Details

analyze2.4s (7.2%)

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)

sample107.0ms (0.3%)

Algorithm

1×

intervals

Results

42.0ms	428×	body	128	nan
26.0ms	256×	body	128	valid
8.0ms	39×	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 (57.0ms)

Iter	Nodes	Cost
0	5453	39

prune8.0ms (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)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(.f64 (/.f64 l Om) (-.f64 U U))
6.3b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
10.0b	(.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)))))))
19.3b	(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:

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	(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 (13.8%)

Counts

4 → 12

Calls

4 calls:

3.5s	(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)))))))
215.0ms	(.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 (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	12	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 21.8b

Counts

123 → 13

Compiler

Compiled 4580 to 2027 computations (55.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U* U)) (cbrt.f64 n)))
5.4b	(.f64 (/.f64 l Om) (-.f64 U U))
10.0b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n)))))))
19.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n))))))))

rewrite67.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64_449`
46×	`pow1_binary64_472`
36×	`add-cbrt-cube_binary64_447`
30×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
28×	`pow-prod-down_binary64_482`
20×	`add-sqr-sqrt_binary64_435`
15×	`-un-lft-identity_binary64_414` `associate-l*_binary64_357`
13×	`add-cube-cbrt_binary64_446` `associate-*r/_binary64_358`
10×	`times-frac_binary64_420`
9×	`associate-r_binary64_356`
7×	`associate-*l/_binary64_359`
4×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `add-log-exp_binary64_450` `flip--_binary64_389` `frac-times_binary64_424`
3×	`*-commutative_binary64_347` `cbrt-undiv_binary64_445` `div-exp_binary64_462`
2×	`distribute-lft-in_binary64_365` `sqrt-div_binary64_430` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `sub-neg_binary64_407` `flip-+_binary64_388` `unswap-sqr_binary64_382`
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 → 117

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U* U)) (cbrt.f64 n)))
10.0ms	(.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 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n)))))))
8.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n))))))))

series6.4s (18.8%)

Counts

4 → 12

Calls

4 calls:

4.9s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n))))))))
1.1s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U U)) (cbrt.f64 n)))))))
297.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (.f64 (/.f64 l Om) (-.f64 U* U)) (cbrt.f64 n)))
115.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify93.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4942	3053
1	4942	3053

prune176.0ms (0.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	129	13	142

Merged error: 21.6b

Counts

142 → 13

Compiler

Compiled 5270 to 2184 computations (58.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.0b	(.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)))))))
10.0b	(.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)))))))
19.3b	(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))))))))
19.3b	(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))))))))

rewrite51.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_472`
24×	`pow-prod-down_binary64_482`
22×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
12×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
8×	`sqrt-pow1_binary64_431` `associate-*r/_binary64_358`
6×	`add-cube-cbrt_binary64_446` `-un-lft-identity_binary64_414` `associate-r*_binary64_356` `add-sqr-sqrt_binary64_435`
4×	`sqrt-div_binary64_430` `flip3-+_binary64_417` `add-log-exp_binary64_450` `flip-+_binary64_388`
2×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `-commutative_binary64_347` `sqrt-prod_binary64_429` `associate-l*_binary64_357` `pow1/2_binary64_491`

Counts

4 → 80

Calls

4 calls:

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)))))))
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))))))))
7.0ms	(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))))))))

series8.7s (25.7%)

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))))))))
3.5s	(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))))))))
813.0ms	(.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)))))))
804.0ms	(.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)))))))

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5758	3652

prune211.0ms (0.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	92	13	105

Merged error: 21.6b

Counts

105 → 13

Compiler

Compiled 6592 to 2908 computations (55.9% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

13.6b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
13.6b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
13.6b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
19.3b	(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)))))))))

rewrite57.0ms (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:

23.0ms	(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 (17.2%)

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)))))))))
759.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
754.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
753.0ms	(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

prune286.0ms (0.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	93	14	107

Merged error: 21.6b

Counts

107 → 14

Compiler

Compiled 8935 to 3357 computations (62.4% saved)

regimes463.0ms (1.4%)

Compiler: Compiled 5706 to 3576 computations (37.3% saved)

bsearch3.0ms (0%)

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

simplify16.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	427	168
1	427	168

end0.0ms (0%)

sample3.5s (10.4%)

Algorithm

1×

intervals

Results

1.3s	13053×	body	128	nan
815.0ms	8000×	body	128	valid
126.0ms	1169×	body	128	invalid

Compiler

Compiled 817 to 499 computations (38.9% saved)

Details

analyze2.4s (7.2%)

sample107.0ms (0.3%)

simplify212.0ms (0.6%)

prune8.0ms (0%)

localize18.0ms (0.1%)

rewrite53.0ms (0.2%)

series4.7s (13.8%)

simplify71.0ms (0.2%)

prune194.0ms (0.6%)

localize22.0ms (0.1%)

rewrite67.0ms (0.2%)

series6.4s (18.8%)

simplify93.0ms (0.3%)

prune176.0ms (0.5%)

localize24.0ms (0.1%)

rewrite51.0ms (0.1%)

series8.7s (25.7%)

simplify58.0ms (0.2%)

prune211.0ms (0.6%)

localize26.0ms (0.1%)

rewrite57.0ms (0.2%)

series5.9s (17.2%)

simplify101.0ms (0.3%)

prune286.0ms (0.8%)

regimes463.0ms (1.4%)

bsearch3.0ms (0%)

simplify16.0ms (0%)

end0.0ms (0%)

sample3.5s (10.4%)

Profiling