Details

analyze3.2s (44.9%)

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)

sample56.0ms (0.8%)

Algorithm

1×

intervals

Results

31.0ms	254×	body	128	valid
4.0ms	12×	body	128	invalid
1.0ms	1×	body	1024	valid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify50.0ms (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%)

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

16.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.5b	(.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)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(*.f64 K (+.f64 m n))
37.5b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite91.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

16.4b

Rules

15×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
6×	`unpow-prod-down_binary64`
6×	`add-exp-log_binary64`

Counts

3 → 56

Calls

3 calls:

10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
5.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 1897 to 941 computations (50.4% saved)

series138.0ms (1.9%)

Error

0.4b

Counts

3 → 48

Calls

3 calls:

61.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
31.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
20.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 3777 to 2500 computations (33.8% saved)

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

540×	`unswap-sqr_binary64`
498×	`associate-l_binary64`
412×	`associate-r_binary64`
306×	`distribute-rgt-in_binary64`
297×	`distribute-lft-in_binary64`

Counts

104 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	1845
1	411	1689
2	1006	1641
3	3104	1638
4	4408	1638
5	4930	1638
6	4949	1638

prune52.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	3	82

Error

0.4b

Counts

82 → 3

Alt Table

Status	Error	Program
	16.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
	16.5b	(.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))))
▶	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 1810 to 903 computations (50.1% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

9×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`

Counts

2 → 28

Calls

2 calls:

8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
1.0ms	(cos.f64 M)

Compiler

Compiled 722 to 375 computations (48.1% saved)

series89.0ms (1.2%)

Error

0.4b

Counts

2 → 30

Calls

2 calls:

57.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
13.0ms	(cos.f64 M)

Compiler

Compiled 1858 to 1242 computations (33.2% saved)

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

510×	`cancel-sign-sub-inv_binary64`
416×	`unswap-sqr_binary64`
402×	`distribute-rgt-in_binary64`
402×	`exp-prod_binary64`
380×	`distribute-lft-in_binary64`

Counts

58 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1088
1	221	983
2	516	935
3	1663	923
4	4186	923
5	4270	923
6	4580	923
7	4987	923
8	4967	923

prune30.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Error

0.4b

Counts

47 → 3

Alt Table

Status	Error	Program
▶	16.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
	16.5b	(.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))))
✓	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 789 to 407 computations (48.4% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 m n))
0.5b	(cbrt.f64 (+.f64 n m))
0.5b	(cbrt.f64 (+.f64 n m))
37.5b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.f64 m n))) 2) M))

rewrite94.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

14×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`

Counts

4 → 54

Calls

4 calls:

15.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.f64 m n))) 2) M))
3.0ms	(cbrt.f64 (+.f64 n m))
3.0ms	(cbrt.f64 (+.f64 n m))
2.0ms	(cbrt.f64 (+.f64 m n))

Compiler

Compiled 2536 to 956 computations (62.3% saved)

series105.0ms (1.4%)

Error

0.4b

Counts

4 → 30

Calls

4 calls:

37.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.f64 m n))) 2) M))
19.0ms	(cbrt.f64 (+.f64 m n))
18.0ms	(cbrt.f64 (+.f64 n m))
17.0ms	(cbrt.f64 (+.f64 n m))

Compiler

Compiled 3419 to 2282 computations (33.3% saved)

simplify113.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

440×	`times-frac_binary64`
426×	`associate-l_binary64`
417×	`associate-r_binary64`
284×	`div-sub_binary64`
245×	`cancel-sign-sub-inv_binary64`

Counts

84 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	129	1071
1	224	1013
2	361	1013
3	706	1013
4	1446	1013
5	3806	1013
6	4954	1013
7	4934	1013

prune37.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	56	3	59

Error

0.4b

Counts

59 → 3

Alt Table

Status	Error	Program
✓	16.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
▶	16.5b	(.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))))
✓	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 1374 to 619 computations (54.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

16.9b	(cbrt.f64 (*.f64 K (+.f64 n m)))
16.9b	(cbrt.f64 (*.f64 K (+.f64 n m)))
16.9b	(cbrt.f64 (*.f64 K (+.f64 n m)))
37.7b	(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))

rewrite89.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

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:

14.0ms	(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))
3.0ms	(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)

series201.0ms (2.8%)

Error

0.4b

Counts

4 → 39

Calls

4 calls:

53.0ms	(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))
41.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
38.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))
38.0ms	(cbrt.f64 (*.f64 K (+.f64 n m)))

Compiler

Compiled 5482 to 3357 computations (38.8% saved)

simplify126.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

340×	`exp-sum_binary64`
271×	`sub-neg_binary64`
250×	`associate-l_binary64`
243×	`unsub-neg_binary64`
242×	`div-sub_binary64`

Counts

84 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1278
1	306	1229
2	592	1193
3	1260	1103
4	2719	1103
5	4209	1103
6	4910	1103
7	4991	1103

prune25.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	54	3	57

Error

0.4b

Counts

57 → 3

Alt Table

Status	Error	Program
	16.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 n m)) (cbrt.f64 (+.f64 n m)))) (cbrt.f64 (+.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))))
	16.5b	(.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))))
	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 953 to 439 computations (53.9% saved)

regimes491.0ms (6.8%)

Accuracy

Total 0.2b remaining (16%)

Threshold costs 0.2b (16%)

Compiler

Compiled 14414 to 9090 computations (36.9% saved)

simplify4.0ms (0.1%)

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	26
1	30	26
2	46	26
3	61	26
4	70	26
5	73	26
6	72	26

end6.0ms (0.1%)

Remove: (sort m n)
Compiler: Compiled 66 to 48 computations (27.3% saved)

sample1.8s (25%)

Algorithm

1×

intervals

Results

1.1s	7825×	body	128	valid
50.0ms	88×	body	512	invalid
45.0ms	67×	body	1024	valid
43.0ms	76×	body	1024	invalid
37.0ms	285×	body	128	invalid
32.0ms	80×	body	512	valid
20.0ms	58×	body	256	invalid
17.0ms	20×	body	2048	invalid
7.0ms	28×	body	256	valid

Compiler

Compiled 179 to 116 computations (35.2% saved)

Details

analyze3.2s (44.9%)

sample56.0ms (0.8%)

simplify50.0ms (0.7%)

prune4.0ms (0%)

localize17.0ms (0.2%)

rewrite91.0ms (1.3%)

series138.0ms (1.9%)

simplify129.0ms (1.8%)

prune52.0ms (0.7%)

localize14.0ms (0.2%)

rewrite41.0ms (0.6%)

series89.0ms (1.2%)

simplify129.0ms (1.8%)

prune30.0ms (0.4%)

localize25.0ms (0.4%)

rewrite94.0ms (1.3%)

series105.0ms (1.4%)

simplify113.0ms (1.6%)

prune37.0ms (0.5%)

localize23.0ms (0.3%)

rewrite89.0ms (1.2%)

series201.0ms (2.8%)

simplify126.0ms (1.7%)

prune25.0ms (0.3%)

regimes491.0ms (6.8%)

simplify4.0ms (0.1%)

end6.0ms (0.1%)

sample1.8s (25%)

Profiling