Details

analyze1.5s (8.7%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample48.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
9.0ms	87×	body	128	invalid
3.0ms	55×	body	128	nan

Compiler

Compiled 40 to 28 computations (30% saved)

simplify106.0ms (0.6%)

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

2.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.7b	(/.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%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	2.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series548.0ms (3.2%)

Counts

2 → 72

Calls

2 calls:

311.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
237.0ms	(*.f64 a (pow.f64 k m))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

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

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-def_binary64`
426×	`fma-neg_binary64`
424×	`associate-/r*_binary64`
331×	`associate-/r/_binary64`
315×	`associate-/l/_binary64`

Counts

124 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	2471
1	511	2183
2	1953	2003
3	4480	1999
4	4945	1999

prune70.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	2	98

Error

2.7b

Counts

98 → 2

Alt Table

Status	Error	Program
▶	2.8b	(/.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)))
✓	2.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 2336 to 1278 computations (45.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(/.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)))
✓	17.2b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series615.0ms (3.6%)

Counts

3 → 84

Calls

3 calls:

311.0ms

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

302.0ms

(/.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)))

2.0ms

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

rewrite29.0ms (0.2%)

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:

7.0ms

(/.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))

simplify232.0ms (1.4%)

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

prune415.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	334	3	337

Error

0.0b

Counts

337 → 3

Alt Table

Status	Error	Program
✓	2.8b	(/.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)))
▶	27.4b	(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)))))))
✓	2.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 10708 to 6624 computations (38.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.1b	(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)))))))
✓	12.0b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 3))
✓	12.1b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 4))
✓	12.9b	(/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))

series2.0s (12%)

Counts

4 → 144

Calls

4 calls:

1.1s	(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)))))))
319.0ms	(/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))
315.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 4))
299.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 3))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-exp-log_binary64`
36×	`div-exp_binary64`
27×	`prod-exp_binary64`
26×	`times-frac_binary64`
21×	`pow-exp_binary64`

Counts

4 → 143

Calls

4 calls:

5.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 3))
5.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 4))
5.0ms	(/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))
0.0ms	(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)))))))

simplify244.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

463×	`times-frac_binary64`
330×	`associate-/l*_binary64`
324×	`associate-/r*_binary64`
261×	`fma-neg_binary64`
171×	`associate-r_binary64`

Counts

287 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	7533
1	1004	7025
2	4586	7021
3	4989	7021
4	4996	7021
5	5021	7021

prune282.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	237	5	242

Error

0.0b

Counts

242 → 5

Alt Table

Status	Error	Program
✓	2.8b	(/.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)))
✓	27.4b	(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)))))))
	33.1b	(.f64 (sqrt.f64 (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)))))))) (sqrt.f64 (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)))))))))
▶	27.5b	(.f64 (.f64 (cbrt.f64 (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)))))))) (cbrt.f64 (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))))))))) (cbrt.f64 (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)))))))))
✓	2.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 12797 to 5799 computations (54.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	12.0b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 3))
	12.1b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 4))
	12.9b	(/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))
✓	14.8b	(cbrt.f64 (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))))))))

series6.2s (36.8%)

Counts

1 → 36

Calls

1 calls:

6.2s

(cbrt.f64 (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))))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 (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))))))))

simplify116.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

358×	`fma-def_binary64`
285×	`times-frac_binary64`
261×	`associate-/l*_binary64`
256×	`associate-+r+_binary64`
241×	`associate-r_binary64`

Counts

49 → 62

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	400	7638
1	1215	6930
2	5159	6930

prune2.2s (13.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	738	0	738
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	738	5	743

Error

0.0b

Counts

743 → 5

Alt Table

Status	Error	Program
✓	2.8b	(/.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)))
✓	27.4b	(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)))))))
	33.1b	(.f64 (sqrt.f64 (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)))))))) (sqrt.f64 (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)))))))))
✓	27.5b	(.f64 (.f64 (cbrt.f64 (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)))))))) (cbrt.f64 (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))))))))) (cbrt.f64 (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)))))))))
✓	2.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 119576 to 55713 computations (53.4% saved)

regimes260.0ms (1.5%)

Accuracy

Total 0.1b remaining (60.1%)

Threshold costs 0.1b (60.1%)

Counts

42 → 2

Compiler

Compiled 8460 to 4422 computations (47.7% saved)

bsearch14.0ms (0.1%)

Steps

Iters	Range		Point
3	2.4178347461426177e+138	5.54000140722942e+142	1.2910446494967518e+141

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	83
1	41	83
2	40	83

end1.0ms (0%)

Compiler: Compiled 60 to 33 computations (45% saved)

sample1.8s (10.7%)

Algorithm

1×

intervals

Results

652.0ms	8000×	body	128	valid
342.0ms	3240×	body	128	invalid
124.0ms	1993×	body	128	nan

Compiler

Compiled 390 to 201 computations (48.5% saved)

Details

analyze1.5s (8.7%)

sample48.0ms (0.3%)

simplify106.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0%)

series548.0ms (3.2%)

rewrite13.0ms (0.1%)

simplify87.0ms (0.5%)

prune70.0ms (0.4%)

localize9.0ms (0.1%)

series615.0ms (3.6%)

rewrite29.0ms (0.2%)

simplify232.0ms (1.4%)

prune415.0ms (2.5%)

localize19.0ms (0.1%)

series2.0s (12%)

rewrite26.0ms (0.2%)

simplify244.0ms (1.4%)

prune282.0ms (1.7%)

localize25.0ms (0.1%)

series6.2s (36.8%)

rewrite2.0ms (0%)

simplify116.0ms (0.7%)

prune2.2s (13.1%)

regimes260.0ms (1.5%)

bsearch14.0ms (0.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.8s (10.7%)

Profiling