Details

analyze2.3s (18.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5136	473
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample56.0ms (0.5%)

Algorithm

1×

intervals

Results

24.0ms	246×	body	128	valid
7.0ms	3×	body	1024	valid
2.0ms	4×	body	1024	invalid
2.0ms	5×	body	512	valid
1.0ms	3×	body	512	invalid
1.0ms	6×	body	256	invalid
1.0ms	2×	body	2048	invalid
0.0ms	2×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

19.3b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
36.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite171.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

19.0b

Rules

22×	`add-sqr-sqrt_binary64_782`
16×	`*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795`
7×	`pow1_binary64_821` `add-exp-log_binary64_798`
6×	`cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `difference-of-squares_binary64_729` `associate-r_binary64_700`
3×	`pow-unpow_binary64_837` `associate-l_binary64_701`
2×	`sub-neg_binary64_753` `times-frac_binary64_766` `distribute-lft-out--_binary64_712` `associate-*r/_binary64_702`
1×	`cos-diff_binary64_897` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `*-commutative_binary64_691` `diff-log_binary64_852` `flip3--_binary64_764` `flip--_binary64_735`

Counts

4 → 73

Calls

4 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 2666 to 1317 computations (50.6% saved)

series812.0ms (6.6%)

Error

2.1b

Counts

4 → 75

Calls

4 calls:

312.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
152.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
149.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
105.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 6214 to 4261 computations (31.4% saved)

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4997	2161
1	4997	2161

prune227.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	139	9	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	9	149

Error

2.0b

Counts

149 → 9

Compiler

Compiled 5006 to 2417 computations (51.7% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite117.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.0b

Rules

19×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
10×	`add-log-exp_binary64_799`
7×	`add-cube-cbrt_binary64_795` `cancel-sign-sub-inv_binary64_726`
6×	`unpow-prod-down_binary64_839`
5×	`difference-of-squares_binary64_729`
4×	`distribute-lft-out--_binary64_712` `pow1_binary64_821` `add-exp-log_binary64_798`
3×	`pow-unpow_binary64_837` `add-cbrt-cube_binary64_796` `diff-log_binary64_852`
2×	`times-frac_binary64_766` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `distribute-lft-out_binary64_711`
1×	`pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `sum-log_binary64_851` `associate--r+_binary64_696`

Counts

3 → 58

Calls

3 calls:

17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
11.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 1750 to 890 computations (49.1% saved)

series1.2s (9.5%)

Error

2.0b

Counts

3 → 78

Calls

3 calls:

643.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
288.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
152.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

Compiler

Compiled 5002 to 3562 computations (28.8% saved)

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5076	2848

prune160.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	136	9	145

Error

2.0b

Counts

145 → 9

Compiler

Compiled 3599 to 1711 computations (52.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
27.5b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

rewrite158.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

2.0b

Rules

21×	`add-sqr-sqrt_binary64_782`
20×	`*-un-lft-identity_binary64_760`
11×	`add-log-exp_binary64_799`
10×	`cancel-sign-sub-inv_binary64_726`
9×	`add-cube-cbrt_binary64_795`
6×	`unpow-prod-down_binary64_839`
5×	`pow1_binary64_821` `add-exp-log_binary64_798` `difference-of-squares_binary64_729`
4×	`cos-sum_binary64_894` `add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712`
3×	`sub-neg_binary64_753` `pow-unpow_binary64_837` `diff-log_binary64_852`
2×	`times-frac_binary64_766` `flip3--_binary64_764` `flip--_binary64_735` `distribute-lft-out_binary64_711`
1×	`cos-diff_binary64_897` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `sum-log_binary64_851` `associate--r+_binary64_696`

Counts

4 → 70

Calls

4 calls:

17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
6.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

Compiler

Compiled 2558 to 1358 computations (46.9% saved)

series1.3s (10.4%)

Error

2.0b

Counts

4 → 89

Calls

4 calls:

651.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
283.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
154.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
76.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

Compiler

Compiled 6965 to 4912 computations (29.5% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4986	3235
1	4986	3235

prune220.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	159	9	168

Error

2.0b

Counts

168 → 9

Compiler

Compiled 5081 to 2585 computations (49.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3))
0.6b	(pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3)
27.5b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

rewrite169.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

2.0b

Rules

18×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
13×	`add-cube-cbrt_binary64_795`
12×	`unpow-prod-down_binary64_839` `cbrt-prod_binary64_791`
6×	`pow1_binary64_821` `add-exp-log_binary64_798` `pow-unpow_binary64_837` `cube-prod_binary64_788`
5×	`add-cbrt-cube_binary64_796`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799`
3×	`cancel-sign-sub-inv_binary64_726` `sqr-pow_binary64_732`
2×	`pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow3_binary64_826` `cube-mult_binary64_790` `difference-of-squares_binary64_729`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753` `rem-cube-cbrt_binary64_783` `pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `times-frac_binary64_766` `distribute-lft-out--_binary64_712` `unpow2_binary64_825`

Counts

4 → 77

Calls

4 calls:

10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
4.0ms	(pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3))

Compiler

Compiled 3037 to 1784 computations (41.3% saved)

series777.0ms (6.3%)

Error

2.0b

Counts

4 → 60

Calls

4 calls:

294.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
239.0ms	(pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3)
84.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
77.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 3))

Compiler

Compiled 5265 to 3791 computations (28% saved)

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5003	2394

prune201.0ms (1.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	137	9	146

Error

2.0b

Counts

146 → 9

Compiler

Compiled 4510 to 2434 computations (46% saved)

regimes923.0ms (7.5%)

Accuracy

Total 0.2b remaining (16.3%)

Threshold costs 0.2b (16.3%)

Compiler

Compiled 11762 to 9588 computations (18.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	33
1	62	33

end0.0ms (0%)

sample3.1s (25.4%)

Algorithm

1×

intervals

Results

821.0ms	7844×	body	128	valid
33.0ms	82×	body	1024	invalid
31.0ms	69×	body	1024	valid
29.0ms	275×	body	128	invalid
27.0ms	88×	body	512	invalid
16.0ms	49×	body	512	valid
8.0ms	42×	body	256	invalid
8.0ms	37×	body	256	valid
8.0ms	14×	body	2048	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 2000 to 1630 computations (18.5% saved)

Details

analyze2.3s (18.8%)

sample56.0ms (0.5%)

simplify50.0ms (0.4%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite171.0ms (1.4%)

series812.0ms (6.6%)

simplify97.0ms (0.8%)

prune227.0ms (1.8%)

localize14.0ms (0.1%)

rewrite117.0ms (0.9%)

series1.2s (9.5%)

simplify81.0ms (0.7%)

prune160.0ms (1.3%)

localize18.0ms (0.1%)

rewrite158.0ms (1.3%)

series1.3s (10.4%)

simplify83.0ms (0.7%)

prune220.0ms (1.8%)

localize23.0ms (0.2%)

rewrite169.0ms (1.4%)

series777.0ms (6.3%)

simplify69.0ms (0.6%)

prune201.0ms (1.6%)

regimes923.0ms (7.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (25.4%)

Profiling