Details

analyze708.0ms (4.1%)

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)

sample134.0ms (0.8%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
28.0ms	80×	body	128	overflowed
22.0ms	26×	body	1024	nan
13.0ms	22×	body	512	nan
3.0ms	10×	body	256	nan
3.0ms	21×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify243.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune9.0ms (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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize22.0ms (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)

rewrite361.0ms (2.1%)

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:

27.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
15.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
11.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series752.0ms (4.3%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

357.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
307.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
50.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify195.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune315.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	9	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Error

0.0b

Counts

135 → 9

Compiler

Compiled 3112 to 1955 computations (37.2% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.3b	(*.f64 n PI.f64)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite381.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

124×	`add-exp-log_binary64_798`
65×	`prod-exp_binary64_809`
36×	`pow-exp_binary64_828`
30×	`div-exp_binary64_811`
18×	`add-sqr-sqrt_binary64_782`
17×	`pow1_binary64_821`
16×	`add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
14×	`times-frac_binary64_766`
13×	`pow-unpow_binary64_837`
12×	`pow-to-exp_binary64_829`
7×	`pow-prod-down_binary64_831`
6×	`associate-r_binary64_700`
5×	`cbrt-unprod_binary64_793` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799` `associate-l_binary64_701`
3×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732` `pow-pow_binary64_832`
2×	`*-commutative_binary64_691` `cbrt-undiv_binary64_794` `div-inv_binary64_757`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r*_binary64_704`

Counts

4 → 118

Calls

4 calls:

22.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
10.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(*.f64 n PI.f64)

Compiler

Compiled 3457 to 2289 computations (33.8% saved)

series517.0ms (3%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

238.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
164.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
52.0ms	(.f64 (.f64 2 PI.f64) n)
40.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1100 to 849 computations (22.8% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4999	2500
1	4999	2500

prune286.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	132	10	142

Error

Counts

142 → 10

Compiler

Compiled 3291 to 2051 computations (37.7% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))
0.3b	(*.f64 n PI.f64)
0.3b	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
0.4b	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

rewrite402.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

164×	`add-exp-log_binary64_798`
94×	`prod-exp_binary64_809`
42×	`pow-exp_binary64_828`
36×	`div-exp_binary64_811`
25×	`add-cbrt-cube_binary64_796`
20×	`pow1_binary64_821`
15×	`associate-r_binary64_700`
14×	`add-sqr-sqrt_binary64_782`
12×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760` `pow-to-exp_binary64_829`
11×	`cbrt-unprod_binary64_793`
10×	`pow-prod-down_binary64_831`
6×	`sqrt-prod_binary64_776`
5×	`associate-l_binary64_701` `times-frac_binary64_766` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799`
3×	`*-commutative_binary64_691`
2×	`cbrt-undiv_binary64_794` `unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r*_binary64_704`

Counts

4 → 122

Calls

4 calls:

20.0ms	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))
19.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
12.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
7.0ms	(*.f64 n PI.f64)

Compiler

Compiled 4152 to 2413 computations (41.9% saved)

series406.0ms (2.3%)

Error

Counts

4 → 15

Calls

4 calls:

242.0ms	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))
52.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
43.0ms	(*.f64 n PI.f64)
42.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

Compiler

Compiled 1208 to 915 computations (24.3% saved)

simplify147.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4970	2604
1	4970	2604

prune289.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	137	10	147

Error

Counts

147 → 10

Compiler

Compiled 3584 to 2137 computations (40.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
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)

rewrite385.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

59×	`add-sqr-sqrt_binary64_782`
37×	`sqrt-prod_binary64_776`
34×	`*-un-lft-identity_binary64_760`
27×	`add-cube-cbrt_binary64_795`
26×	`times-frac_binary64_766`
19×	`associate-l_binary64_701`
15×	`pow1_binary64_821` `associate-r_binary64_700`
13×	`unswap-sqr_binary64_728`
12×	`add-exp-log_binary64_798` `unpow-prod-down_binary64_839`
8×	`add-cbrt-cube_binary64_796` `unpow-prod-up_binary64_838`
6×	`sqr-pow_binary64_732` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `pow-unpow_binary64_837`
5×	`pow-pow_binary64_832`
4×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `add-log-exp_binary64_799`
3×	`pow-sub_binary64_836` `sqrt-div_binary64_777` `rem-sqrt-square_binary64_773`
2×	`cbrt-unprod_binary64_793` `*-commutative_binary64_691` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `div-inv_binary64_757` `sub-neg_binary64_753` `pow1/2_binary64_840` `difference-of-squares_binary64_729`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `inv-pow_binary64_845` `pow-flip_binary64_834` `distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779`

Counts

4 → 132

Calls

4 calls:

30.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
20.0ms	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
7.0ms	(*.f64 n PI.f64)
6.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 3143 to 2145 computations (31.8% saved)

series537.0ms (3.1%)

Error

Counts

4 → 21

Calls

4 calls:

217.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
211.0ms	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
43.0ms	(*.f64 n PI.f64)
26.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 1565 to 1197 computations (23.5% saved)

simplify289.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (223.0ms)

Iter	Nodes	Cost
0	4959	3225
1	4959	3225

prune330.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	154	9	163

Error

Counts

163 → 9

Compiler

Compiled 3323 to 2224 computations (33.1% saved)

regimes1.7s (9.8%)

Accuracy

Total 0.4b remaining (99.7%)

Threshold costs 0.4b (99.7%)

Compiler

Compiled 10844 to 8879 computations (18.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	32
1	23	32

end0.0ms (0%)

sample8.8s (50.5%)

Algorithm

1×

intervals

Results

1.2s	1389×	body	1024	nan
1.1s	8000×	body	128	valid
619.0ms	2347×	body	128	overflowed
417.0ms	704×	body	512	nan
110.0ms	328×	body	256	nan
104.0ms	981×	body	128	nan
40.0ms	238×	body	128	invalid

Compiler

Compiled 2543 to 2084 computations (18% saved)

Details

analyze708.0ms (4.1%)

sample134.0ms (0.8%)

simplify243.0ms (1.4%)

prune9.0ms (0%)

localize22.0ms (0.1%)

rewrite361.0ms (2.1%)

series752.0ms (4.3%)

simplify195.0ms (1.1%)

prune315.0ms (1.8%)

localize33.0ms (0.2%)

rewrite381.0ms (2.2%)

series517.0ms (3%)

simplify136.0ms (0.8%)

prune286.0ms (1.6%)

localize43.0ms (0.2%)

rewrite402.0ms (2.3%)

series406.0ms (2.3%)

simplify147.0ms (0.8%)

prune289.0ms (1.7%)

localize23.0ms (0.1%)

rewrite385.0ms (2.2%)

series537.0ms (3.1%)

simplify289.0ms (1.7%)

prune330.0ms (1.9%)

regimes1.7s (9.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.8s (50.5%)

Profiling