Details

analyze3.0s (19.8%)

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)

sample2.3s (15.4%)

Symmetry

(sort m n)

Results

1.9s	8100×	body	128	valid
85.0ms	91×	body	1024	invalid
69.0ms	318×	body	128	invalid
53.0ms	60×	body	1024	valid
46.0ms	81×	body	512	invalid
35.0ms	63×	body	512	valid
22.0ms	52×	body	256	invalid
20.0ms	17×	body	2048	invalid
12.0ms	32×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify61.0ms (0.4%)

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

16.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.4b	(.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)

localize19.0ms (0.1%)

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 K (+.f64 m n)) 2)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	37.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series109.0ms (0.7%)

Counts

4 → 168

Calls

4 calls:

54.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
28.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
18.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

19.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

simplify242.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-neg_binary64`
352×	`associate-r_binary64`
328×	`associate-l_binary64`
328×	`fma-def_binary64`
260×	`*-commutative_binary64`

Counts

324 → 312

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	582	11581
1	1318	9114
2	4525	9114
3	5114	9114

prune420.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	309	3	312
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	310	3	313

Error

0.4b

Counts

313 → 3

Alt Table

Status	Error	Program
	16.4b	(.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))))
	16.4b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	0.5b	(*.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 15185 to 7419 computations (51.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.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)

series47.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

47.0ms

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

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`fma-def_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
3×	`add-log-exp_binary64`

Counts

1 → 25

Calls

1 calls:

11.0ms

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

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

737×	`distribute-rgt-in_binary64`
733×	`fma-neg_binary64`
455×	`fma-def_binary64`
381×	`associate--l+_binary64`
377×	`associate-+l+_binary64`

Counts

73 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	1735
1	293	1532
2	742	1518
3	2610	1516
4	4954	1516
5	5359	1516

prune332.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	249	3	252

Error

0.4b

Counts

252 → 3

Alt Table

Status	Error	Program
▶	16.4b	(.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))))
	16.4b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.5b	(*.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 9243 to 4585 computations (50.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))
✓	0.4b	(.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))))
✓	0.6b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
	37.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series4.0s (26.4%)

Counts

3 → 144

Calls

3 calls:

2.1s

(*.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))))

1.8s

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

28.0ms

(*.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))))

rewrite22.0ms (0.1%)

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:

7.0ms

(*.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))))

5.0ms

(*.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))))

2.0ms

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

simplify178.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

534×	`fma-def_binary64`
514×	`*-commutative_binary64`
308×	`sub-neg_binary64`
288×	`associate-+r+_binary64`
244×	`+-commutative_binary64`

Counts

237 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	527	9902
1	1703	8918
2	4364	8821
3	5103	8821

prune1.1s (7.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	537	1	538
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	538	3	541

Error

0.4b

Counts

541 → 3

Alt Table

Status	Error	Program
▶	16.4b	(.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 2)) (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))))
	16.4b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.5b	(*.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 46689 to 24166 computations (48.2% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 2))
	0.6b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
✓	24.5b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
	37.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.2s (7.8%)

Counts

2 → 48

Calls

2 calls:

1.2s	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 2))
10.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-prod_binary64`
7×	`cos-sum_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 35

Calls

2 calls:

5.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 2))

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-neg_binary64`
587×	`*-commutative_binary64`
525×	`fma-def_binary64`
421×	`cancel-sign-sub-inv_binary64`
310×	`unswap-sqr_binary64`

Counts

83 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	2481
1	463	2430
2	1596	2336
3	4253	2318
4	4989	2318
5	4899	2318

prune363.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	201	4	205

Error

0.4b

Counts

205 → 4

Alt Table

Status	Error	Program
	16.4b	(.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 2)) (cbrt.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (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))))
	16.4b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) 2)))) (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))))
	16.4b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.5b	(*.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 15001 to 8195 computations (45.4% saved)

regimes1.2s (8.2%)

Accuracy

Total 0.1b remaining (12.1%)

Threshold costs 0.1b (12.1%)

Counts

155 → 1

Compiler

Compiled 33248 to 22500 computations (32.3% 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	18	33
1	32	33
2	47	33
3	61	33
4	69	33
5	72	33
6	72	33

end134.0ms (0.9%)

Remove: (sort m n)
Compiler: Compiled 299 to 214 computations (28.4% saved)

Details

analyze3.0s (19.8%)

sample2.3s (15.4%)

simplify61.0ms (0.4%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series109.0ms (0.7%)

rewrite59.0ms (0.4%)

simplify242.0ms (1.6%)

prune420.0ms (2.8%)

localize15.0ms (0.1%)

series47.0ms (0.3%)

rewrite13.0ms (0.1%)

simplify82.0ms (0.5%)

prune332.0ms (2.2%)

localize22.0ms (0.1%)

series4.0s (26.4%)

rewrite22.0ms (0.1%)

simplify178.0ms (1.2%)

prune1.1s (7.1%)

localize28.0ms (0.2%)

series1.2s (7.8%)

rewrite10.0ms (0.1%)

simplify105.0ms (0.7%)

prune363.0ms (2.4%)

regimes1.2s (8.2%)

simplify3.0ms (0%)

end134.0ms (0.9%)

Profiling