Details

analyze1.3s (17.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
15.6%	84.3%	0.1%	7
18.7%	81.1%	0.1%	8
25.7%	73.3%	0.9%	9
28.5%	60.8%	10.7%	10
30.2%	58.7%	11.1%	11
32.7%	52.2%	15.2%	12
33.5%	39.2%	27.4%	13
34.3%	37.8%	27.9%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.9s (24.6%)

Results

1.2s	8256×	body	128	valid
559.0ms	3870×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

614×	`*-commutative_binary64`
613×	`associate-l_binary64`
526×	`sqr-pow_binary64`
394×	`associate-*r/_binary64`
380×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	55	17
3	104	17
4	225	17
5	591	17
6	1774	17
7	2466	17
8	2534	17
9	2692	17
10	2908	17
11	3166	17
12	3656	17
13	4497	17
14	5019	17

prune3.0ms (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

2.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.0b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series302.0ms (4%)

Counts

1 → 36

Calls

1 calls:

302.0ms

(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`div-exp_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 25

Calls

1 calls:

4.0ms

(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

828×	`associate-/l*_binary64`
641×	`times-frac_binary64`
418×	`fma-neg_binary64`
375×	`fma-def_binary64`
245×	`cancel-sign-sub-inv_binary64`

Counts

61 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	1853
1	434	1591
2	1557	1415
3	4869	1411
4	5084	1411

prune53.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	4	60

Error

2.0b

Counts

60 → 4

Alt Table

Status	Error	Program
▶	2.1b	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	2.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) (cbrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))) (cbrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))))
✓	2.0b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
	2.1b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))

Compiler

Compiled 1728 to 1004 computations (41.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.1b	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	13.5b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series394.0ms (5.2%)

Counts

4 → 96

Calls

4 calls:

290.0ms	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
57.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
44.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite57.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`add-sqr-sqrt_binary64`
152×	`times-frac_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`
85×	`sqrt-prod_binary64`

Counts

4 → 242

Calls

4 calls:

22.0ms	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
4.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
1.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify238.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

539×	`cancel-sign-sub-inv_binary64`
411×	`fma-neg_binary64`
274×	`associate-r_binary64`
259×	`associate-*l/_binary64`
254×	`*-commutative_binary64`

Counts

338 → 385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	10930
1	1170	9931
2	3836	9583
3	4903	9583
4	4999	9583

prune589.0ms (7.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	421	2	423
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	423	4	427

Error

0.0b

Counts

427 → 4

Alt Table

Status	Error	Program
	26.1b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
▶	2.1b	(.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))))
✓	2.0b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
	2.1b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))

Compiler

Compiled 13761 to 8621 computations (37.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.1b	(.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	13.5b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series297.0ms (3.9%)

Counts

2 → 48

Calls

2 calls:

295.0ms

(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))))

2.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-sqr-sqrt_binary64`
87×	`sqrt-prod_binary64`
53×	`add-exp-log_binary64`
42×	`times-frac_binary64`
32×	`sqrt-pow1_binary64`

Counts

2 → 164

Calls

2 calls:

17.0ms

(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))))

8.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))

simplify195.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-neg_binary64`
474×	`fma-def_binary64`
289×	`cancel-sign-sub-inv_binary64`
240×	`times-frac_binary64`
221×	`associate-r_binary64`

Counts

212 → 241

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	312	6191
1	802	4798
2	2972	4474
3	4306	4453
4	4949	4453
5	5034	4453

prune535.0ms (7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	424	0	424
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	424	4	428

Error

0.0b

Counts

428 → 4

Alt Table

Status	Error	Program
	26.1b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	2.1b	(.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))))
✓	2.0b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
▶	2.1b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))

Compiler

Compiled 15651 to 10507 computations (32.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	1.9b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

series537.0ms (7.1%)

Counts

2 → 72

Calls

2 calls:

283.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
254.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
36×	`times-frac_binary64`
26×	`div-exp_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

2 → 89

Calls

2 calls:

8.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
4.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

simplify126.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
360×	`cancel-sign-sub-inv_binary64`
251×	`fma-neg_binary64`
214×	`associate-r_binary64`
162×	`neg-mul-1_binary64`

Counts

161 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	4810
1	696	4018
2	2746	3945
3	4282	3936
4	4879	3936

prune175.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	163	4	167

Error

0.0b

Counts

167 → 4

Alt Table

Status	Error	Program
	26.1b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	2.1b	(.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))))
	13.7b	(/.f64 1 (fma.f64 k (/.f64 k (.f64 a (pow.f64 k m))) (fma.f64 k (/.f64 10 (.f64 a (pow.f64 k m))) (/.f64 (pow.f64 k (neg.f64 m)) a))))
✓	2.0b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 4502 to 2586 computations (42.6% saved)

regimes529.0ms (6.9%)

Accuracy

Total 0.0b remaining (44.4%)

Threshold costs 0.0b (44.4%)

Counts

97 → 2

Compiler

Compiled 8004 to 5698 computations (28.8% saved)

bsearch18.0ms (0.2%)

Steps

Iters	Range		Point
4	8.235619023268693e+21	1.0427362106566516e+29	7.762650172158733e+25

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	52
1	28	52
2	27	52

end89.0ms (1.2%)

Compiler: Compiled 179 to 105 computations (41.3% saved)

Details

analyze1.3s (17.3%)

sample1.9s (24.6%)

simplify104.0ms (1.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series302.0ms (4%)

rewrite5.0ms (0.1%)

simplify69.0ms (0.9%)

prune53.0ms (0.7%)

localize9.0ms (0.1%)

series394.0ms (5.2%)

rewrite57.0ms (0.8%)

simplify238.0ms (3.1%)

prune589.0ms (7.7%)

localize11.0ms (0.1%)

series297.0ms (3.9%)

rewrite49.0ms (0.6%)

simplify195.0ms (2.6%)

prune535.0ms (7%)

localize8.0ms (0.1%)

series537.0ms (7.1%)

rewrite18.0ms (0.2%)

simplify126.0ms (1.7%)

prune175.0ms (2.3%)

regimes529.0ms (6.9%)

bsearch18.0ms (0.2%)

simplify2.0ms (0%)

end89.0ms (1.2%)

Profiling