Details

analyze1.3s (13.7%)

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 (20.1%)

Results

1.2s	8256×	body	128	valid
532.0ms	3726×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify106.0ms (1.1%)

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

2.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.4b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series556.0ms (6%)

Counts

3 → 84

Calls

3 calls:

325.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
228.0ms	(*.f64 a (pow.f64 k m))
2.0ms	(fma.f64 k (+.f64 k 10) 1)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

5.0ms	(*.f64 a (pow.f64 k m))
4.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
0.0ms	(fma.f64 k (+.f64 k 10) 1)

simplify108.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-def_binary64`
533×	`fma-neg_binary64`
331×	`associate-/r/_binary64`
315×	`associate-/l/_binary64`
249×	`cancel-sign-sub-inv_binary64`

Counts

146 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2692
1	520	2369
2	1962	2188
3	4053	2184
4	4928	2184
5	4971	2184

prune120.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Error

2.4b

Counts

119 → 5

Alt Table

Status	Error	Program
	2.4b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	2.6b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
▶	2.4b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	13.7b	(.f64 (sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))))
	13.5b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k 10 1))

Compiler

Compiled 2770 to 1511 computations (45.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.2b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	2.3b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series331.0ms (3.6%)

Counts

2 → 60

Calls

2 calls:

284.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
44.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`

Counts

2 → 97

Calls

2 calls:

15.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

simplify133.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

788×	`times-frac_binary64`
592×	`fma-def_binary64`
399×	`fma-neg_binary64`
388×	`cancel-sign-sub-inv_binary64`
218×	`associate-r_binary64`

Counts

157 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	4566
1	722	4205
2	2577	3821
3	4685	3821
4	4973	3821

prune222.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	209	6	215

Error

2.4b

Counts

215 → 6

Alt Table

Status	Error	Program
▶	2.4b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	2.6b	(.f64 a (.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))) (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))))
	5.7b	(*.f64 a (cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) 3)))
	2.6b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	2.4b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	13.5b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k 10 1))

Compiler

Compiled 5432 to 3100 computations (42.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.1b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	14.2b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series608.0ms (6.6%)

Counts

3 → 84

Calls

3 calls:

311.0ms

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

294.0ms

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

2.0ms

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

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
63×	`sqrt-prod_binary64`
52×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`

Counts

3 → 143

Calls

3 calls:

9.0ms

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

5.0ms

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

1.0ms

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

simplify285.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-def_binary64`
487×	`cancel-sign-sub-inv_binary64`
351×	`fma-neg_binary64`
193×	`associate-r_binary64`
167×	`associate-/l*_binary64`

Counts

227 → 259

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	8152
1	896	7370
2	2897	6812
3	4807	6731
4	4983	6731
5	4985	6731

prune458.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	332	3	335
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	335	6	341

Error

0.0b

Counts

341 → 6

Alt Table

Status	Error	Program
	2.5b	(/.f64 (/.f64 (pow.f64 k m) (/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) 3) a)) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	2.4b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	2.6b	(.f64 a (.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))) (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))))
	29.9b	(fma.f64 99 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 4)) (fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (fma.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10 (/.f64 -980 (/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))))))
	5.7b	(*.f64 a (cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) 3)))
▶	2.4b	(/.f64 (/.f64 a 1) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))

Compiler

Compiled 10899 to 6756 computations (38% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))
✓	2.4b	(/.f64 (/.f64 a 1) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))

series320.0ms (3.5%)

Counts

2 → 60

Calls

2 calls:

288.0ms	(/.f64 (/.f64 a 1) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
32.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))

rewrite101.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

874×	`times-frac_binary64`
396×	`*-un-lft-identity_binary64`
396×	`add-sqr-sqrt_binary64`
396×	`add-cube-cbrt_binary64`
138×	`unpow-prod-down_binary64`

Counts

2 → 440

Calls

2 calls:

14.0ms	(/.f64 (/.f64 a 1) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
3.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))

simplify375.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

489×	`cancel-sign-sub-inv_binary64`
382×	`associate-/r/_binary64`
306×	`associate-r_binary64`
293×	`*-commutative_binary64`
273×	`associate-/l/_binary64`

Counts

500 → 620

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	568	18827
1	1198	18052
2	4063	17850
3	4964	17850

prune866.0ms (9.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	640	1	641
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	641	6	647

Error

0.0b

Counts

647 → 6

Alt Table

Status	Error	Program
	2.5b	(/.f64 (/.f64 (pow.f64 k m) (/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) 3) a)) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	2.4b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	2.6b	(.f64 a (.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))) (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) (cbrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))))
	5.7b	(*.f64 a (cbrt.f64 (pow.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) 3)))
	28.7b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	2.4b	(/.f64 (/.f64 a 1) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))

Compiler

Compiled 20459 to 12086 computations (40.9% saved)

regimes1.3s (13.9%)

Accuracy

Total 0.0b remaining (62.3%)

Threshold costs 0.0b (62.3%)

Counts

224 → 2

Compiler

Compiled 23604 to 16302 computations (30.9% saved)

bsearch13.0ms (0.1%)

Steps

Iters	Range		Point
1	5.0068490561792015e+84	1.897124881123948e+88	3.084320511355429e+86

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	84
1	39	84
2	38	84

end128.0ms (1.4%)

Compiler: Compiled 272 to 163 computations (40.1% saved)

Details

analyze1.3s (13.7%)

sample1.9s (20.1%)

simplify106.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series556.0ms (6%)

rewrite12.0ms (0.1%)

simplify108.0ms (1.2%)

prune120.0ms (1.3%)

localize10.0ms (0.1%)

series331.0ms (3.6%)

rewrite25.0ms (0.3%)

simplify133.0ms (1.4%)

prune222.0ms (2.4%)

localize9.0ms (0.1%)

series608.0ms (6.6%)

rewrite29.0ms (0.3%)

simplify285.0ms (3.1%)

prune458.0ms (5%)

localize9.0ms (0.1%)

series320.0ms (3.5%)

rewrite101.0ms (1.1%)

simplify375.0ms (4.1%)

prune866.0ms (9.4%)

regimes1.3s (13.9%)

bsearch13.0ms (0.1%)

simplify3.0ms (0%)

end128.0ms (1.4%)

Profiling