Details

analyze4.5s (16.7%)

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)

sample92.0ms (0.3%)

Algorithm

1×

intervals

Results

47.0ms	248×	body	128	valid
4.0ms	5×	body	1024	invalid
3.0ms	12×	body	128	invalid
2.0ms	4×	body	512	valid
2.0ms	2×	body	1024	valid
1.0ms	2×	body	512	invalid
1.0ms	1×	body	2048	invalid
1.0ms	2×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify121.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	5097	43

prune12.0ms (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

18.6b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize53.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite149.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_782`
16×	`*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795`
8×	`associate-r_binary64_700`
7×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
5×	`exp-sum_binary64_806`
4×	`cos-sum_binary64_894`
3×	`associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`distribute-lft-out_binary64_711` `difference-of-squares_binary64_729` `sub-neg_binary64_753`
1×	`unswap-sqr_binary64_728` `unpow2_binary64_825` `prod-exp_binary64_809` `flip3-+_binary64_763` `exp-diff_binary64_808` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `sqr-pow_binary64_732` `cos-diff_binary64_897` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `times-frac_binary64_766` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 69

Calls

4 calls:

54.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
34.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
24.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
22.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series4.3s (16.1%)

Counts

4 → 93

Calls

4 calls:

2.1s	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
1.3s	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
648.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
296.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 7883 to 5702 computations (27.7% saved)

simplify237.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	5055	5503

prune638.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	7	163

Error

1.7b

Counts

163 → 7

Compiler

Compiled 6558 to 2868 computations (56.3% saved)

localize34.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_782`
8×	`*-un-lft-identity_binary64_760`
6×	`unpow-prod-down_binary64_839`
4×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
3×	`add-exp-log_binary64_798` `pow1_binary64_821` `pow-unpow_binary64_837`
2×	`difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796`
1×	`distribute-lft-out_binary64_711` `unpow2_binary64_825` `flip3-+_binary64_763` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `sum-log_binary64_851` `sqr-pow_binary64_732` `times-frac_binary64_766` `pow-pow_binary64_832`

Counts

2 → 33

Calls

2 calls:

35.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
26.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series1.9s (7%)

Counts

2 → 60

Calls

2 calls:

1.3s	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
629.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 2534 to 2103 computations (17% saved)

simplify183.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	5112	1931

prune233.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Error

1.7b

Counts

100 → 7

Compiler

Compiled 2628 to 1195 computations (54.5% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
26.0b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

rewrite154.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_782`
16×	`*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795`
8×	`associate-r_binary64_700`
7×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
5×	`exp-sum_binary64_806`
4×	`cos-sum_binary64_894`
3×	`associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`distribute-lft-out_binary64_711` `difference-of-squares_binary64_729` `sub-neg_binary64_753`
1×	`unswap-sqr_binary64_728` `unpow2_binary64_825` `prod-exp_binary64_809` `flip3-+_binary64_763` `exp-diff_binary64_808` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `sqr-pow_binary64_732` `cos-diff_binary64_897` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `times-frac_binary64_766` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 69

Calls

4 calls:

58.0ms	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
35.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
25.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
20.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

series3.3s (12.2%)

Counts

4 → 84

Calls

4 calls:

1.3s	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
1.2s	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
583.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
139.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

Compiler

Compiled 5127 to 4031 computations (21.4% saved)

simplify208.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	5142	4093

prune500.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	153	7	160

Error

1.7b

Counts

160 → 7

Compiler

Compiled 5322 to 2620 computations (50.8% saved)

localize54.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (sqrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))) (sqrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
26.0b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

rewrite224.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_760`
11×	`associate-r_binary64_700`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
8×	`sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795` `add-log-exp_binary64_799` `add-sqr-sqrt_binary64_782`
7×	`cancel-sign-sub-inv_binary64_726`
5×	`exp-sum_binary64_806`
4×	`cos-sum_binary64_894` `exp-diff_binary64_808` `sqrt-div_binary64_777`
3×	`distribute-lft-out_binary64_711` `prod-exp_binary64_809` `associate-*r/_binary64_702` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `sum-log_binary64_851` `sub-neg_binary64_753`
1×	`associate-l/_binary64_703` `frac-times_binary64_770` `associate-l_binary64_701` `cos-diff_binary64_897` `-commutative_binary64_691`

Counts

4 → 65

Calls

4 calls:

108.0ms	(.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (sqrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))) (sqrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
44.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
37.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
14.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

series3.7s (13.9%)

Counts

4 → 88

Calls

4 calls:

1.2s	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
1.2s	(.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (sqrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))) (sqrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
1.2s	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
159.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

Compiler

Compiled 7503 to 5496 computations (26.7% saved)

simplify147.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4981	4644
1	4981	4644

prune702.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	154	6	160

Error

1.7b

Counts

160 → 6

Compiler

Compiled 7497 to 3808 computations (49.2% saved)

regimes1.1s (4%)

Accuracy

Total 0.1b remaining (9.7%)

Threshold costs 0.1b (9.7%)

Compiler

Compiled 6302 to 4950 computations (21.5% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	70	47
1	70	47

end0.0ms (0%)

sample4.2s (15.7%)

Algorithm

1×

intervals

Results

1.5s	7828×	body	128	valid
71.0ms	89×	body	1024	invalid
61.0ms	71×	body	1024	valid
51.0ms	64×	body	512	valid
50.0ms	263×	body	128	invalid
48.0ms	82×	body	512	invalid
24.0ms	24×	body	2048	invalid
21.0ms	53×	body	256	invalid
16.0ms	35×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 1099 to 862 computations (21.6% saved)

Details

analyze4.5s (16.7%)

sample92.0ms (0.3%)

simplify121.0ms (0.5%)

prune12.0ms (0%)

localize53.0ms (0.2%)

rewrite149.0ms (0.6%)

series4.3s (16.1%)

simplify237.0ms (0.9%)

prune638.0ms (2.4%)

localize34.0ms (0.1%)

rewrite67.0ms (0.3%)

series1.9s (7%)

simplify183.0ms (0.7%)

prune233.0ms (0.9%)

localize43.0ms (0.2%)

rewrite154.0ms (0.6%)

series3.3s (12.2%)

simplify208.0ms (0.8%)

prune500.0ms (1.9%)

localize54.0ms (0.2%)

rewrite224.0ms (0.8%)

series3.7s (13.9%)

simplify147.0ms (0.5%)

prune702.0ms (2.6%)

regimes1.1s (4%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample4.2s (15.7%)

Profiling