Details

analyze2.3s (18.9%)

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)

sample3.6s (29%)

Results

2.4s	8256×	body	128	valid
1.1s	3770×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify109.0ms (0.9%)

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

prune5.0ms (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

1.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	1.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series933.0ms (7.6%)

Counts

2 → 72

Calls

2 calls:

567.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
366.0ms	(*.f64 a (pow.f64 k m))

rewrite24.0ms (0.2%)

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:

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

simplify140.0ms (1.1%)

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

prune171.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Error

1.4b

Counts

98 → 5

Alt Table

Status	Error	Program
	1.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	1.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	1.4b	(*.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))))
	36.5b	(/.f64 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
▶	1.4b	(/.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)))

Compiler

Compiled 2471 to 1370 computations (44.6% saved)

localize19.0ms (0.2%)

Local error

Found 3 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)))
✓	14.4b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series442.0ms (3.6%)

Counts

2 → 48

Calls

2 calls:

439.0ms	(/.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)))
3.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite45.0ms (0.4%)

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:

14.0ms	(/.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)))
4.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify260.0ms (2.1%)

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 → 185

Iterations

Useful iterations: 3 (0.0ms)

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

prune569.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	261	5	266

Error

1.4b

Counts

266 → 5

Alt Table

Status	Error	Program
	1.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	1.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
▶	1.4b	(*.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))))
	36.5b	(/.f64 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
✓	1.4b	(/.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)))

Compiler

Compiled 8184 to 5101 computations (37.7% saved)

localize20.0ms (0.2%)

Local error

Found 3 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 (/.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))))
	14.4b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series514.0ms (4.2%)

Counts

2 → 60

Calls

2 calls:

445.0ms	(*.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))))
68.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))

rewrite107.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`add-sqr-sqrt_binary64`
134×	`times-frac_binary64`
72×	`*-un-lft-identity_binary64`
72×	`add-cube-cbrt_binary64`
70×	`sqrt-prod_binary64`

Counts

2 → 186

Calls

2 calls:

47.0ms	(*.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))))
8.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))

simplify325.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

866×	`times-frac_binary64`
681×	`fma-def_binary64`
257×	`associate-r_binary64`
241×	`associate-/l*_binary64`
240×	`associate-*r/_binary64`

Counts

246 → 278

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	9196
1	968	8312
2	3210	8098
3	5104	8098

prune861.0ms (7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	354	0	354
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	354	5	359

Error

1.4b

Counts

359 → 5

Alt Table

Status	Error	Program
	1.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
▶	1.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
✓	1.4b	(*.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))))
	36.5b	(/.f64 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
✓	1.4b	(/.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)))

Compiler

Compiled 11755 to 7425 computations (36.8% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	1.4b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series487.0ms (4%)

Counts

2 → 60

Calls

2 calls:

428.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
59.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

rewrite35.0ms (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:

13.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
7.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

simplify209.0ms (1.7%)

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

prune376.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	189	5	194

Error

1.4b

Counts

194 → 5

Alt Table

Status	Error	Program
	1.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	1.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
✓	1.4b	(*.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))))
	36.5b	(/.f64 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
✓	1.4b	(/.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)))

Compiler

Compiled 4993 to 2841 computations (43.1% saved)

regimes527.0ms (4.3%)

Accuracy

Total 0.1b remaining (3.7%)

Threshold costs 0.1b (3.7%)

Counts

72 → 1

Compiler

Compiled 5516 to 3726 computations (32.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	17	31
2	16	31

end187.0ms (1.5%)

Compiler: Compiled 147 to 102 computations (30.6% saved)

Details

analyze2.3s (18.9%)

sample3.6s (29%)

simplify109.0ms (0.9%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series933.0ms (7.6%)

rewrite24.0ms (0.2%)

simplify140.0ms (1.1%)

prune171.0ms (1.4%)

localize19.0ms (0.2%)

series442.0ms (3.6%)

rewrite45.0ms (0.4%)

simplify260.0ms (2.1%)

prune569.0ms (4.6%)

localize20.0ms (0.2%)

series514.0ms (4.2%)

rewrite107.0ms (0.9%)

simplify325.0ms (2.6%)

prune861.0ms (7%)

localize15.0ms (0.1%)

series487.0ms (4%)

rewrite35.0ms (0.3%)

simplify209.0ms (1.7%)

prune376.0ms (3.1%)

regimes527.0ms (4.3%)

simplify4.0ms (0%)

end187.0ms (1.5%)

Profiling