Details

analyze2.2s (30.1%)

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)

sample51.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	253×	body	128	valid
1.0ms	12×	body	128	invalid
1.0ms	3×	body	512	invalid
1.0ms	1×	body	2048	invalid
0.0ms	1×	body	1024	valid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify138.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5097	43

prune6.0ms (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: 14.2b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize255.0ms (3.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.4b	(/.f64 (*.f64 K (+.f64 m n)) 2)
33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
12×	`add-exp-log_binary64_798`
11×	`add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796`
7×	`pow1_binary64_821`
6×	`unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `associate-r_binary64_700` `associate-*r/_binary64_702` `times-frac_binary64_766`
3×	`cancel-sign-sub-inv_binary64_726` `associate-/r_binary64_704` `associate-l*_binary64_701` `pow-unpow_binary64_837`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `flip3-+_binary64_763` `associate-/l/_binary64_707` `difference-of-squares_binary64_729` `flip-+_binary64_734` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `distribute-lft-out_binary64_711` `unpow2_binary64_825` `distribute-lft-in_binary64_709` `pow-exp_binary64_828` `div-inv_binary64_757` `distribute-rgt-in_binary64_710` `associate-/l_binary64_705` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `sqr-pow_binary64_732` `cos-diff_binary64_897` `clear-num_binary64_759` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 79

Calls

4 calls:

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

series199.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
54.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
40.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
24.0ms	(*.f64 K (+.f64 m n))

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5237	1297

prune147.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 0.6b

Counts

92 → 4

Compiler

Compiled 3107 to 1547 computations (50.2% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (+.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)

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_782`
12×	`*-un-lft-identity_binary64_760`
7×	`add-log-exp_binary64_799`
6×	`add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
4×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `pow1_binary64_821`
3×	`cancel-sign-sub-inv_binary64_726` `add-cbrt-cube_binary64_796` `pow-unpow_binary64_837`
2×	`distribute-lft-out--_binary64_712` `times-frac_binary64_766`
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` `sub-neg_binary64_753` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

3 → 50

Calls

3 calls:

15.0ms	(+.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)

series194.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

120.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
55.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
18.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4936	989
1	4936	989

prune70.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	59	4	63

Merged error: 0.6b

Counts

63 → 4

Compiler

Compiled 1538 to 858 computations (44.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2)))
0.3b	(/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2))
0.4b	(/.f64 K (sqrt.f64 2))
34.0b	(cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2)) M))

rewrite61.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_782`
44×	`times-frac_binary64_766`
40×	`*-un-lft-identity_binary64_760`
38×	`add-cube-cbrt_binary64_795`
28×	`sqrt-prod_binary64_776`
22×	`associate-r_binary64_700`
20×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
12×	`associate-/r*_binary64_704`
6×	`cbrt-undiv_binary64_794` `div-exp_binary64_811` `pow1_binary64_821`
5×	`associate-/l/_binary64_707`
4×	`associate-l/_binary64_703` `prod-exp_binary64_809` `cos-sum_binary64_894` `flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734` `associate-/l_binary64_705` `frac-times_binary64_770` `associate-l_binary64_701` `cbrt-unprod_binary64_793`
3×	`unswap-sqr_binary64_728` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757`
2×	`frac-2neg_binary64_771` `associate-*r/_binary64_702` `clear-num_binary64_759`
1×	`distribute-lft-out_binary64_711` `cos-diff_binary64_897` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 132

Calls

4 calls:

16.0ms	(*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2)))
15.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2)) M))
11.0ms	(/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2))
4.0ms	(/.f64 K (sqrt.f64 2))

series474.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

268.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2)) M))
110.0ms	(/.f64 (*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2))) (sqrt.f64 2))
61.0ms	(*.f64 (+.f64 m n) (/.f64 K (sqrt.f64 2)))
34.0ms	(/.f64 K (sqrt.f64 2))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4961	2179
1	4961	2179

prune249.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	145	3	148

Merged error: 0.6b

Counts

148 → 3

Compiler

Compiled 5364 to 3053 computations (43.1% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 K (sqrt.f64 2))
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
33.8b	(cos.f64 (-.f64 (*.f64 (/.f64 (+.f64 m n) (fabs.f64 (cbrt.f64 2))) (/.f64 (/.f64 K (sqrt.f64 2)) (sqrt.f64 (cbrt.f64 2)))) M))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
18×	`times-frac_binary64_766`
12×	`sqrt-prod_binary64_776`
6×	`add-exp-log_binary64_798` `associate-/r*_binary64_704` `add-cbrt-cube_binary64_796` `cbrt-prod_binary64_791`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `pow1_binary64_821`
3×	`cancel-sign-sub-inv_binary64_726` `associate-/l*_binary64_705`
2×	`pow1/3_binary64_842`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `cos-diff_binary64_897` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 73

Calls

4 calls:

28.0ms	(cos.f64 (-.f64 (*.f64 (/.f64 (+.f64 m n) (fabs.f64 (cbrt.f64 2))) (/.f64 (/.f64 K (sqrt.f64 2)) (sqrt.f64 (cbrt.f64 2)))) M))
4.0ms	(/.f64 K (sqrt.f64 2))
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)

series537.0ms (7.3%)

Counts

4 → 8

Calls

4 calls:

504.0ms	(cos.f64 (-.f64 (*.f64 (/.f64 (+.f64 m n) (fabs.f64 (cbrt.f64 2))) (/.f64 (/.f64 K (sqrt.f64 2)) (sqrt.f64 (cbrt.f64 2)))) M))
33.0ms	(/.f64 K (sqrt.f64 2))
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5028	1485

prune170.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	81	3	84

Merged error: 0.6b

Counts

84 → 3

Compiler

Compiled 3503 to 2264 computations (35.4% saved)

regimes271.0ms (3.7%)

Compiler: Compiled 3584 to 2802 computations (21.8% 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 (25.4%)

Algorithm

1×

intervals

Results

832.0ms	7858×	body	128	valid
36.0ms	86×	body	1024	invalid
29.0ms	279×	body	128	invalid
25.0ms	84×	body	512	invalid
25.0ms	54×	body	1024	valid
18.0ms	54×	body	512	valid
13.0ms	62×	body	256	invalid
9.0ms	16×	body	2048	invalid
8.0ms	33×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 633 to 496 computations (21.6% saved)

Details

analyze2.2s (30.1%)

sample51.0ms (0.7%)

simplify138.0ms (1.9%)

prune6.0ms (0.1%)

localize255.0ms (3.4%)

rewrite44.0ms (0.6%)

series199.0ms (2.7%)

simplify63.0ms (0.9%)

prune147.0ms (2%)

localize14.0ms (0.2%)

rewrite42.0ms (0.6%)

series194.0ms (2.6%)

simplify71.0ms (1%)

prune70.0ms (0.9%)

localize22.0ms (0.3%)

rewrite61.0ms (0.8%)

series474.0ms (6.4%)

simplify82.0ms (1.1%)

prune249.0ms (3.4%)

localize30.0ms (0.4%)

rewrite43.0ms (0.6%)

series537.0ms (7.3%)

simplify59.0ms (0.8%)

prune170.0ms (2.3%)

regimes271.0ms (3.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (25.4%)

Profiling