Details

analyze2.2s (28%)

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)

sample50.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	250×	body	128	valid
6.0ms	11×	body	128	invalid
1.0ms	3×	body	1024	valid
1.0ms	2×	body	2048	invalid
1.0ms	4×	body	256	invalid
1.0ms	2×	body	512	valid
1.0ms	2×	body	512	invalid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify133.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

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: 14.7b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize19.0ms (0.2%)

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)
0.2b	(/.f64 (*.f64 K (+.f64 m n)) 2)
32.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite45.0ms (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:

14.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
6.0ms	(*.f64 K (+.f64 m n))

series185.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
53.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
33.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
23.0ms	(*.f64 K (+.f64 m n))

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5237	1297

prune148.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 1.2b

Counts

92 → 5

Compiler

Compiled 3160 to 1584 computations (49.9% saved)

localize13.0ms (0.2%)

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

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_760`
13×	`add-sqr-sqrt_binary64_782`
10×	`add-log-exp_binary64_799`
6×	`add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
4×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
3×	`distribute-lft-out_binary64_711` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837`
2×	`diff-log_binary64_852` `sum-log_binary64_851`
1×	`unpow2_binary64_825` `flip3-+_binary64_763` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `associate--r+_binary64_696` `sqr-pow_binary64_732` `sub-neg_binary64_753` `times-frac_binary64_766` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

3 → 53

Calls

3 calls:

16.0ms	(-.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)

series315.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

137.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
122.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
55.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5488	1364

prune79.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	62	5	67

Merged error: 1.2b

Counts

67 → 5

Compiler

Compiled 1688 to 945 computations (44% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

16.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
16.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
16.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
32.9b	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) M))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`cbrt-prod_binary64_791`
11×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
9×	`times-frac_binary64_766`
4×	`cos-sum_binary64_894` `add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`pow1/3_binary64_842` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757` `cbrt-div_binary64_792`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753`

Counts

4 → 60

Calls

4 calls:

14.0ms	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) M))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

series663.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))) M))
160.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
160.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
143.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4941	1269
1	4941	1269

prune140.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	72	5	77

Merged error: 1.2b

Counts

77 → 5

Compiler

Compiled 3683 to 1844 computations (49.9% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

16.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
16.4b	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
17.0b	(cbrt.f64 (*.f64 K n))
30.2b	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 K n)))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) M))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod_binary64_791`
9×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
6×	`times-frac_binary64_766`
4×	`cos-sum_binary64_894` `add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`pow1/3_binary64_842` `cancel-sign-sub-inv_binary64_726`
2×	`div-inv_binary64_757` `cbrt-div_binary64_792`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753`

Counts

4 → 53

Calls

4 calls:

14.0ms	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 K n)))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) M))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
5.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
2.0ms	(cbrt.f64 (*.f64 K n))

series700.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(cos.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (.f64 (cbrt.f64 1/2) (cbrt.f64 (.f64 K n)))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) M))
147.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
137.0ms	(cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
55.0ms	(cbrt.f64 (*.f64 K n))

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4954	1607
1	4954	1607

prune137.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	64	6	70

Merged error: 1.2b

Counts

70 → 6

Compiler

Compiled 3421 to 1721 computations (49.7% saved)

regimes400.0ms (5.2%)

Compiler: Compiled 5906 to 4416 computations (25.2% 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%)

sample2.1s (27.3%)

Algorithm

1×

intervals

Results

837.0ms	7826×	body	128	valid
33.0ms	311×	body	128	invalid
33.0ms	72×	body	1024	valid
29.0ms	69×	body	1024	invalid
27.0ms	89×	body	512	invalid
25.0ms	64×	body	512	valid
14.0ms	67×	body	256	invalid
11.0ms	20×	body	2048	invalid
8.0ms	37×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 1020 to 765 computations (25% saved)

Details

analyze2.2s (28%)

sample50.0ms (0.7%)

simplify133.0ms (1.7%)

prune5.0ms (0.1%)

localize19.0ms (0.2%)

rewrite45.0ms (0.6%)

series185.0ms (2.4%)

simplify56.0ms (0.7%)

prune148.0ms (1.9%)

localize13.0ms (0.2%)

rewrite45.0ms (0.6%)

series315.0ms (4.1%)

simplify50.0ms (0.6%)

prune79.0ms (1%)

localize25.0ms (0.3%)

rewrite37.0ms (0.5%)

series663.0ms (8.6%)

simplify81.0ms (1.1%)

prune140.0ms (1.8%)

localize32.0ms (0.4%)

rewrite33.0ms (0.4%)

series700.0ms (9.1%)

simplify59.0ms (0.8%)

prune137.0ms (1.8%)

regimes400.0ms (5.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (27.3%)

Profiling