Details

analyze4.1s (18.6%)

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)

sample93.0ms (0.4%)

Algorithm

1×

intervals

Results

45.0ms	248×	body	128	valid
6.0ms	7×	body	1024	invalid
3.0ms	4×	body	1024	valid
2.0ms	13×	body	128	invalid
2.0ms	3×	body	512	invalid
1.0ms	2×	body	512	valid
1.0ms	2×	body	256	valid
1.0ms	2×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify267.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5097	43

prune10.0ms (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

14.3b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(-.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)
32.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite325.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

14.2b

Rules

20×	`*-un-lft-identity_binary64_760`
18×	`add-sqr-sqrt_binary64_782`
11×	`add-log-exp_binary64_799`
10×	`cancel-sign-sub-inv_binary64_726`
9×	`add-cube-cbrt_binary64_795`
6×	`unpow-prod-down_binary64_839`
5×	`pow1_binary64_821` `add-exp-log_binary64_798`
4×	`cos-sum_binary64_894` `add-cbrt-cube_binary64_796` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`
3×	`sub-neg_binary64_753` `pow-unpow_binary64_837` `diff-log_binary64_852`
2×	`flip3--_binary64_764` `flip--_binary64_735` `distribute-lft-out_binary64_711`
1×	`cos-diff_binary64_897` `times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `sum-log_binary64_851` `associate--r+_binary64_696`

Counts

4 → 69

Calls

4 calls:

43.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
23.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
20.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
18.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

Compiler

Compiled 2698 to 1339 computations (50.4% saved)

series2.5s (11.4%)

Error

1.7b

Counts

4 → 91

Calls

4 calls:

1.2s	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
525.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
326.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
234.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 7843 to 5373 computations (31.5% saved)

simplify120.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5050	3430

prune460.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	154	6	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	6	161

Error

1.6b

Counts

161 → 6

Compiler

Compiled 5387 to 2568 computations (52.3% saved)

localize37.0ms (0.2%)

Local error

Found 3 expressions with local error:

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 (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)

rewrite260.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

Rules

20×	`*-un-lft-identity_binary64_760`
18×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
8×	`add-log-exp_binary64_799` `cancel-sign-sub-inv_binary64_726` `associate-r_binary64_700`
6×	`unpow-prod-down_binary64_839` `pow1_binary64_821`
5×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `exp-sum_binary64_806`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `distribute-lft-out_binary64_711` `associate-l_binary64_701`
2×	`diff-log_binary64_852` `sub-neg_binary64_753`
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` `sum-log_binary64_851` `flip3--_binary64_764` `flip--_binary64_735` `associate--r+_binary64_696` `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`

Counts

3 → 65

Calls

3 calls:

48.0ms

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

36.0ms

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

23.0ms

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

Compiler

Compiled 2067 to 1040 computations (49.7% saved)

series2.6s (11.7%)

Error

1.6b

Counts

3 → 73

Calls

3 calls:

1.1s

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

752.0ms

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

524.0ms

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

Compiler

Compiled 5821 to 4008 computations (31.1% saved)

simplify162.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5020	3800

prune300.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	138	6	144

Error

1.6b

Counts

144 → 6

Compiler

Compiled 3854 to 1788 computations (53.6% saved)

localize38.0ms (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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
27.7b	(cos.f64 (.f64 1/2 (.f64 m K)))

rewrite215.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

Rules

15×	`*-un-lft-identity_binary64_760`
13×	`add-sqr-sqrt_binary64_782`
8×	`add-log-exp_binary64_799`
6×	`add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
4×	`pow1_binary64_821` `add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726`
3×	`add-cbrt-cube_binary64_796` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837`
2×	`diff-log_binary64_852` `distribute-lft-out_binary64_711`
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` `sum-log_binary64_851` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `associate--r+_binary64_696`

Counts

3 → 48

Calls

3 calls:

37.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
23.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
5.0ms	(cos.f64 (.f64 1/2 (.f64 m K)))

Compiler

Compiled 1645 to 894 computations (45.7% saved)

series2.0s (9%)

Error

1.6b

Counts

3 → 68

Calls

3 calls:

1.2s	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
540.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
85.0ms	(cos.f64 (.f64 1/2 (.f64 m K)))

Compiler

Compiled 5226 to 3721 computations (28.8% saved)

simplify142.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4968	2624
1	4968	2624

prune305.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	116	6	122

Error

1.6b

Counts

122 → 6

Compiler

Compiled 3539 to 1799 computations (49.2% saved)

localize47.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))
27.7b	(cos.f64 (.f64 1/2 (.f64 K m)))
27.7b	(cos.f64 (.f64 1/2 (.f64 K m)))
27.7b	(cos.f64 (.f64 1/2 (.f64 K m)))

rewrite158.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

Rules

5×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
4×	`pow1_binary64_821` `add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
3×	`cbrt-prod_binary64_791`
1×	`pow1/3_binary64_842`

Counts

4 → 32

Calls

4 calls:

5.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))
5.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))
5.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))
4.0ms	(cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))

Compiler

Compiled 1545 to 909 computations (41.2% saved)

series722.0ms (3.3%)

Error

1.6b

Counts

4 → 32

Calls

4 calls:

334.0ms	(cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))
104.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))
103.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))
83.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))

Compiler

Compiled 3730 to 2732 computations (26.8% saved)

simplify175.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4731	694
1	4731	694

prune229.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	64	6	70

Error

1.6b

Counts

70 → 6

Compiler

Compiled 2772 to 1592 computations (42.6% saved)

regimes1.4s (6.5%)

Accuracy

Total 0.2b remaining (15.2%)

Threshold costs 0.2b (15.2%)

Compiler

Compiled 8918 to 7608 computations (14.7% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	62	31
1	62	31

end0.0ms (0%)

sample5.2s (23.9%)

Algorithm

1×

intervals

Results

1.5s	7841×	body	128	valid
70.0ms	88×	body	1024	invalid
68.0ms	72×	body	1024	valid
52.0ms	265×	body	128	invalid
47.0ms	82×	body	512	invalid
35.0ms	56×	body	512	valid
27.0ms	53×	body	256	invalid
12.0ms	30×	body	256	valid
12.0ms	11×	body	2048	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 1525 to 1299 computations (14.8% saved)

Details

analyze4.1s (18.6%)

sample93.0ms (0.4%)

simplify267.0ms (1.2%)

prune10.0ms (0%)

localize39.0ms (0.2%)

rewrite325.0ms (1.5%)

series2.5s (11.4%)

simplify120.0ms (0.5%)

prune460.0ms (2.1%)

localize37.0ms (0.2%)

rewrite260.0ms (1.2%)

series2.6s (11.7%)

simplify162.0ms (0.7%)

prune300.0ms (1.4%)

localize38.0ms (0.2%)

rewrite215.0ms (1%)

series2.0s (9%)

simplify142.0ms (0.6%)

prune305.0ms (1.4%)

localize47.0ms (0.2%)

rewrite158.0ms (0.7%)

series722.0ms (3.3%)

simplify175.0ms (0.8%)

prune229.0ms (1%)

regimes1.4s (6.5%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample5.2s (23.9%)

Profiling