Details

analyze2.3s (9%)

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)

sample100.0ms (0.4%)

Algorithm

1×

intervals

Results

42.0ms	424×	body	128	nan
24.0ms	256×	body	128	valid
4.0ms	41×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify222.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5453	39

prune210.0ms (0.8%)

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: 32.3b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
5.9b	(.f64 (/.f64 l Om) (-.f64 U U))
9.2b	(.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)))))))
22.8b	(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))))))))

rewrite53.0ms (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:

11.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.0ms	(.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)))))))
8.0ms	(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 (18.3%)

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))))))))
777.0ms	(.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)))))))
203.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
115.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify73.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4961	2903
1	4961	2903

prune173.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Merged error: 23.2b

Counts

123 → 9

Compiler

Compiled 4326 to 1876 computations (56.6% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

22.8b	(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))))))))))
23.7b	(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))))))))
23.7b	(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))))))))
23.7b	(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))))))))

rewrite66.0ms (0.3%)

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))))))))

series8.8s (34.4%)

Counts

4 → 12

Calls

4 calls:

3.6s	(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))))))))

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4978	8663
1	4978	8663

prune327.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	95	9	104

Merged error: 23.2b

Counts

104 → 9

Compiler

Compiled 9506 to 3932 computations (58.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
5.9b	(.f64 (/.f64 l Om) (-.f64 U U))
9.2b	(.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)))))))
23.7b	(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))))))))

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
21×	`add-sqr-sqrt_binary64_435`
20×	`pow1_binary64_472`
17×	`associate-l_binary64_357`
16×	`*-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` `pow-prod-down_binary64_482`
9×	`associate-r_binary64_356`
6×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `sub-neg_binary64_407`
4×	`flip3--_binary64_418` `add-log-exp_binary64_450` `flip--_binary64_389` `frac-times_binary64_424`
3×	`*-commutative_binary64_347`
2×	`associate-*l/_binary64_359` `flip3-+_binary64_417` `cbrt-div_binary64_443` `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` `cbrt-prod_binary64_442` `pow1/3_binary64_493`

Counts

4 → 105

Calls

4 calls:

12.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.0ms	(.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)))))))
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))))))))

series2.9s (11.4%)

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))))))))
805.0ms	(.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)))))))
210.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
118.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4981	2892
1	4981	2892

prune166.0ms (0.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	115	11	126

Merged error: 18.6b

Counts

126 → 11

Compiler

Compiled 4509 to 2110 computations (53.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
5.9b	(.f64 (/.f64 l Om) (-.f64 U U))
12.1b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
13.1b	(cbrt.f64 (.f64 (.f64 2 n) U))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_435`
18×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
16×	`-un-lft-identity_binary64_414` `associate-l*_binary64_357`
14×	`add-cube-cbrt_binary64_446`
11×	`pow1_binary64_472`
10×	`times-frac_binary64_420`
9×	`associate-*r/_binary64_358`
7×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
6×	`sub-neg_binary64_407` `associate-r_binary64_356`
5×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366`
4×	`flip3--_binary64_418` `cbrt-prod_binary64_442` `pow-prod-down_binary64_482` `add-log-exp_binary64_450` `flip--_binary64_389` `frac-times_binary64_424`
2×	`associate-l/_binary64_359` `cbrt-div_binary64_443` `-commutative_binary64_347` `cbrt-undiv_binary64_445` `pow1/3_binary64_493` `unswap-sqr_binary64_382` `div-exp_binary64_462`
1×	`distribute-lft-out--_binary64_368` `flip3-+_binary64_417` `difference-of-squares_binary64_383` `div-inv_binary64_411` `flip-+_binary64_388`

Counts

4 → 91

Calls

4 calls:

11.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
4.0ms	(cbrt.f64 (.f64 (.f64 2 n) U))
3.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))

series1.3s (5%)

Counts

4 → 12

Calls

4 calls:

786.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
203.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
162.0ms	(cbrt.f64 (.f64 (.f64 2 n) U))
121.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5415	1995

prune148.0ms (0.6%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	99	15	114

Merged error: 13.2b

Counts

114 → 15

Compiler

Compiled 3708 to 1764 computations (52.4% saved)

regimes365.0ms (1.4%)

Compiler: Compiled 4914 to 3432 computations (30.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	46
1	44	46

end0.0ms (0%)

sample3.3s (13%)

Algorithm

1×

intervals

Results

1.2s	12756×	body	128	nan
769.0ms	8000×	body	128	valid
117.0ms	1201×	body	128	invalid

Compiler

Compiled 637 to 444 computations (30.3% saved)

Details

analyze2.3s (9%)

sample100.0ms (0.4%)

simplify222.0ms (0.9%)

prune210.0ms (0.8%)

localize17.0ms (0.1%)

rewrite53.0ms (0.2%)

series4.7s (18.3%)

simplify73.0ms (0.3%)

prune173.0ms (0.7%)

localize27.0ms (0.1%)

rewrite66.0ms (0.3%)

series8.8s (34.4%)

simplify109.0ms (0.4%)

prune327.0ms (1.3%)

localize24.0ms (0.1%)

rewrite53.0ms (0.2%)

series2.9s (11.4%)

simplify80.0ms (0.3%)

prune166.0ms (0.6%)

localize28.0ms (0.1%)

rewrite40.0ms (0.2%)

series1.3s (5%)

simplify44.0ms (0.2%)

prune148.0ms (0.6%)

regimes365.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (13%)

Profiling