Details

analyze2.3s (32.3%)

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

27.0ms	250×	body	128	valid
1.0ms	2×	body	1024	valid
1.0ms	3×	body	512	invalid
1.0ms	2×	body	512	valid
1.0ms	6×	body	128	invalid
1.0ms	1×	body	1024	invalid
0.0ms	2×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5053	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: 14.5b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(*.f64 K (+.f64 m n))
32.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64` `times-frac_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `cos-sum_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
7.0ms	(*.f64 K (+.f64 m n))

series396.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
118.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
76.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
47.0ms	(*.f64 K (+.f64 m n))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5052	1189

prune143.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 1.4b

Counts

89 → 5

Compiler

Compiled 3025 to 1531 computations (49.4% saved)

localize14.0ms (0.2%)

Local error

Found 2 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)

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`diff-log_binary64` `add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

2 → 37

Calls

2 calls:

17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series383.0ms (5.3%)

Counts

2 → 6

Calls

2 calls:

280.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
103.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify36.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5173	1008

prune58.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	43	5	48

Merged error: 1.4b

Counts

48 → 5

Compiler

Compiled 1239 to 707 computations (42.9% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3))
0.6b	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3)
32.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64` `cbrt-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`unpow-prod-down_binary64` `cube-prod_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64`
2×	`associate-*r/_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `cos-sum_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(*.f64 K (+.f64 m n))
4.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3))

series822.0ms (11.4%)

Counts

4 → 12

Calls

4 calls:

482.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3)
150.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
145.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3))
46.0ms	(*.f64 K (+.f64 m n))

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4957	1522
1	4957	1522

prune138.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	87	6	93

Merged error: 1.4b

Counts

93 → 6

Compiler

Compiled 3305 to 1769 computations (46.5% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cos.f64 M)) (.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M)))
0.2b	(.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M))
37.5b	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
37.6b	(sin.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`sin-mult_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `cos-mult_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 45

Calls

4 calls:

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

series511.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

304.0ms	(+.f64 (.f64 (cos.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cos.f64 M)) (.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M)))
119.0ms	(.f64 (sin.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (sin.f64 M))
47.0ms	(sin.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))
41.0ms	(cos.f64 (/.f64 (*.f64 K (+.f64 m n)) 2))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5322	1403

prune102.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	57	6	63

Merged error: 1.4b

Counts

63 → 6

Compiler

Compiled 2711 to 1251 computations (53.9% saved)

regimes104.0ms (1.4%)

Compiler: Compiled 1035 to 870 computations (15.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	26
1	62	26

end0.0ms (0%)

sample1.6s (22.6%)

Algorithm

1×

intervals

Results

855.0ms	7825×	body	128	valid
39.0ms	72×	body	1024	valid
39.0ms	332×	body	128	invalid
35.0ms	75×	body	1024	invalid
27.0ms	83×	body	512	invalid
25.0ms	73×	body	512	valid
19.0ms	22×	body	2048	invalid
14.0ms	64×	body	256	invalid
7.0ms	30×	body	256	valid

Compiler

Compiled 252 to 209 computations (17.1% saved)

Details

analyze2.3s (32.3%)

sample51.0ms (0.7%)

simplify50.0ms (0.7%)

prune5.0ms (0.1%)

localize22.0ms (0.3%)

rewrite49.0ms (0.7%)

series396.0ms (5.5%)

simplify76.0ms (1.1%)

prune143.0ms (2%)

localize14.0ms (0.2%)

rewrite33.0ms (0.5%)

series383.0ms (5.3%)

simplify36.0ms (0.5%)

prune58.0ms (0.8%)

localize27.0ms (0.4%)

rewrite32.0ms (0.4%)

series822.0ms (11.4%)

simplify53.0ms (0.7%)

prune138.0ms (1.9%)

localize31.0ms (0.4%)

rewrite24.0ms (0.3%)

series511.0ms (7.1%)

simplify82.0ms (1.1%)

prune102.0ms (1.4%)

regimes104.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (22.6%)

Profiling