Details

analyze3.4s (40.9%)

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)

sample65.0ms (0.8%)

Algorithm

1×

intervals

Results

37.0ms	252×	body	128	valid
2.0ms	14×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	3×	body	512	invalid
1.0ms	2×	body	512	valid
1.0ms	2×	body	256	invalid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

605×	`exp-prod_binary64`
532×	`exp-sum_binary64`
375×	`associate-l_binary64`
303×	`associate-r_binary64`
251×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	125	43
3	361	43
4	1141	43
5	4044	43
6	5121	43

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

14.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.7b	(.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 99 to 66 computations (33.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
35.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite126.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

14.6b

Rules

16×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`

Counts

4 → 68

Calls

4 calls:

11.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
9.0ms	(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 K (+.f64 m n))

Compiler

Compiled 2346 to 1174 computations (50% saved)

series309.0ms (3.7%)

Error

0.8b

Counts

4 → 86

Calls

4 calls:

117.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
70.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
41.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
26.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 6811 to 4450 computations (34.7% saved)

simplify145.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

426×	`associate--l+_binary64`
391×	`associate-+l+_binary64`
376×	`distribute-rgt-in_binary64`
360×	`distribute-lft-in_binary64`
344×	`unswap-sqr_binary64`

Counts

154 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3114
1	591	2877
2	1509	2757
3	3964	2757
4	4877	2757
5	4934	2757

prune80.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Error

0.8b

Counts

126 → 3

Alt Table

Status	Error	Program
✓	14.7b	(.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))))
▶	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (.f64 K (+.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))))

Compiler

Compiled 2496 to 1222 computations (51% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

11.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 914 to 485 computations (46.9% saved)

series227.0ms (2.7%)

Error

0.8b

Counts

2 → 60

Calls

2 calls:

124.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
65.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 3840 to 2540 computations (33.9% saved)

simplify131.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

477×	`unswap-sqr_binary64`
424×	`associate--l+_binary64`
371×	`associate-+l+_binary64`
290×	`sub-neg_binary64`
247×	`log-prod_binary64`

Counts

93 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2223
1	364	2047
2	904	1927
3	3008	1927
4	4357	1927
5	4841	1927
6	4943	1927

prune50.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	83	3	86

Error

0.8b

Counts

86 → 3

Alt Table

Status	Error	Program
✓	14.7b	(.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))))
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	14.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (.f64 K (+.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))))

Compiler

Compiled 1270 to 622 computations (51% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

15.0b	(cbrt.f64 (*.f64 K (+.f64 n m)))
15.0b	(cbrt.f64 (*.f64 K (+.f64 n m)))
15.0b	(cbrt.f64 (*.f64 K (+.f64 n m)))
35.3b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (*.f64 K (+.f64 n m)))) 2) M))

rewrite78.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

6×	`cbrt-div_binary64`
6×	`associate-*r/_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

4 → 45

Calls

4 calls:

9.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (*.f64 K (+.f64 n m)))) 2) M))
5.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
3.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
3.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))

Compiler

Compiled 2489 to 808 computations (67.5% saved)

series262.0ms (3.2%)

Error

0.7b

Counts

4 → 44

Calls

4 calls:

57.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
55.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (*.f64 K (+.f64 n m)))) 2) M))
54.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
48.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))

Compiler

Compiled 6186 to 3818 computations (38.3% saved)

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

630×	`times-frac_binary64`
306×	`div-sub_binary64`
268×	`exp-sum_binary64`
261×	`*-commutative_binary64`
185×	`distribute-rgt-in_binary64`

Counts

89 → 58

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	159	1513
1	348	1464
2	708	1428
3	1560	1266
4	3170	1263
5	4853	1263
6	4923	1263

prune43.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	58	3	61

Error

0.8b

Counts

61 → 3

Alt Table

Status	Error	Program
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	14.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (.f64 K m))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	14.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (.f64 K (+.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))))

Compiler

Compiled 1339 to 601 computations (55.1% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

13.3b	(cbrt.f64 (*.f64 K m))
15.0b	(cbrt.f64 (*.f64 K (+.f64 n m)))
15.0b	(cbrt.f64 (*.f64 K (+.f64 n m)))
31.8b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (*.f64 K m))) 2) M))

rewrite79.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`cbrt-div_binary64`
4×	`associate-*r/_binary64`

Counts

4 → 43

Calls

4 calls:

8.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (*.f64 K m))) 2) M))
3.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
3.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
2.0ms	(cbrt.f64 (*.f64 K m))

Compiler

Compiled 2261 to 789 computations (65.1% saved)

series281.0ms (3.4%)

Error

0.8b

Counts

4 → 41

Calls

4 calls:

108.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (*.f64 K m))) 2) M))
46.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
46.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
38.0ms	(cbrt.f64 (*.f64 K m))

Compiler

Compiled 5762 to 3791 computations (34.2% saved)

simplify148.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

347×	`associate-l_binary64`
322×	`associate-r_binary64`
301×	`cancel-sign-sub-inv_binary64`
277×	`distribute-rgt-neg-in_binary64`
265×	`exp-sum_binary64`

Counts

84 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	213	1891
1	471	1798
2	949	1761
3	2559	1629
4	4379	1625
5	4904	1625
6	4875	1625
7	4944	1625

prune42.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	52	4	56

Error

0.8b

Counts

56 → 4

Alt Table

Status	Error	Program
	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (.f64 K m))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	46.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (/.f64 (cbrt.f64 (.f64 K (+.f64 (pow.f64 n 3) (pow.f64 m 3)))) (cbrt.f64 (+.f64 (.f64 n n) (.f64 m (-.f64 m n))))) (cbrt.f64 (.f64 K (+.f64 n m)))) (cbrt.f64 (.f64 K m))) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	34.3b	(.f64 (.f64 (sqrt.f64 (cos.f64 (-.f64 (.f64 (/.f64 (cbrt.f64 (.f64 K m)) 2) (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m))))) M))) (sqrt.f64 (cos.f64 (-.f64 (.f64 (/.f64 (cbrt.f64 (.f64 K m)) 2) (.f64 (cbrt.f64 (.f64 K (+.f64 n m))) (cbrt.f64 (.f64 K (+.f64 n m))))) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 1419 to 632 computations (55.5% saved)

regimes601.0ms (7.3%)

Accuracy

Total 0.1b remaining (7.9%)

Threshold costs 0.1b (7.9%)

Compiler

Compiled 15254 to 9846 computations (35.5% saved)

simplify4.0ms (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)

sample1.9s (22.9%)

Algorithm

1×

intervals

Results

1.1s	7862×	body	128	valid
49.0ms	326×	body	128	invalid
43.0ms	71×	body	1024	invalid
34.0ms	55×	body	1024	valid
29.0ms	75×	body	512	invalid
25.0ms	29×	body	2048	invalid
21.0ms	50×	body	512	valid
14.0ms	54×	body	256	invalid
9.0ms	32×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 269 to 169 computations (37.2% saved)

Details

analyze3.4s (40.9%)

sample65.0ms (0.8%)

simplify59.0ms (0.7%)

prune4.0ms (0.1%)

localize19.0ms (0.2%)

rewrite126.0ms (1.5%)

series309.0ms (3.7%)

simplify145.0ms (1.8%)

prune80.0ms (1%)

localize18.0ms (0.2%)

rewrite60.0ms (0.7%)

series227.0ms (2.7%)

simplify131.0ms (1.6%)

prune50.0ms (0.6%)

localize25.0ms (0.3%)

rewrite78.0ms (0.9%)

series262.0ms (3.2%)

simplify109.0ms (1.3%)

prune43.0ms (0.5%)

localize30.0ms (0.4%)

rewrite79.0ms (1%)

series281.0ms (3.4%)

simplify148.0ms (1.8%)

prune42.0ms (0.5%)

regimes601.0ms (7.3%)

simplify4.0ms (0%)

end8.0ms (0.1%)

sample1.9s (22.9%)

Profiling