Details

analyze2.3s (30.6%)

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)

sample47.0ms (0.6%)

Algorithm

1×

intervals

Results

28.0ms	251×	body	128	valid
2.0ms	5×	body	1024	invalid
1.0ms	3×	body	512	valid
1.0ms	3×	body	512	invalid
1.0ms	3×	body	256	invalid
1.0ms	6×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify140.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (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

Merged error: 18.2b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
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)
38.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`cancel-sign-sub-inv_binary64_726` `unpow-prod-down_binary64_839`
5×	`add-exp-log_binary64_798` `pow1_binary64_821`
4×	`cos-sum_binary64_894` `add-cbrt-cube_binary64_796`
3×	`difference-of-squares_binary64_729` `pow-unpow_binary64_837`
2×	`distribute-lft-out--_binary64_712` `sub-neg_binary64_753`
1×	`diff-log_binary64_852` `distribute-lft-out_binary64_711` `unpow2_binary64_825` `flip3-+_binary64_763` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `sum-log_binary64_851` `sqr-pow_binary64_732` `cos-diff_binary64_897` `times-frac_binary64_766` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 61

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))
8.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

series295.0ms (4%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
80.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
51.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
47.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5162	1379

prune116.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Merged error: 1.2b

Counts

74 → 5

Compiler

Compiled 2657 to 1330 computations (49.9% saved)

localize13.0ms (0.2%)

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)

rewrite43.0ms (0.6%)

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:

23.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
17.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series180.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

127.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
52.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5012	707

prune51.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	39	5	44

Merged error: 1.2b

Counts

44 → 5

Compiler

Compiled 1114 to 639 computations (42.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.1b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.6b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
38.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
12×	`cos-sum_binary64_894` `add-cube-cbrt_binary64_795`
9×	`cancel-sign-sub-inv_binary64_726`
8×	`exp-diff_binary64_808`
6×	`exp-prod_binary64_812` `pow1_binary64_821` `unpow-prod-down_binary64_839`
5×	`add-exp-log_binary64_798` `add-log-exp_binary64_799`
4×	`log-div_binary64_847` `add-cbrt-cube_binary64_796` `log-pow_binary64_849` `log-prod_binary64_846`
3×	`cos-diff_binary64_897` `sub-neg_binary64_753` `pow-unpow_binary64_837`
2×	`difference-of-squares_binary64_729` `exp-sum_binary64_806`
1×	`unpow2_binary64_825` `pow-exp_binary64_828` `rem-exp-log_binary64_800` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `rem-log-exp_binary64_801` `sqr-pow_binary64_732` `times-frac_binary64_766` `pow-pow_binary64_832`

Counts

4 → 69

Calls

4 calls:

10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
10.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series416.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
126.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
80.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
52.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5075	1716

prune134.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	80	6	86

Merged error: 1.2b

Counts

86 → 6

Compiler

Compiled 3177 to 1649 computations (48.1% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3))
0.6b	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)))
0.8b	(pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)
38.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite60.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_791`
19×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
17×	`log-prod_binary64_846`
16×	`cos-sum_binary64_894`
12×	`cancel-sign-sub-inv_binary64_726` `exp-diff_binary64_808` `cube-div_binary64_789` `cube-prod_binary64_788` `unpow-prod-down_binary64_839`
8×	`cbrt-div_binary64_792`
7×	`cos-diff_binary64_897`
6×	`exp-sum_binary64_806` `pow1_binary64_821`
5×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
4×	`log-div_binary64_847` `add-log-exp_binary64_799` `sub-neg_binary64_753` `pow-pow_binary64_832`
3×	`cube-mult_binary64_790` `exp-prod_binary64_812` `unpow3_binary64_826` `sqr-pow_binary64_732` `pow-unpow_binary64_837`
2×	`pow1/3_binary64_842` `log-pow_binary64_849`
1×	`rem-cbrt-cube_binary64_784` `pow-exp_binary64_828` `rem-cube-cbrt_binary64_783` `pow-to-exp_binary64_829` `rem-log-exp_binary64_801`

Counts

4 → 102

Calls

4 calls:

13.0ms	(pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)
13.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)))
11.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series708.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

363.0ms	(pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)
146.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3)))
125.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))) 3))
74.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify147.0ms (2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5177	3032

prune207.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	114	6	120

Merged error: 1.2b

Counts

120 → 6

Compiler

Compiled 4535 to 2409 computations (46.9% saved)

regimes321.0ms (4.3%)

Compiler: Compiled 4484 to 3438 computations (23.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	26
1	62	26

end0.0ms (0%)

sample1.9s (25.7%)

Algorithm

1×

intervals

Results

769.0ms	7817×	body	128	valid
34.0ms	89×	body	1024	invalid
33.0ms	77×	body	1024	valid
30.0ms	284×	body	128	invalid
20.0ms	70×	body	512	invalid
19.0ms	63×	body	512	valid
10.0ms	51×	body	256	invalid
9.0ms	43×	body	256	valid
8.0ms	15×	body	2048	invalid

Compiler

Compiled 783 to 602 computations (23.1% saved)

Details

analyze2.3s (30.6%)

sample47.0ms (0.6%)

simplify140.0ms (1.9%)

prune5.0ms (0.1%)

localize23.0ms (0.3%)

rewrite48.0ms (0.7%)

series295.0ms (4%)

simplify71.0ms (1%)

prune116.0ms (1.6%)

localize13.0ms (0.2%)

rewrite43.0ms (0.6%)

series180.0ms (2.4%)

simplify35.0ms (0.5%)

prune51.0ms (0.7%)

localize21.0ms (0.3%)

rewrite46.0ms (0.6%)

series416.0ms (5.6%)

simplify66.0ms (0.9%)

prune134.0ms (1.8%)

localize26.0ms (0.4%)

rewrite60.0ms (0.8%)

series708.0ms (9.6%)

simplify147.0ms (2%)

prune207.0ms (2.8%)

regimes321.0ms (4.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (25.7%)

Profiling