Details

analyze462.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample105.0ms (0.9%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
21.0ms	34×	body	1024	nan
13.0ms	30×	body	512	nan
12.0ms	66×	body	128	overflowed
2.0ms	30×	body	128	nan
2.0ms	8×	body	256	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify155.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune14.0ms (0.1%)

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

0.3b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite256.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`times-frac_binary64_766`
42×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
33×	`add-cube-cbrt_binary64_795`
26×	`add-exp-log_binary64_798`
22×	`pow-unpow_binary64_837`
18×	`sqrt-prod_binary64_776`
14×	`pow1_binary64_821`
10×	`add-cbrt-cube_binary64_796`
9×	`prod-exp_binary64_809`
8×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
6×	`pow-prod-down_binary64_831` `pow-exp_binary64_828` `associate-/r*_binary64_704` `difference-of-squares_binary64_729`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700` `distribute-lft-out--_binary64_712` `pow-pow_binary64_832`
2×	`pow-to-exp_binary64_829` `div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836`
1×	`associate-l_binary64_701` `*-commutative_binary64_691` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

3 → 115

Calls

3 calls:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
6.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series509.0ms (4.4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

255.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
188.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
42.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune238.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Error

0.0b

Counts

135 → 10

Compiler

Compiled 3085 to 1948 computations (36.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.2b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.3b	(*.f64 n PI.f64)
0.3b	(*.f64 n PI.f64)

rewrite576.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64_766`
132×	`add-sqr-sqrt_binary64_782`
128×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
111×	`sqrt-prod_binary64_776`
28×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
27×	`add-exp-log_binary64_798`
24×	`associate-/l*_binary64_705`
14×	`pow1_binary64_821`
13×	`add-cbrt-cube_binary64_796`
11×	`div-exp_binary64_811`
8×	`div-inv_binary64_757`
6×	`associate-l_binary64_701` `associate-r_binary64_700` `associate-/r*_binary64_704`
5×	`pow-prod-down_binary64_831` `prod-exp_binary64_809`
4×	`add-log-exp_binary64_799`
3×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778`
2×	`cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `pow1/2_binary64_840`

Counts

4 → 241

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 8806 to 4891 computations (44.5% saved)

series274.0ms (2.4%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

183.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
28.0ms	(*.f64 n PI.f64)
22.0ms	(*.f64 n PI.f64)
22.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 1094 to 837 computations (23.5% saved)

simplify161.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5004	11439

prune527.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	254	2	256
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	258	8	266

Error

Counts

266 → 8

Compiler

Compiled 8705 to 5360 computations (38.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 n PI.f64)
0.3b	(.f64 (.f64 n (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite115.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64_782`
13×	`pow1_binary64_821`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
9×	`sqrt-prod_binary64_776` `associate-r_binary64_700`
4×	`add-log-exp_binary64_799` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `associate-l_binary64_701`
2×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `*-commutative_binary64_691`
1×	`unswap-sqr_binary64_728`

Counts

4 → 65

Calls

4 calls:

10.0ms	(.f64 (.f64 n (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64))
4.0ms	(*.f64 n PI.f64)
3.0ms	(sqrt.f64 PI.f64)
3.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1808 to 831 computations (54% saved)

series62.0ms (0.5%)

Error

Counts

4 → 6

Calls

4 calls:

29.0ms	(.f64 (.f64 n (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64))
27.0ms	(*.f64 n PI.f64)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 378 to 266 computations (29.6% saved)

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4938	502
1	4938	502

prune96.0ms (0.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	71	8	79

Error

Counts

79 → 8

Compiler

Compiled 1915 to 966 computations (49.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.2b	(sqrt.f64 (/.f64 1 k))
0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
0.3b	(*.f64 n PI.f64)

rewrite216.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

53×	`add-sqr-sqrt_binary64_782`
37×	`sqrt-prod_binary64_776`
28×	`*-un-lft-identity_binary64_760`
26×	`times-frac_binary64_766`
24×	`add-cube-cbrt_binary64_795`
19×	`associate-l_binary64_701`
15×	`associate-r_binary64_700`
14×	`pow1_binary64_821`
13×	`unswap-sqr_binary64_728`
11×	`add-exp-log_binary64_798`
8×	`add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
6×	`sqrt-pow1_binary64_778`
5×	`sqr-pow_binary64_732`
4×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `add-log-exp_binary64_799` `unpow-prod-up_binary64_838`
3×	`sqrt-div_binary64_777` `cancel-sign-sub-inv_binary64_726` `rem-sqrt-square_binary64_773`
2×	`cbrt-unprod_binary64_793` `*-commutative_binary64_691` `pow-sub_binary64_836` `div-inv_binary64_757` `pow1/2_binary64_840`
1×	`pow-to-exp_binary64_829` `pow-exp_binary64_828` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `sub-neg_binary64_753` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 113

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
3.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 2685 to 1842 computations (31.4% saved)

series272.0ms (2.4%)

Error

Counts

4 → 15

Calls

4 calls:

175.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
38.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
25.0ms	(*.f64 n PI.f64)
13.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 958 to 774 computations (19.2% saved)

simplify139.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5038	2450

prune162.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	128	8	136

Error

Counts

136 → 8

Compiler

Compiled 2722 to 1838 computations (32.5% saved)

regimes1.1s (9.3%)

Accuracy

Total 0.4b remaining (99.7%)

Threshold costs 0.4b (99.7%)

Compiler

Compiled 11763 to 9692 computations (17.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	30
1	15	30

end0.0ms (0%)

sample5.9s (50.8%)

Algorithm

1×

intervals

Results

785.0ms	8000×	body	128	valid
747.0ms	1255×	body	1024	nan
422.0ms	2324×	body	128	overflowed
272.0ms	668×	body	512	nan
77.0ms	324×	body	256	nan
73.0ms	961×	body	128	nan
28.0ms	237×	body	128	invalid

Compiler

Compiled 2716 to 2238 computations (17.6% saved)

Details

analyze462.0ms (4%)

sample105.0ms (0.9%)

simplify155.0ms (1.3%)

prune14.0ms (0.1%)

localize11.0ms (0.1%)

rewrite256.0ms (2.2%)

series509.0ms (4.4%)

simplify117.0ms (1%)

prune238.0ms (2.1%)

localize11.0ms (0.1%)

rewrite576.0ms (5%)

series274.0ms (2.4%)

simplify161.0ms (1.4%)

prune527.0ms (4.6%)

localize17.0ms (0.1%)

rewrite115.0ms (1%)

series62.0ms (0.5%)

simplify102.0ms (0.9%)

prune96.0ms (0.8%)

localize10.0ms (0.1%)

rewrite216.0ms (1.9%)

series272.0ms (2.4%)

simplify139.0ms (1.2%)

prune162.0ms (1.4%)

regimes1.1s (9.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.9s (50.8%)

Profiling