Details

analyze527.0ms (5.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4942	44
1	4942	44
0	2	2
1	2	2

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

Symmetry

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample71.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
17.0ms	39×	body	1024	nan
10.0ms	78×	body	128	overflowed
4.0ms	12×	body	512	nan
2.0ms	13×	body	256	nan
2.0ms	42×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite211.0ms (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×	`difference-of-squares_binary64_729` `pow-prod-down_binary64_831` `pow-exp_binary64_828` `associate-/r*_binary64_704`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`distribute-lft-out--_binary64_712` `pow-pow_binary64_832` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700`
2×	`div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836` `pow-to-exp_binary64_829`
1×	`cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

3 → 115

Calls

3 calls:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.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)

series420.0ms (4.4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

201.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
166.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
28.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune185.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	125	8	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Error

0.0b

Counts

135 → 8

Compiler

Compiled 3087 to 2095 computations (32.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite196.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 116

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
8.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 2812 to 2087 computations (25.8% saved)

series321.0ms (3.4%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

126.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
119.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
28.0ms	(.f64 n (.f64 2 PI.f64))
23.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1589 to 1224 computations (23% saved)

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4939	3141
1	4939	3141

prune177.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	137	8	145

Error

Counts

145 → 8

Compiler

Compiled 3204 to 2234 computations (30.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite278.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

72×	`times-frac_binary64_766`
58×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
55×	`add-cube-cbrt_binary64_795`
48×	`sqrt-prod_binary64_776`
32×	`unpow-prod-down_binary64_839` `unpow-prod-up_binary64_838`
24×	`cancel-sign-sub-inv_binary64_726`
22×	`pow1_binary64_821`
15×	`add-exp-log_binary64_798`
12×	`associate-/r*_binary64_704`
11×	`add-cbrt-cube_binary64_796`
9×	`pow-prod-down_binary64_831`
8×	`sub-neg_binary64_753` `sqr-pow_binary64_732`
6×	`sqrt-pow1_binary64_778` `pow-unpow_binary64_837` `associate-/l*_binary64_705`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799`
3×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `associate-l_binary64_701` `div-exp_binary64_811`
2×	`pow1/2_binary64_840` `difference-of-squares_binary64_729` `pow-sub_binary64_836` `pow-to-exp_binary64_829` `pow-exp_binary64_828`
1×	`distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779` `associate-r_binary64_700` `*-commutative_binary64_691` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r/_binary64_706`

Counts

4 → 166

Calls

4 calls:

11.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
9.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)))
6.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 4443 to 2875 computations (35.3% saved)

series340.0ms (3.5%)

Error

Counts

4 → 21

Calls

4 calls:

138.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)))
128.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
28.0ms	(.f64 n (.f64 2 PI.f64))
24.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1615 to 1232 computations (23.7% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5077	5257

prune239.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	187	8	195

Error

Counts

195 → 8

Compiler

Compiled 4661 to 2834 computations (39.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite101.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`pow1_binary64_821`
16×	`add-exp-log_binary64_798`
11×	`add-cbrt-cube_binary64_796`
10×	`add-sqr-sqrt_binary64_782`
8×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
7×	`pow-prod-down_binary64_831`
6×	`sqrt-pow1_binary64_778`
4×	`add-log-exp_binary64_799` `sqrt-prod_binary64_776` `prod-exp_binary64_809` `div-exp_binary64_811` `times-frac_binary64_766` `associate-/l*_binary64_705`
3×	`associate-l_binary64_701` `associate-r_binary64_700`
2×	`pow1/2_binary64_840` `cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793`
1×	`pow-to-exp_binary64_829` `pow-exp_binary64_828` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r_binary64_704` `unswap-sqr_binary64_728` `-commutative_binary64_691`

Counts

4 → 67

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) k) (sqrt.f64 k)))
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 1674 to 909 computations (45.7% saved)

series254.0ms (2.6%)

Error

Counts

4 → 15

Calls

4 calls:

174.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) k) (sqrt.f64 k)))
26.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
22.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
19.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1100 to 805 computations (26.8% saved)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4998	1430
1	4998	1430

prune83.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	82	8	90

Error

Counts

90 → 8

Compiler

Compiled 1752 to 944 computations (46.1% saved)

regimes862.0ms (9%)

Accuracy

Total 0.4b remaining (99.4%)

Threshold costs 0.4b (99.4%)

Compiler

Compiled 11550 to 9582 computations (17% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	22
1	25	22

Removed

()

end0.0ms (0%)

sample4.8s (50.4%)

Algorithm

1×

intervals

Results

627.0ms	1357×	body	1024	nan
600.0ms	8000×	body	128	valid
323.0ms	2345×	body	128	overflowed
203.0ms	656×	body	512	nan
59.0ms	313×	body	256	nan
55.0ms	965×	body	128	nan
21.0ms	240×	body	128	invalid

Compiler

Compiled 2907 to 2414 computations (17% saved)

Details

analyze527.0ms (5.5%)

sample71.0ms (0.7%)

simplify53.0ms (0.6%)

prune5.0ms (0%)

localize16.0ms (0.2%)

rewrite211.0ms (2.2%)

series420.0ms (4.4%)

simplify93.0ms (1%)

prune185.0ms (1.9%)

localize10.0ms (0.1%)

rewrite196.0ms (2%)

series321.0ms (3.4%)

simplify102.0ms (1.1%)

prune177.0ms (1.8%)

localize10.0ms (0.1%)

rewrite278.0ms (2.9%)

series340.0ms (3.5%)

simplify93.0ms (1%)

prune239.0ms (2.5%)

localize9.0ms (0.1%)

rewrite101.0ms (1%)

series254.0ms (2.6%)

simplify94.0ms (1%)

prune83.0ms (0.9%)

regimes862.0ms (9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.8s (50.4%)

Profiling