Details

analyze1.4s (14.6%)

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)

sample157.0ms (1.6%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
13.0ms	107×	body	128	invalid
3.0ms	53×	body	128	nan

Compiler

Compiled 40 to 28 computations (30% saved)

simplify103.0ms (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

2.8b

Counts

3 → 1

Alt Table

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

series547.0ms (5.6%)

Counts

2 → 72

Calls

2 calls:

304.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
242.0ms	(*.f64 a (pow.f64 k m))

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))

simplify89.0ms (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 → 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

prune101.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

2.7b

Counts

98 → 3

Alt Table

Status	Error	Program
	2.8b	(*.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))))
▶	2.8b	(/.f64 (.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2))) (fma.f64 k (+.f64 k 10) 1))
	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)))

Compiler

Compiled 2415 to 1334 computations (44.8% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2)))
✓	0.0b	(*.f64 a (pow.f64 k (/.f64 m 2)))
✓	2.8b	(/.f64 (.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2))) (fma.f64 k (+.f64 k 10) 1))

series897.0ms (9.3%)

Counts

3 → 108

Calls

3 calls:

330.0ms	(.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2)))
326.0ms	(/.f64 (.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2))) (fma.f64 k (+.f64 k 10) 1))
241.0ms	(*.f64 a (pow.f64 k (/.f64 m 2)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-exp-log_binary64`
45×	`prod-exp_binary64`
19×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`pow-exp_binary64`

Counts

3 → 94

Calls

3 calls:

8.0ms	(.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2)))
7.0ms	(/.f64 (.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2))) (fma.f64 k (+.f64 k 10) 1))
4.0ms	(*.f64 a (pow.f64 k (/.f64 m 2)))

simplify138.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
408×	`associate-/l/_binary64`
263×	`fma-neg_binary64`
250×	`associate-r_binary64`
249×	`associate-l_binary64`

Counts

202 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4890
1	629	4440
2	2490	3366
3	4546	3359
4	4877	3359

prune166.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	163	3	166

Error

2.7b

Counts

166 → 3

Alt Table

Status	Error	Program
	2.8b	(*.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))))
✓	2.8b	(/.f64 (.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2))) (fma.f64 k (+.f64 k 10) 1))
▶	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)))

Compiler

Compiled 4855 to 3196 computations (34.2% 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 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)))
✓	14.6b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series622.0ms (6.4%)

Counts

3 → 84

Calls

3 calls:

317.0ms

(/.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))

rewrite31.0ms (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:

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))

simplify229.0ms (2.4%)

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

prune353.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	335	3	338

Error

0.0b

Counts

338 → 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)))
▶	26.9b	(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)))))))
✓	2.8b	(/.f64 (.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2))) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 10716 to 6630 computations (38.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.0b	(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)))))))
✓	15.1b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 3))
✓	15.7b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 4))
✓	15.9b	(/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))

series1.9s (19.9%)

Counts

4 → 144

Calls

4 calls:

1.0s	(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)))))))
300.0ms	(/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))
297.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 3))
290.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 k 4))

rewrite27.0ms (0.3%)

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

simplify234.0ms (2.4%)

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

prune250.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	239	3	242

Error

0.0b

Counts

242 → 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)))
✓	26.9b	(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)))))))
✓	2.8b	(/.f64 (.f64 (.f64 a (pow.f64 k (/.f64 m 2))) (pow.f64 k (/.f64 m 2))) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 12357 to 5601 computations (54.7% saved)

regimes589.0ms (6.1%)

Accuracy

Total 0.1b remaining (68.4%)

Threshold costs 0.1b (68.4%)

Counts

128 → 2

Compiler

Compiled 11076 to 7658 computations (30.9% saved)

bsearch23.0ms (0.2%)

Steps

Iters	Range		Point
6	9.420723414922224e+132	4.0412598906011696e+133	1.2939891137448822e+133

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (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	38	90
1	43	90
2	42	90

end1.0ms (0%)

Compiler: Compiled 65 to 39 computations (40% saved)

sample1.7s (17.6%)

Algorithm

1×

intervals

Results

680.0ms	8000×	body	128	valid
352.0ms	3127×	body	128	invalid
120.0ms	1913×	body	128	nan

Compiler

Compiled 179 to 111 computations (38% saved)

Details

analyze1.4s (14.6%)

sample157.0ms (1.6%)

simplify103.0ms (1.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series547.0ms (5.6%)

rewrite11.0ms (0.1%)

simplify89.0ms (0.9%)

prune101.0ms (1%)

localize14.0ms (0.1%)

series897.0ms (9.3%)

rewrite26.0ms (0.3%)

simplify138.0ms (1.4%)

prune166.0ms (1.7%)

localize10.0ms (0.1%)

series622.0ms (6.4%)

rewrite31.0ms (0.3%)

simplify229.0ms (2.4%)

prune353.0ms (3.6%)

localize20.0ms (0.2%)

series1.9s (19.9%)

rewrite27.0ms (0.3%)

simplify234.0ms (2.4%)

prune250.0ms (2.6%)

regimes589.0ms (6.1%)

bsearch23.0ms (0.2%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.7s (17.6%)

Profiling