Details

analyze2.9s (33.2%)

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)

sample2.2s (24.8%)

Symmetry

(sort m n)

Results

1.8s	8116×	body	128	valid
64.0ms	82×	body	1024	invalid
57.0ms	276×	body	128	invalid
50.0ms	59×	body	1024	valid
49.0ms	87×	body	512	invalid
30.0ms	48×	body	512	valid
29.0ms	23×	body	2048	invalid
20.0ms	53×	body	256	invalid
13.0ms	33×	body	256	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify69.0ms (0.8%)

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

14.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.4b	(.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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	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)
✓	33.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series98.0ms (1.1%)

Counts

4 → 168

Calls

4 calls:

48.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
26.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
17.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
70×	`add-sqr-sqrt_binary64`
57×	`prod-diff_binary64`
42×	`add-cube-cbrt_binary64`
26×	`fabs-mul_binary64`

Counts

4 → 156

Calls

4 calls:

17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(*.f64 K (+.f64 m n))
7.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify211.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
385×	`associate-r_binary64`
362×	`associate-l_binary64`
329×	`fma-def_binary64`
268×	`*-commutative_binary64`

Counts

324 → 305

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	11388
1	1288	8942
2	4458	8942
3	5047	8942

prune463.0ms (5.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	299	6	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	300	6	306

Error

1.2b

Counts

306 → 6

Alt Table

Status	Error	Program
	9.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	47.9b	(*.f64 (cos.f64 (-.f64 (/.f64 (exp.f64 (+.f64 (log.f64 K) (log.f64 (+.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))))
	14.4b	(.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))))
	14.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.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))))
	14.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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 15208 to 7399 computations (51.3% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	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)

prune340.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	183	6	189

Error

1.2b

Counts

189 → 6

Alt Table

Status	Error	Program
▶	9.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	47.9b	(*.f64 (cos.f64 (-.f64 (/.f64 (exp.f64 (+.f64 (log.f64 K) (log.f64 (+.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))))
	14.4b	(.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))))
	14.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.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))))
	14.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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 7613 to 3848 computations (49.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
✓	0.0b	(-.f64 (.f64 1/2 (.f64 n K)) M)
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	23.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series16.0ms (0.2%)

Counts

2 → 21

Calls

2 calls:

10.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
7.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cos-sum_binary64`
6×	`cancel-sign-sub-inv_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`prod-diff_binary64`

Counts

2 → 37

Calls

2 calls:

6.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
4.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-neg_binary64`
534×	`cancel-sign-sub-inv_binary64`
404×	`fma-def_binary64`
337×	`neg-mul-1_binary64`
310×	`distribute-rgt-neg-in_binary64`

Counts

58 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1151
1	261	1073
2	895	1012
3	2154	992
4	4491	984
5	4965	984

prune426.0ms (4.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	245	7	252

Error

1.2b

Counts

252 → 7

Alt Table

Status	Error	Program
	14.4b	(.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))))
	28.7b	(.f64 (cos.f64 (expm1.f64 (log1p.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	9.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	47.9b	(*.f64 (cos.f64 (-.f64 (/.f64 (exp.f64 (+.f64 (log.f64 K) (log.f64 (+.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))))
	14.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.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))))
▶	14.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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 11098 to 5762 computations (48.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.f64 K) (+.f64 m n)))
✓	0.5b	(*.f64 (cbrt.f64 K) (cbrt.f64 K))
✓	0.6b	(cbrt.f64 K)
✓	33.1b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.f64 K) (+.f64 m n))) 2) M))

series118.0ms (1.3%)

Counts

4 → 108

Calls

4 calls:

36.0ms	(*.f64 (cbrt.f64 K) (cbrt.f64 K))
35.0ms	(cbrt.f64 K)
28.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.f64 K) (+.f64 m n))) 2) M))
18.0ms	(.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.f64 K) (+.f64 m n)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
25×	`cos-sum_binary64`
23×	`pow1_binary64`

Counts

4 → 120

Calls

4 calls:

14.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.f64 K) (+.f64 m n))) 2) M))
8.0ms	(.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (cbrt.f64 K) (+.f64 m n)))
4.0ms	(*.f64 (cbrt.f64 K) (cbrt.f64 K))
1.0ms	(cbrt.f64 K)

simplify162.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

659×	`times-frac_binary64`
493×	`associate-l_binary64`
486×	`associate-r_binary64`
467×	`unswap-sqr_binary64`
280×	`fma-neg_binary64`

Counts

228 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	402	5010
1	770	3918
2	3189	3741
3	4174	3642
4	4993	3642

prune444.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	229	6	235
Fresh	4	0	4
Picked	1	0	1
Done	1	1	2
Total	235	7	242

Error

1.1b

Counts

242 → 7

Alt Table

Status	Error	Program
	14.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 K)) 5) (cbrt.f64 (cbrt.f64 K))) (.f64 (cbrt.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))))
✓	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	37.8b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (pow.f64 K 1/3)) (.f64 (cbrt.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))))
	37.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (cbrt.f64 K) (*.f64 (pow.f64 K 2/3) (+.f64 n m))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	37.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 K 2/3)) (cbrt.f64 (pow.f64 K 2/3))) (.f64 (cbrt.f64 (cbrt.f64 K)) (cbrt.f64 (cbrt.f64 K)))) (.f64 (cbrt.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))))
	14.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)))) (.f64 (cbrt.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))))
	14.4b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (sqrt.f64 2)) (/.f64 (.f64 (cbrt.f64 K) (+.f64 m n)) (sqrt.f64 2)) (neg.f64 (.f64 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (.f64 M 1)))) (.f64 (sin.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (sqrt.f64 2)) (/.f64 (.f64 (cbrt.f64 K) (+.f64 m n)) (sqrt.f64 2)) (neg.f64 (.f64 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 11715 to 4956 computations (57.7% saved)

regimes822.0ms (9.4%)

Accuracy

Total 0.2b remaining (17.9%)

Threshold costs 0.2b (17.9%)

Counts

106 → 1

Compiler

Compiled 22718 to 14526 computations (36.1% saved)

simplify3.0ms (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	31
1	28	31
2	45	31
3	60	31
4	69	31
5	72	31
6	72	31

end188.0ms (2.2%)

Remove: (sort m n)
Compiler: Compiled 430 to 289 computations (32.8% saved)

Details

analyze2.9s (33.2%)

sample2.2s (24.8%)

simplify69.0ms (0.8%)

prune4.0ms (0%)

localize18.0ms (0.2%)

series98.0ms (1.1%)

rewrite57.0ms (0.6%)

simplify211.0ms (2.4%)

prune463.0ms (5.3%)

localize15.0ms (0.2%)

prune340.0ms (3.9%)

localize20.0ms (0.2%)

series16.0ms (0.2%)

rewrite12.0ms (0.1%)

simplify121.0ms (1.4%)

prune426.0ms (4.9%)

localize23.0ms (0.3%)

series118.0ms (1.3%)

rewrite37.0ms (0.4%)

simplify162.0ms (1.9%)

prune444.0ms (5.1%)

regimes822.0ms (9.4%)

simplify3.0ms (0%)

end188.0ms (2.2%)

Profiling