Details

analyze1.5s (12.7%)

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)

sample51.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
11.0ms	110×	body	128	invalid
3.0ms	58×	body	128	nan

Compiler

Compiled 40 to 28 computations (30% saved)

simplify114.0ms (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

2.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	2.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

rewrite11.0ms (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))

series1.1s (9.3%)

Counts

2 → 72

Calls

2 calls:

671.0ms	(*.f64 a (pow.f64 k m))
394.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

simplify101.0ms (0.9%)

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 → 217

Iterations

Useful iterations: 3 (0.0ms)

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

prune91.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	216	2	218

Error

2.1b

Counts

218 → 2

Alt Table

Status	Error	Program
▶	2.2b	(/.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)))
	2.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))

Compiler

Compiled 2361 to 1292 computations (45.3% saved)

localize10.0ms (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 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	17.5b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))
✓	17.5b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64`
57×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`

Counts

2 → 112

Calls

2 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)))
1.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series393.0ms (3.4%)

Counts

2 → 48

Calls

2 calls:

390.0ms	(/.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))

simplify174.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

686×	`associate-/r*_binary64`
476×	`associate-/r/_binary64`
467×	`fma-def_binary64`
440×	`fma-neg_binary64`
290×	`cancel-sign-sub-inv_binary64`

Counts

160 → 292

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	274	5935
1	725	5417
2	2259	5031
3	4945	5026
4	5146	5026

prune270.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	441	1	442
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	441	3	444

Error

2.1b

Counts

444 → 3

Alt Table

Status	Error	Program
▶	2.2b	(*.f64 (/.f64 (/.f64 a (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) 1) (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	2.2b	(/.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)))
	2.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))

Compiler

Compiled 8163 to 5089 computations (37.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.3b	(*.f64 (/.f64 (/.f64 a (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) 1) (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	17.5b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))
	17.5b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))
	17.5b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite530.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

1590×	`times-frac_binary64`
1341×	`add-sqr-sqrt_binary64`
1038×	`sqrt-prod_binary64`
549×	`*-un-lft-identity_binary64`
465×	`add-cube-cbrt_binary64`

Counts

1 → 740

Calls

1 calls:

393.0ms

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

series382.0ms (3.3%)

Counts

1 → 36

Calls

1 calls:

382.0ms

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

simplify932.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

762×	`associate-/l*_binary64`
459×	`associate-r_binary64`
436×	`associate-l_binary64`
290×	`associate-/r*_binary64`
288×	`times-frac_binary64`

Counts

776 → 1549

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	634	49770
1	1622	47257
2	4973	47239
3	5111	47239

prune1.3s (11.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	2122	1	2123
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	2122	4	2126

Error

0.0b

Counts

2126 → 4

Alt Table

Status	Error	Program
✓	2.2b	(*.f64 (/.f64 (/.f64 a (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) 1) (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	2.2b	(/.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)))
▶	2.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	35.3b	(fma.f64 (/.f64 a k) (/.f64 (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k))))) k) (.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10))

Compiler

Compiled 42374 to 29634 computations (30.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	2.1b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

rewrite15.0ms (0.1%)

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:

6.0ms	(/.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)))

series821.0ms (7.1%)

Counts

2 → 72

Calls

2 calls:

415.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
405.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

simplify163.0ms (1.4%)

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 → 302

Iterations

Useful iterations: 3 (0.0ms)

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

prune318.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	519	1	520
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	520	4	524

Error

0.0b

Counts

524 → 4

Alt Table

Status	Error	Program
✓	2.2b	(*.f64 (/.f64 (/.f64 a (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) 1) (/.f64 (/.f64 (pow.f64 k m) (sqrt.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	14.7b	(/.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))))
✓	2.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	35.3b	(fma.f64 (/.f64 a k) (/.f64 (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k))))) k) (.f64 (/.f64 (.f64 a (exp.f64 (neg.f64 (.f64 m (neg.f64 (log.f64 k)))))) (pow.f64 k 3)) -10))

Compiler

Compiled 5312 to 3011 computations (43.3% saved)

regimes906.0ms (7.9%)

Accuracy

Total 0.0b remaining (70.7%)

Threshold costs 0.0b (70.7%)

Compiler

Compiled 13064 to 9130 computations (30.1% saved)

bsearch15.0ms (0.1%)

Steps

Iters	Range		Point
3	1.3851549757423743e+23	4.521787758671721e+23	2.2014896057993437e+23

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`cancel-sign-sub-inv_binary64`
12×	`distribute-lft-neg-in_binary64`
12×	`distribute-rgt-neg-in_binary64`
7×	`distribute-lft-neg-out_binary64`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	68
1	48	60
2	62	60
3	82	60
4	90	60
5	93	60
6	88	60

end1.0ms (0%)

Compiler: Compiled 43 to 25 computations (41.9% saved)

sample2.3s (20.2%)

Algorithm

1×

intervals

Results

886.0ms	8000×	body	128	valid
478.0ms	3248×	body	128	invalid
174.0ms	1930×	body	128	nan

Compiler

Compiled 178 to 112 computations (37.1% saved)

Details

analyze1.5s (12.7%)

sample51.0ms (0.4%)

simplify114.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite11.0ms (0.1%)

series1.1s (9.3%)

simplify101.0ms (0.9%)

prune91.0ms (0.8%)

localize10.0ms (0.1%)

rewrite20.0ms (0.2%)

series393.0ms (3.4%)

simplify174.0ms (1.5%)

prune270.0ms (2.3%)

localize14.0ms (0.1%)

rewrite530.0ms (4.6%)

series382.0ms (3.3%)

simplify932.0ms (8.1%)

prune1.3s (11.3%)

localize11.0ms (0.1%)

rewrite15.0ms (0.1%)

series821.0ms (7.1%)

simplify163.0ms (1.4%)

prune318.0ms (2.8%)

regimes906.0ms (7.9%)

bsearch15.0ms (0.1%)

simplify6.0ms (0%)

end1.0ms (0%)

sample2.3s (20.2%)

Profiling