Details

analyze2.2s (17.4%)

Algorithm

1×

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)

sample48.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	252×	body	128	valid
1.0ms	14×	body	128	invalid
1.0ms	4×	body	512	invalid
1.0ms	5×	body	256	invalid
1.0ms	2×	body	512	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify138.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5097	43

prune11.0ms (0.1%)

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

14.4b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize20.0ms (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 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
30.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite153.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

14.4b

Rules

16×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
9×	`add-cube-cbrt_binary64_795`
7×	`pow1_binary64_821` `add-exp-log_binary64_798`
6×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `associate-r_binary64_700`
3×	`cancel-sign-sub-inv_binary64_726` `pow-unpow_binary64_837` `associate-l_binary64_701`
2×	`difference-of-squares_binary64_729` `flip3-+_binary64_763` `associate-*r/_binary64_702` `flip-+_binary64_734` `distribute-lft-out_binary64_711`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753` `times-frac_binary64_766` `distribute-lft-out--_binary64_712` `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` `*-commutative_binary64_691` `sum-log_binary64_851` `+-commutative_binary64_690`

Counts

4 → 68

Calls

4 calls:

14.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
6.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 2523 to 1267 computations (49.8% saved)

series1.2s (9.3%)

Error

0.8b

Counts

4 → 84

Calls

4 calls:

584.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
295.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
107.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
73.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 7422 to 5017 computations (32.4% saved)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5045	2691

prune216.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	147	5	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	5	153

Error

0.8b

Counts

153 → 5

Compiler

Compiled 5133 to 2372 computations (53.8% saved)

localize17.0ms (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 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite170.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

23×	`*-un-lft-identity_binary64_760`
19×	`add-sqr-sqrt_binary64_782`
11×	`add-log-exp_binary64_799`
10×	`add-cube-cbrt_binary64_795`
8×	`associate-r_binary64_700` `cancel-sign-sub-inv_binary64_726`
7×	`pow1_binary64_821`
6×	`unpow-prod-down_binary64_839` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`exp-sum_binary64_806`
4×	`distribute-lft-out_binary64_711`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `associate-l_binary64_701`
2×	`sum-log_binary64_851` `sub-neg_binary64_753` `diff-log_binary64_852`
1×	`times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `exp-diff_binary64_808` `associate-r/_binary64_702` `-commutative_binary64_691` `flip3--_binary64_764` `flip--_binary64_735` `associate--r+_binary64_696`

Counts

4 → 77

Calls

4 calls:

22.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
18.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
14.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 2450 to 1239 computations (49.4% saved)

series2.1s (16.1%)

Error

0.8b

Counts

4 → 106

Calls

4 calls:

641.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
581.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
429.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
274.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 8169 to 5626 computations (31.1% saved)

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5089	4831

prune215.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	183	5	188

Error

0.8b

Counts

188 → 5

Compiler

Compiled 4979 to 2245 computations (54.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (cos.f64 M) (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M)))
0.3b	(.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M))
37.7b	(sin.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
37.7b	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

rewrite111.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

8×	`add-sqr-sqrt_binary64_782`
6×	`pow1_binary64_821` `add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
3×	`associate-l_binary64_701` `associate-r_binary64_700`
2×	`sin-mult_binary64_915`
1×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691` `sum-log_binary64_851` `cos-mult_binary64_914` `frac-add_binary64_768` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690`

Counts

4 → 45

Calls

4 calls:

7.0ms	(.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M))
6.0ms	(+.f64 (.f64 (cos.f64 M) (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M)))
3.0ms	(sin.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
2.0ms	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

Compiler

Compiled 2434 to 1123 computations (53.9% saved)

series852.0ms (6.7%)

Error

0.8b

Counts

4 → 43

Calls

4 calls:

374.0ms	(+.f64 (.f64 (cos.f64 M) (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M)))
245.0ms	(.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M))
92.0ms	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
77.0ms	(sin.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

Compiler

Compiled 5501 to 3562 computations (35.2% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5506	2066

prune161.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	88	5	93

Error

0.8b

Counts

93 → 5

Compiler

Compiled 4175 to 1952 computations (53.2% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 M) (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2)))
0.9b	(.f64 (sin.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))) M)
37.7b	(sin.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
37.7b	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

rewrite125.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

12×	`add-sqr-sqrt_binary64_782`
8×	`pow1_binary64_821` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
6×	`associate-l_binary64_701` `associate-r_binary64_700`
4×	`add-log-exp_binary64_799` `distribute-rgt-in_binary64_710` `sin-sum_binary64_893` `distribute-lft-in_binary64_709`
2×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`cos-mult_binary64_914`

Counts

4 → 55

Calls

4 calls:

6.0ms	(.f64 (sin.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))) M)
4.0ms	(.f64 (cos.f64 M) (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2)))
4.0ms	(sin.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
2.0ms	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

Compiler

Compiled 2735 to 1305 computations (52.3% saved)

series721.0ms (5.7%)

Error

0.8b

Counts

4 → 45

Calls

4 calls:

250.0ms	(.f64 (cos.f64 M) (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2)))
242.0ms	(.f64 (sin.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))) M)
85.0ms	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
77.0ms	(sin.f64 (.f64 1/2 (.f64 K (+.f64 n m))))

Compiler

Compiled 5920 to 3906 computations (34% saved)

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4976	1790
1	4976	1790

prune169.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	100	5	105

Error

0.8b

Counts

105 → 5

Compiler

Compiled 4437 to 2093 computations (52.8% saved)

regimes827.0ms (6.5%)

Accuracy

Total 0.2b remaining (18%)

Threshold costs 0.2b (18%)

Compiler

Compiled 11378 to 8988 computations (21% 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%)

sample2.9s (23.1%)

Algorithm

1×

intervals

Results

805.0ms	7848×	body	128	valid
41.0ms	90×	body	1024	invalid
31.0ms	88×	body	512	invalid
29.0ms	292×	body	128	invalid
28.0ms	62×	body	1024	valid
19.0ms	58×	body	512	valid
13.0ms	15×	body	2048	invalid
13.0ms	63×	body	256	invalid
7.0ms	32×	body	256	valid

Compiler

Compiled 1936 to 1530 computations (21% saved)

Details

analyze2.2s (17.4%)

sample48.0ms (0.4%)

simplify138.0ms (1.1%)

prune11.0ms (0.1%)

localize20.0ms (0.2%)

rewrite153.0ms (1.2%)

series1.2s (9.3%)

simplify70.0ms (0.6%)

prune216.0ms (1.7%)

localize17.0ms (0.1%)

rewrite170.0ms (1.3%)

series2.1s (16.1%)

simplify90.0ms (0.7%)

prune215.0ms (1.7%)

localize28.0ms (0.2%)

rewrite111.0ms (0.9%)

series852.0ms (6.7%)

simplify70.0ms (0.5%)

prune161.0ms (1.3%)

localize29.0ms (0.2%)

rewrite125.0ms (1%)

series721.0ms (5.7%)

simplify92.0ms (0.7%)

prune169.0ms (1.3%)

regimes827.0ms (6.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (23.1%)

Profiling