Details

analyze1.4s (18%)

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)

sample57.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
12.0ms	120×	body	128	invalid
4.0ms	65×	body	128	nan

Compiler

Compiled 40 to 28 computations (30% saved)

simplify104.0ms (1.3%)

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	0.5b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series658.0ms (8.2%)

Counts

3 → 84

Calls

3 calls:

371.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
285.0ms	(*.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)

simplify111.0ms (1.4%)

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

prune126.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Error

0.5b

Counts

119 → 5

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
▶	0.5b	(*.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))))
	0.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	17.3b	(.f64 (pow.f64 k m) (-.f64 a (.f64 (*.f64 k 10) a)))
	11.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))))

Compiler

Compiled 2772 to 1511 computations (45.5% saved)

localize10.0ms (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)))
✓	0.0b	(*.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))))
✓	13.9b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series408.0ms (5.1%)

Counts

4 → 96

Calls

4 calls:

295.0ms	(*.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))))
60.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
48.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
4.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite59.0ms (0.7%)

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:

22.0ms	(*.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))))
4.0ms	(/.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))

simplify250.0ms (3.1%)

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

prune453.0ms (5.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	422	1	423
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	423	5	428

Error

Counts

428 → 5

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	17.3b	(.f64 (pow.f64 k m) (-.f64 a (.f64 (*.f64 k 10) a)))
	11.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))))
	27.8b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
	0.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))

Compiler

Compiled 13796 to 8635 computations (37.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.2b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	0.3b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series330.0ms (4.1%)

Counts

2 → 60

Calls

2 calls:

287.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
42.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

rewrite18.0ms (0.2%)

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:

7.0ms	(*.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))

simplify123.0ms (1.5%)

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

prune202.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	210	5	215

Error

Counts

215 → 5

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
▶	0.5b	(.f64 (.f64 a (sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) (sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))))
✓	0.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	11.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))))
	27.8b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))

Compiler

Compiled 5404 to 3070 computations (43.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 a (sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) (sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))))
✓	0.0b	(*.f64 a (sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))))
	0.2b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	6.2b	(sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series672.0ms (8.4%)

Counts

3 → 96

Calls

3 calls:

322.0ms

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

298.0ms

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

52.0ms

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

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`sqrt-prod_binary64`
69×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
56×	`associate-r_binary64`
48×	`*-un-lft-identity_binary64`

Counts

3 → 139

Calls

3 calls:

12.0ms

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

9.0ms

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

4.0ms

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

simplify190.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
527×	`fma-neg_binary64`
441×	`associate-l_binary64`
430×	`associate-r_binary64`
298×	`*-commutative_binary64`

Counts

235 → 307

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	422	7688
1	1064	6700
2	3548	6362
3	4901	6362
4	5023	6362

prune699.0ms (8.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	567	0	567
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	567	5	572

Error

Counts

572 → 5

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	0.5b	(.f64 (.f64 a (sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) (sqrt.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))))
✓	0.5b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	11.8b	(.f64 (sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))))
	27.8b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))

Compiler

Compiled 21937 to 13054 computations (40.5% saved)

regimes412.0ms (5.1%)

Accuracy

Total 1.8b remaining (96.9%)

Threshold costs 0b (0%)

Counts

108 → 1

Compiler

Compiled 8652 to 5702 computations (34.1% saved)

simplify2.0ms (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

end1.0ms (0%)

Compiler: Compiled 24 to 17 computations (29.2% saved)

sample1.6s (20%)

Algorithm

1×

intervals

Results

641.0ms	8000×	body	128	valid
329.0ms	3180×	body	128	invalid
113.0ms	1986×	body	128	nan

Compiler

Compiled 159 to 104 computations (34.6% saved)

Details

analyze1.4s (18%)

sample57.0ms (0.7%)

simplify104.0ms (1.3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series658.0ms (8.2%)

rewrite12.0ms (0.2%)

simplify111.0ms (1.4%)

prune126.0ms (1.6%)

localize10.0ms (0.1%)

series408.0ms (5.1%)

rewrite59.0ms (0.7%)

simplify250.0ms (3.1%)

prune453.0ms (5.7%)

localize9.0ms (0.1%)

series330.0ms (4.1%)

rewrite18.0ms (0.2%)

simplify123.0ms (1.5%)

prune202.0ms (2.5%)

localize10.0ms (0.1%)

series672.0ms (8.4%)

rewrite42.0ms (0.5%)

simplify190.0ms (2.4%)

prune699.0ms (8.7%)

regimes412.0ms (5.1%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.6s (20%)

Profiling