Details

analyze2.9s (34.9%)

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)

sample107.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort m n)

Results

38.0ms	253×	body	128	valid
1.0ms	11×	body	128	invalid
1.0ms	2×	body	1024	invalid
1.0ms	1×	body	2048	invalid
1.0ms	2×	body	512	invalid
1.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify60.0ms (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

12.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.7b	(.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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	30.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series59.0ms (0.7%)

Counts

4 → 156

Calls

4 calls:

26.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
19.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`cos-sum_binary64`
24×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

4 → 108

Calls

4 calls:

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)
5.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
5.0ms	(*.f64 K (+.f64 m n))

simplify159.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

429×	`fma-neg_binary64`
332×	`associate-r_binary64`
300×	`associate-l_binary64`
225×	`*-commutative_binary64`
213×	`fma-def_binary64`

Counts

264 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	438	6329
1	903	5067
2	3136	4940
3	4779	4856
4	4939	4856

prune389.0ms (4.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	227	4	231
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	228	4	232

Error

0.7b

Counts

232 → 4

Alt Table

Status	Error	Program
	12.6b	(.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))))
▶	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))))
	12.7b	(.f64 (log.f64 (exp.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))))
	7.6b	(.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))))

Compiler

Compiled 10000 to 4774 computations (52.3% saved)

localize15.0ms (0.2%)

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)

series98.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

52.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
46.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
26×	`fabs-mul_binary64`
24×	`add-cube-cbrt_binary64`

Counts

2 → 98

Calls

2 calls:

20.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
11.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

simplify272.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
495×	`distribute-rgt-in_binary64`
451×	`cancel-sign-sub-inv_binary64`
357×	`sub-neg_binary64`
202×	`fma-def_binary64`

Counts

194 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	230	7742
1	682	6065
2	2189	5159
3	4411	5151
4	4987	5151
5	4997	5151
6	4925	5151

prune429.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	245	4	249

Error

0.7b

Counts

249 → 4

Alt Table

Status	Error	Program
	12.6b	(.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))))
✓	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))))
	12.7b	(.f64 (log.f64 (exp.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))))
▶	7.6b	(.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))))

Compiler

Compiled 9043 to 4510 computations (50.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (.f64 K m)) M)
✓	0.0b	(.f64 1/2 (.f64 K m))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	23.0b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

series24.0ms (0.3%)

Counts

3 → 21

Calls

3 calls:

12.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
7.0ms	(-.f64 (.f64 1/2 (.f64 K m)) M)
5.0ms	(.f64 1/2 (.f64 K m))

rewrite58.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

3 → 57

Calls

3 calls:

45.0ms	(.f64 1/2 (.f64 K m))
5.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
5.0ms	(-.f64 (.f64 1/2 (.f64 K m)) M)

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-neg_binary64`
559×	`cancel-sign-sub-inv_binary64`
383×	`*-commutative_binary64`
365×	`neg-mul-1_binary64`
364×	`fma-def_binary64`

Counts

78 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	1319
1	311	1247
2	1047	1184
3	2380	1162
4	4565	1162
5	4988	1162

prune256.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	144	5	149

Error

0.7b

Counts

149 → 5

Alt Table

Status	Error	Program
	12.6b	(.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))))
✓	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))))
	29.7b	(.f64 (cos.f64 (-.f64 (.f64 (sqrt.f64 (.f64 1/2 (.f64 K m))) (sqrt.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))))
▶	7.6b	(.f64 (log.f64 (exp.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))))
	7.6b	(.f64 (log1p.f64 (expm1.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))))

Compiler

Compiled 5294 to 2762 computations (47.8% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.1b	(exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))
✓	0.6b	(log.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))
	23.0b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

series40.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))
12.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`exp-diff_binary64`
14×	`cos-sum_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 46

Calls

2 calls:

10.0ms	(exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))
6.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

624×	`cancel-sign-sub-inv_binary64`
387×	`neg-mul-1_binary64`
383×	`neg-sub0_binary64`
266×	`unsub-neg_binary64`
260×	`associate--l+_binary64`

Counts

94 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	241	2707
1	480	2566
2	1753	2345
3	4215	2258
4	4997	2258

prune398.0ms (4.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	192	6	198

Error

0.7b

Counts

198 → 6

Alt Table

Status	Error	Program
	12.6b	(.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))))
✓	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))))
	29.7b	(.f64 (cos.f64 (-.f64 (.f64 (sqrt.f64 (.f64 1/2 (.f64 K m))) (sqrt.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))))
	7.7b	(.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (cbrt.f64 (exp.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))))
	7.6b	(.f64 (log.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))) (cbrt.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))))
	7.6b	(.f64 (log1p.f64 (expm1.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))))

Compiler

Compiled 8283 to 4385 computations (47.1% saved)

regimes595.0ms (7.3%)

Accuracy

Total 0.2b remaining (12%)

Threshold costs 0.2b (12%)

Counts

80 → 1

Compiler

Compiled 15092 to 10404 computations (31.1% 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

end8.0ms (0.1%)

Remove: (sort m n)
Compiler: Compiled 75 to 54 computations (28% saved)

sample2.0s (24.3%)

Algorithm

1×

intervals

Results

1.1s	7830×	body	128	valid
58.0ms	99×	body	1024	invalid
51.0ms	84×	body	1024	valid
42.0ms	299×	body	128	invalid
33.0ms	86×	body	512	invalid
23.0ms	55×	body	512	valid
22.0ms	25×	body	2048	invalid
10.0ms	42×	body	256	invalid
8.0ms	30×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 312 to 217 computations (30.4% saved)

Details

analyze2.9s (34.9%)

sample107.0ms (1.3%)

simplify60.0ms (0.7%)

prune4.0ms (0%)

localize18.0ms (0.2%)

series59.0ms (0.7%)

rewrite36.0ms (0.4%)

simplify159.0ms (1.9%)

prune389.0ms (4.8%)

localize15.0ms (0.2%)

series98.0ms (1.2%)

rewrite44.0ms (0.5%)

simplify272.0ms (3.3%)

prune429.0ms (5.3%)

localize18.0ms (0.2%)

series24.0ms (0.3%)

rewrite58.0ms (0.7%)

simplify102.0ms (1.3%)

prune256.0ms (3.1%)

localize23.0ms (0.3%)

series40.0ms (0.5%)

rewrite19.0ms (0.2%)

simplify95.0ms (1.2%)

prune398.0ms (4.9%)

regimes595.0ms (7.3%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample2.0s (24.3%)

Profiling