Details

analyze2.3s (7.3%)

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)

sample101.0ms (0.3%)

Algorithm

1×

intervals

Results

43.0ms	408×	body	128	nan
24.0ms	256×	body	128	valid
3.0ms	33×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify210.0ms (0.7%)

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: 32.5b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
7.4b	(.f64 (/.f64 l Om) (-.f64 U U))
11.1b	(.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)))))))
20.4b	(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))))))))

rewrite52.0ms (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)))))))
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))))))))

series4.6s (14.5%)

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))))))))
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)))))))
208.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
114.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	2903
1	4961	2903

prune191.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 23.0b

Counts

123 → 11

Compiler

Compiled 4511 to 1982 computations (56.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
5.9b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
7.4b	(.f64 (/.f64 l Om) (-.f64 U U))
20.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

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

series5.5s (17.1%)

Counts

4 → 12

Calls

4 calls:

3.9s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))
820.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
632.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
126.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify118.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4957	3388
1	4957	3388

prune175.0ms (0.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	114	15	129

Merged error: 19.2b

Counts

129 → 15

Compiler

Compiled 4682 to 2066 computations (55.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

16.7b	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
16.7b	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
16.7b	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
20.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))))

rewrite64.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`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` `pow1_binary64_472`
15×	`pow-prod-down_binary64_482`
14×	`associate-*l/_binary64_359`
7×	`sqrt-pow1_binary64_431`
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` `pow1/3_binary64_493`
1×	`sqrt-prod_binary64_429` `pow1/2_binary64_491`

Counts

4 → 75

Calls

4 calls:

19.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))))
5.0ms	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
5.0ms	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
5.0ms	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series7.6s (23.7%)

Counts

4 → 12

Calls

4 calls:

4.3s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))))))
1.1s	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.1s	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
1.1s	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify91.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5260	8114

prune294.0ms (0.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	85	17	102

Merged error: 19.1b

Counts

102 → 17

Compiler

Compiled 9284 to 3676 computations (60.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.9b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
11.9b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
11.9b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
20.4b	(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)))))))))

rewrite58.0ms (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:

22.0ms	(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 (18.5%)

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)))))))))
786.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
772.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))
772.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))))))

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5165	8429

prune281.0ms (0.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	14	14
Picked	1	0	1
Done	0	2	2
Total	94	17	111

Merged error: 19.1b

Counts

111 → 17

Compiler

Compiled 8935 to 3357 computations (62.4% saved)

regimes529.0ms (1.7%)

Compiler: Compiled 7450 to 4440 computations (40.4% saved)

bsearch47.0ms (0.1%)

Steps

Iters	Range		Point
6	-4.437370271988686e-305	-7.368626793695857e-306	-7.486729739335176e-306

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	86
1	48	86

end0.0ms (0%)

sample3.5s (11%)

Algorithm

1×

intervals

Results

1.3s	12905×	body	128	nan
787.0ms	8000×	body	128	valid
118.0ms	1169×	body	128	invalid

Compiler

Compiled 981 to 580 computations (40.9% saved)

Details

analyze2.3s (7.3%)

sample101.0ms (0.3%)

simplify210.0ms (0.7%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite52.0ms (0.2%)

series4.6s (14.5%)

simplify74.0ms (0.2%)

prune191.0ms (0.6%)

localize17.0ms (0.1%)

rewrite50.0ms (0.2%)

series5.5s (17.1%)

simplify118.0ms (0.4%)

prune175.0ms (0.5%)

localize24.0ms (0.1%)

rewrite64.0ms (0.2%)

series7.6s (23.7%)

simplify91.0ms (0.3%)

prune294.0ms (0.9%)

localize23.0ms (0.1%)

rewrite58.0ms (0.2%)

series5.9s (18.5%)

simplify105.0ms (0.3%)

prune281.0ms (0.9%)

regimes529.0ms (1.7%)

bsearch47.0ms (0.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (11%)

Profiling