Details

analyze2.9s (29.9%)

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 35 to 24 computations (31.4% saved)

sample2.1s (22.1%)

Symmetry

(sort m n)

Results

1.7s	8089×	body	128	valid
96.0ms	117×	body	1024	invalid
66.0ms	308×	body	128	invalid
62.0ms	68×	body	1024	valid
34.0ms	59×	body	512	valid
33.0ms	29×	body	2048	invalid
32.0ms	60×	body	512	invalid
23.0ms	57×	body	256	invalid
16.0ms	39×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

691×	`exp-prod_binary64`
507×	`exp-sum_binary64`
446×	`fma-neg_binary64`
375×	`associate-l_binary64`
251×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	129	43
3	384	43
4	1266	43
5	4023	43
6	4945	43
7	5019	43

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

15.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 128 to 80 computations (37.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)
✓	34.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series91.0ms (0.9%)

Counts

4 → 180

Calls

4 calls:

38.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
22.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
14.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
38×	`add-cube-cbrt_binary64`
25×	`cos-sum_binary64`

Counts

4 → 129

Calls

4 calls:

11.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
9.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

simplify189.0ms (2%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-neg_binary64`
284×	`associate-r_binary64`
268×	`fma-def_binary64`
241×	`distribute-rgt-neg-in_binary64`
240×	`associate-l_binary64`

Counts

309 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	447	8684
1	953	6801
2	3082	6605
3	4887	6605
4	5040	6605

prune307.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	259	4	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	260	4	264

Error

0.8b

Counts

264 → 4

Alt Table

Status	Error	Program
	15.7b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 11853 to 5587 computations (52.9% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

series7.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

7.0ms

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

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
49×	`times-frac_binary64`
48×	`prod-diff_binary64`

Counts

1 → 83

Calls

1 calls:

9.0ms

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

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1011×	`fma-def_binary64`
456×	`distribute-rgt-in_binary64`
400×	`fma-neg_binary64`
398×	`distribute-lft-in_binary64`
288×	`times-frac_binary64`

Counts

119 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	2560
1	213	1627
2	596	1258
3	1855	1257
4	4398	1257
5	4945	1257
6	4891	1257

prune256.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	208	4	212

Error

0.8b

Counts

212 → 4

Alt Table

Status	Error	Program
	15.7b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	10.3b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 6761 to 3109 computations (54% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)
✓	30.2b	(cos.f64 (.f64 1/2 (.f64 K m)))

series5.0ms (0%)

Counts

1 → 8

Calls

1 calls:

5.0ms

(cos.f64 (*.f64 1/2 (*.f64 K m)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 9

Calls

1 calls:

1.0ms

(cos.f64 (*.f64 1/2 (*.f64 K m)))

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

611×	`distribute-rgt-neg-in_binary64`
528×	`distribute-lft-neg-in_binary64`
489×	`fma-def_binary64`
393×	`unsub-neg_binary64`
369×	`*-commutative_binary64`

Counts

17 → 17

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	40	316
1	93	289
2	242	281
3	960	277
4	2431	265
5	3705	259
6	4723	241
7	5139	241

prune285.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	226	3	229

Error

0.8b

Counts

229 → 3

Alt Table

Status	Error	Program
▶	10.3b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m)))) (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (cbrt.f64 (cos.f64 (.f64 1/2 (*.f64 K m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 8042 to 3988 computations (50.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m)))) (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m)))))
✓	0.2b	(.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m)))) (cbrt.f64 (cos.f64 (.f64 1/2 (*.f64 K m)))))
✓	0.4b	(cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))
	30.2b	(cos.f64 (.f64 1/2 (.f64 K m)))

series860.0ms (8.9%)

Counts

3 → 72

Calls

3 calls:

547.0ms

(*.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))

308.0ms

(cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))

5.0ms

(*.f64 (*.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))) (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

9.0ms

(*.f64 (*.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))) (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))

6.0ms

(*.f64 (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))) (cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))

1.0ms

(cbrt.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))

simplify128.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

688×	`unswap-sqr_binary64`
393×	`fma-neg_binary64`
378×	`cancel-sign-sub-inv_binary64`
316×	`log-prod_binary64`
255×	`*-commutative_binary64`

Counts

165 → 138

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	127	2961
1	280	2569
2	869	2442
3	1843	2374
4	4488	2338
5	4854	2338
6	4943	2338

prune435.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	235	5	240

Error

0.8b

Counts

240 → 5

Alt Table

Status	Error	Program
	10.3b	(.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 (.f64 K m))) 2)) (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) 8) (cbrt.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m)))) (cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))) (cbrt.f64 (cos.f64 (.f64 1/2 (*.f64 K m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 11352 to 6751 computations (40.5% saved)

regimes1.5s (15.9%)

Accuracy

Total 0.2b remaining (13%)

Threshold costs 0.2b (13%)

Counts

203 → 1

Compiler

Compiled 43298 to 30642 computations (29.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	30	26
2	46	26
3	61	26
4	70	26
5	73	26
6	72	26

end139.0ms (1.4%)

Remove: (sort m n)
Compiler: Compiled 280 to 202 computations (27.9% saved)

Details

analyze2.9s (29.9%)

sample2.1s (22.1%)

simplify62.0ms (0.6%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series91.0ms (0.9%)

rewrite44.0ms (0.5%)

simplify189.0ms (2%)

prune307.0ms (3.2%)

localize13.0ms (0.1%)

series7.0ms (0.1%)

rewrite18.0ms (0.2%)

simplify105.0ms (1.1%)

prune256.0ms (2.6%)

localize16.0ms (0.2%)

series5.0ms (0%)

rewrite2.0ms (0%)

simplify72.0ms (0.7%)

prune285.0ms (3%)

localize20.0ms (0.2%)

series860.0ms (8.9%)

rewrite22.0ms (0.2%)

simplify128.0ms (1.3%)

prune435.0ms (4.5%)

regimes1.5s (15.9%)

simplify4.0ms (0%)

end139.0ms (1.4%)

Profiling