Details

analyze1.5s (21%)

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)

sample2.0s (28.6%)

Results

1.3s	8256×	body	128	valid
566.0ms	3781×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify106.0ms (1.5%)

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

1.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.6b	(/.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	(*.f64 a (pow.f64 k m))
✓	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	1.6b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series530.0ms (7.6%)

Counts

3 → 84

Calls

3 calls:

293.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
234.0ms	(*.f64 a (pow.f64 k m))
2.0ms	(fma.f64 k (+.f64 k 10) 1)

rewrite12.0ms (0.2%)

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)

simplify104.0ms (1.5%)

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

prune89.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	4	119

Error

1.6b

Counts

119 → 4

Alt Table

Status	Error	Program
	25.2b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
▶	1.6b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	1.7b	(*.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))))
	11.3b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k 10 1))

Compiler

Compiled 2700 to 1465 computations (45.7% 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 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	1.6b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series335.0ms (4.8%)

Counts

2 → 60

Calls

2 calls:

293.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
41.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

rewrite22.0ms (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:

10.0ms	(*.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))

simplify120.0ms (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

prune186.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	210	4	214

Error

1.6b

Counts

214 → 4

Alt Table

Status	Error	Program
	25.2b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
✓	1.6b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
▶	1.7b	(*.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))))
	11.3b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k 10 1))

Compiler

Compiled 5306 to 3014 computations (43.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 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 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.1b	(*.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))))
✓	14.2b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series390.0ms (5.6%)

Counts

4 → 96

Calls

4 calls:

286.0ms	(*.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))))
55.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
46.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
2.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`add-sqr-sqrt_binary64`
152×	`times-frac_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`
85×	`sqrt-prod_binary64`

Counts

4 → 242

Calls

4 calls:

23.0ms	(*.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))))
5.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
1.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify288.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

539×	`cancel-sign-sub-inv_binary64`
411×	`fma-neg_binary64`
274×	`associate-r_binary64`
259×	`associate-*l/_binary64`
254×	`*-commutative_binary64`

Counts

338 → 385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	10930
1	1170	9931
2	3836	9583
3	4903	9583
4	4999	9583

prune450.0ms (6.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	422	1	423
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	423	4	427

Error

0.0b

Counts

427 → 4

Alt Table

Status	Error	Program
✓	1.6b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	27.3b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
▶	25.2b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
✓	1.7b	(*.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))))

Compiler

Compiled 13707 to 8578 computations (37.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	11.6b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))

series279.0ms (4%)

Counts

1 → 36

Calls

1 calls:

279.0ms

(/.f64 (*.f64 a (pow.f64 k m)) (*.f64 k k))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`prod-exp_binary64`
8×	`div-exp_binary64`
4×	`cbrt-unprod_binary64`

Counts

1 → 27

Calls

1 calls:

5.0ms

(/.f64 (*.f64 a (pow.f64 k m)) (*.f64 k k))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-l_binary64`
596×	`associate-r_binary64`
496×	`associate-/r*_binary64`
404×	`fma-def_binary64`
391×	`associate-*l/_binary64`

Counts

63 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1109
1	261	961
2	1017	937
3	4558	937
4	4966	937

prune114.0ms (1.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	80	4	84

Error

0.0b

Counts

84 → 4

Alt Table

Status	Error	Program
✓	25.2b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
✓	1.6b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
✓	1.7b	(*.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))))
	15.6b	(/.f64 (*.f64 a (/.f64 (pow.f64 k m) k)) k)

Compiler

Compiled 1393 to 448 computations (67.8% saved)

regimes243.0ms (3.5%)

Accuracy

Total 0.3b remaining (92.2%)

Threshold costs 0.3b (92.2%)

Counts

48 → 3

Compiler

Compiled 3040 to 2034 computations (33.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	111
1	29	111
2	28	111

end79.0ms (1.1%)

Compiler: Compiled 219 to 119 computations (45.7% saved)

Details

analyze1.5s (21%)

sample2.0s (28.6%)

simplify106.0ms (1.5%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series530.0ms (7.6%)

rewrite12.0ms (0.2%)

simplify104.0ms (1.5%)

prune89.0ms (1.3%)

localize7.0ms (0.1%)

series335.0ms (4.8%)

rewrite22.0ms (0.3%)

simplify120.0ms (1.7%)

prune186.0ms (2.7%)

localize9.0ms (0.1%)

series390.0ms (5.6%)

rewrite60.0ms (0.9%)

simplify288.0ms (4.1%)

prune450.0ms (6.5%)

localize5.0ms (0.1%)

series279.0ms (4%)

rewrite7.0ms (0.1%)

simplify58.0ms (0.8%)

prune114.0ms (1.6%)

regimes243.0ms (3.5%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end79.0ms (1.1%)

Profiling