Details

analyze2.9s (20.2%)

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)

sample2.1s (14.8%)

Symmetry

(sort m n)

Results

1.7s	8106×	body	128	valid
67.0ms	87×	body	1024	invalid
59.0ms	287×	body	128	invalid
47.0ms	52×	body	1024	valid
46.0ms	86×	body	512	invalid
33.0ms	60×	body	512	valid
26.0ms	57×	body	256	invalid
23.0ms	21×	body	2048	invalid
14.0ms	37×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify60.0ms (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

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 (0.1%)

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)
✓	35.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series92.0ms (0.6%)

Counts

4 → 168

Calls

4 calls:

47.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
23.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite58.0ms (0.4%)

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))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
4.0ms	(*.f64 K (+.f64 m n))

simplify213.0ms (1.5%)

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

prune357.0ms (2.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	302	3	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	303	3	306

Error

0.8b

Counts

306 → 3

Alt Table

Status	Error	Program
	14.4b	(.f64 (expm1.f64 (log1p.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))))
▶	0.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	28.6b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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 14930 to 7231 computations (51.6% saved)

localize15.0ms (0.1%)

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)

prune181.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	183	3	186

Error

0.8b

Counts

186 → 3

Alt Table

Status	Error	Program
▶	14.4b	(.f64 (expm1.f64 (log1p.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))))
✓	0.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	28.6b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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 7335 to 3680 computations (49.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
✓	0.5b	(log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
	35.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.7s (11.8%)

Counts

2 → 96

Calls

2 calls:

1.7s	(log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
25.0ms	(expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.0ms	(expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-r_binary64`
350×	`associate-l_binary64`
295×	`fma-def_binary64`
271×	`associate-/l*_binary64`
215×	`times-frac_binary64`

Counts

118 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	359	5081
1	1170	4668
2	5213	4668

prune312.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	244	3	247

Error

0.8b

Counts

247 → 3

Alt Table

Status	Error	Program
▶	14.4b	(.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))))) (cbrt.f64 (expm1.f64 (log1p.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))))
	28.6b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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))))
✓	0.8b	(*.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 14473 to 7519 computations (48% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))
	0.5b	(log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
✓	0.5b	(cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))
	35.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series3.8s (26.4%)

Counts

2 → 96

Calls

2 calls:

2.0s

(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))

1.8s

(cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms

(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))

1.0ms

(cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))

simplify118.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

871×	`associate-r_binary64`
769×	`associate-l_binary64`
424×	`fma-def_binary64`
177×	`*-commutative_binary64`
135×	`sqr-pow_binary64`

Counts

151 → 153

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	447	7490
1	1442	6897
2	5089	6897

prune1.4s (10%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	661	2	663
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	662	4	666

Error

0.8b

Counts

666 → 4

Alt Table

Status	Error	Program
	14.3b	(.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.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))))
	28.6b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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 (.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (expm1.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))))) (expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 (log1p.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))))
✓	0.8b	(*.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 66883 to 36875 computations (44.9% saved)

regimes563.0ms (3.9%)

Accuracy

Total 0.2b remaining (15.3%)

Threshold costs 0.2b (15.3%)

Counts

80 → 1

Compiler

Compiled 17402 to 11880 computations (31.7% 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

end255.0ms (1.8%)

Remove: (sort m n)
Compiler: Compiled 325 to 227 computations (30.2% saved)

Details

analyze2.9s (20.2%)

sample2.1s (14.8%)

simplify60.0ms (0.4%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series92.0ms (0.6%)

rewrite58.0ms (0.4%)

simplify213.0ms (1.5%)

prune357.0ms (2.5%)

localize15.0ms (0.1%)

prune181.0ms (1.3%)

localize21.0ms (0.1%)

series1.7s (11.8%)

rewrite1.0ms (0%)

simplify84.0ms (0.6%)

prune312.0ms (2.2%)

localize26.0ms (0.2%)

series3.8s (26.4%)

rewrite10.0ms (0.1%)

simplify118.0ms (0.8%)

prune1.4s (10%)

regimes563.0ms (3.9%)

simplify3.0ms (0%)

end255.0ms (1.8%)

Profiling