Details

analyze2.9s (34.1%)

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)

sample2.5s (29.1%)

Symmetry

(sort m n)

Results

2.1s	8078×	body	128	valid
77.0ms	82×	body	1024	invalid
62.0ms	278×	body	128	invalid
55.0ms	61×	body	1024	valid
47.0ms	70×	body	512	valid
41.0ms	70×	body	512	invalid
24.0ms	17×	body	2048	invalid
19.0ms	46×	body	256	valid
18.0ms	47×	body	256	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify59.0ms (0.7%)

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

14.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.9b	(.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 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
✓	0.0b	(exp.f64 (-.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)
✓	35.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series141.0ms (1.6%)

Counts

4 → 180

Calls

4 calls:

59.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
39.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
21.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
20.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite43.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

250×	`add-sqr-sqrt_binary64`
243×	`log1p-expm1-u_binary64`
243×	`expm1-log1p-u_binary64`
234×	`add-log-exp_binary64`
232×	`add-cube-cbrt_binary64`

Counts

4 → 73

Calls

4 calls:

41.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
41.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
41.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
41.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	70
1	482	70
2	5038	70

simplify168.0ms (2%)

Algorithm

1×	egg-herbie

Rules

622×	`associate-r_binary64`
534×	`fma-def_binary64`
461×	`associate-l_binary64`
392×	`fma-neg_binary64`
231×	`associate--l+_binary64`

Counts

253 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	377	8722
1	1285	7628
2	4939	7626
3	5295	7626

prune251.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	182	4	186
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	4	187

Error

1.1b

Counts

187 → 4

Alt Table

Status	Error	Program
	34.4b	(.f64 (pow.f64 (sqrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	9.6b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.9b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.3b	(*.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 11102 to 5440 computations (51% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.0ms (0%)

Counts

1 → 4

Calls

1 calls:

2.0ms

(cos.f64 M)

rewrite86.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

444×	`log1p-udef_binary64`
250×	`log1p-expm1-u_binary64`
250×	`expm1-log1p-u_binary64`
231×	`add-cbrt-cube_binary64`
230×	`add-cube-cbrt_binary64`

Counts

1 → 33

Calls

1 calls:

86.0ms

(cos.f64 M)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	58	3
2	655	3
3	4733	3
4	5597	3

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-neg_binary64`
777×	`cancel-sign-sub-inv_binary64`
431×	`sub-neg_binary64`
308×	`distribute-rgt-neg-in_binary64`
286×	`unswap-sqr_binary64`

Counts

37 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	56
1	53	52
2	126	48
3	354	46
4	1236	46
5	3968	46
6	4386	46
7	4739	46
8	4899	46

prune239.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	177	4	181

Error

1.1b

Counts

181 → 4

Alt Table

Status	Error	Program
	34.4b	(.f64 (pow.f64 (sqrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	9.6b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.3b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l))))
	18.1b	(.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (cos.f64 M))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (cos.f64 M))) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 8723 to 4256 computations (51.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l)
✓	0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l)))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)
✓	16.3b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6))

series167.0ms (1.9%)

Counts

4 → 168

Calls

4 calls:

59.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)
53.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l)))
38.0ms	(+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l)
17.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6))

rewrite83.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

968×	`prod-diff_binary64`
199×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
187×	`add-log-exp_binary64`

Counts

4 → 96

Calls

4 calls:

81.0ms	(+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l)
81.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l)))
81.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)
81.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	74
1	397	66
2	4595	66
3	6462	66

simplify165.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-r_binary64`
435×	`associate-l_binary64`
342×	`associate--l+_binary64`
276×	`associate--r+_binary64`
227×	`+-commutative_binary64`

Counts

264 → 223

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	511	10645
1	1871	10152
2	5218	10152

prune326.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	223	4	227

Error

1.1b

Counts

227 → 4

Alt Table

Status	Error	Program
	34.4b	(.f64 (pow.f64 (sqrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	9.6b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.3b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l))))
	18.1b	(.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (cos.f64 M))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (cos.f64 M))) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 13537 to 7352 computations (45.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
	0.0b	(exp.f64 (-.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)
✓	26.1b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

series9.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

9.0ms

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

rewrite110.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

821×	`prod-diff_binary64`
545×	`fma-udef_binary64`
324×	`fma-def_binary64`
238×	`fma-neg_binary64`
189×	`expm1-udef_binary64`

Counts

1 → 52

Calls

1 calls:

109.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	199	12
2	2512	12
3	4678	12
4	4601	12
5	5065	12

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

572×	`neg-mul-1_binary64`
497×	`fma-neg_binary64`
401×	`distribute-rgt-neg-in_binary64`
397×	`distribute-lft-neg-in_binary64`
329×	`associate-r_binary64`

Counts

64 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	362
1	142	362
2	450	330
3	1844	303
4	4719	303
5	5178	303

prune381.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	199	5	204
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	202	6	208

Error

1.0b

Counts

208 → 6

Alt Table

Status	Error	Program
	9.6b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M))) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	19.2b	(.f64 (-.f64 (cos.f64 M) (.f64 (.f64 K m) (+.f64 (.f64 (sin.f64 M) -1/2) (.f64 (.f64 K m) (*.f64 (cos.f64 M) 1/8))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.3b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 6)) l))))
	31.6b	(.f64 (+.f64 (.f64 (cos.f64 (/.f64 (.f64 1/4 (pow.f64 (.f64 K m) 2)) (fma.f64 1/2 (.f64 K m) M))) (cos.f64 (/.f64 (.f64 M M) (fma.f64 1/2 (.f64 K m) M)))) (.f64 (sin.f64 (/.f64 (.f64 1/4 (pow.f64 (.f64 K m) 2)) (fma.f64 1/2 (.f64 K m) M))) (sin.f64 (/.f64 (.f64 M M) (fma.f64 1/2 (*.f64 K m) M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	41.8b	(.f64 (+.f64 (.f64 (cos.f64 (/.f64 (.f64 1/8 (pow.f64 (.f64 K m) 3)) (fma.f64 M (fma.f64 1/2 (.f64 K m) M) (.f64 1/4 (pow.f64 (.f64 K m) 2))))) (cos.f64 (/.f64 (pow.f64 M 3) (fma.f64 M (fma.f64 1/2 (.f64 K m) M) (.f64 1/4 (pow.f64 (.f64 K m) 2)))))) (.f64 (sin.f64 (/.f64 (.f64 1/8 (pow.f64 (.f64 K m) 3)) (fma.f64 M (fma.f64 1/2 (.f64 K m) M) (.f64 1/4 (pow.f64 (.f64 K m) 2))))) (sin.f64 (/.f64 (pow.f64 M 3) (fma.f64 M (fma.f64 1/2 (.f64 K m) M) (.f64 1/4 (pow.f64 (*.f64 K m) 2))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	28.2b	(.f64 (+.f64 (.f64 (cos.f64 (exp.f64 (log1p.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))) (cos.f64 1)) (.f64 (sin.f64 (exp.f64 (log1p.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))) (sin.f64 1))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 11360 to 5744 computations (49.4% saved)

regimes509.0ms (5.9%)

Accuracy

Total 0.1b remaining (6.9%)

Threshold costs 0.1b (6.9%)

Counts

72 → 1

Compiler

Compiled 14228 to 9870 computations (30.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	32	43
2	49	43
3	64	43
4	73	43
5	76	43
6	76	43

end212.0ms (2.5%)

Remove: (sort m n)
Compiler: Compiled 473 to 312 computations (34% saved)

Details

analyze2.9s (34.1%)

sample2.5s (29.1%)

simplify59.0ms (0.7%)

prune4.0ms (0%)

localize18.0ms (0.2%)

series141.0ms (1.6%)

rewrite43.0ms (0.5%)

simplify168.0ms (2%)

prune251.0ms (2.9%)

localize13.0ms (0.1%)

series2.0ms (0%)

rewrite86.0ms (1%)

simplify83.0ms (1%)

prune239.0ms (2.8%)

localize14.0ms (0.2%)

series167.0ms (1.9%)

rewrite83.0ms (1%)

simplify165.0ms (1.9%)

prune326.0ms (3.8%)

localize21.0ms (0.2%)

series9.0ms (0.1%)

rewrite110.0ms (1.3%)

simplify60.0ms (0.7%)

prune381.0ms (4.4%)

regimes509.0ms (5.9%)

simplify3.0ms (0%)

end212.0ms (2.5%)

Profiling