cube-cbrt_binary64_446` `cbrt-prod_binary64_442` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450` `flip-+_binary64_388` `pow1/3_binary64_493` `add-sqr-sqrt_binary64_435`

Counts

4 → 44

Calls

4 calls:

8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series7.1s (20%)

Counts

4 → 12

Calls

4 calls:

1.8s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.8s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.7s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.7s	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5179	2760

prune288.0ms (0.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	56	14	70

Merged error: 19.3b

Counts

70 → 14

Compiler

Compiled 8444 to 3679 computations (56.4% saved)

regimes492.0ms (1.4%)

Compiler: Compiled 6482 to 3784 computations (41.6% saved)

bsearch225.0ms (0.6%)

Steps

Iters	Range	Point
7	1.3813626235032825e-188	8.075925475936597e-187	9.132669359376227e-188
8	3.82656781506019e-246	1.0494171687130168e-241	2.4664257672184813e-245
7	3.6584968644803915e-303	5.774867186302213e-301	8.057802521813321e-302

Iters

Range

Point

1.3813626235032825e-188

8.075925475936597e-187

9.132669359376227e-188

3.82656781506019e-246

1.0494171687130168e-241

2.4664257672184813e-245

3.6584968644803915e-303

5.774867186302213e-301

8.057802521813321e-302

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	66	205
1	66	205

end0.0ms (0%)

sample3.5s (9.8%)

Algorithm

1×

intervals

Results

1.3s	13025×	body	128	nan
791.0ms	8000×	body	128	valid
127.0ms	1256×	body	128	invalid

Compiler

Compiled 938 to 530 computations (43.5% saved)

Details

analyze2.3s (6.6%)

sample103.0ms (0.3%)

simplify212.0ms (0.6%)

prune5.0ms (0%)

localize222.0ms (0.6%)

rewrite57.0ms (0.2%)

series4.7s (13.2%)

simplify71.0ms (0.2%)

prune194.0ms (0.5%)

localize23.0ms (0.1%)

rewrite65.0ms (0.2%)

series5.9s (16.7%)

simplify101.0ms (0.3%)

prune314.0ms (0.9%)

localize27.0ms (0.1%)

rewrite67.0ms (0.2%)

series8.9s (25.1%)

simplify108.0ms (0.3%)

prune333.0ms (0.9%)

localize30.0ms (0.1%)

rewrite51.0ms (0.1%)

series7.1s (20%)

simplify65.0ms (0.2%)

prune288.0ms (0.8%)

regimes492.0ms (1.4%)

bsearch225.0ms (0.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.5s (9.8%)

Profiling