Details

analyze261.0ms (11.8%)

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
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample891.0ms (40.1%)

Results

861.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
6×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	11
2	32	11
3	38	11
4	38	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

Compiler

Compiled 67 to 39 computations (41.8% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	0.0b	(+.f64 (.f64 x 2) (.f64 x x))

series13.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

10.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
3.0ms	(+.f64 (.f64 x 2) (.f64 x x))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
5×	`fma-def_binary64`
4×	`sum-log_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

2 → 34

Calls

2 calls:

5.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
3.0ms	(+.f64 (.f64 x 2) (.f64 x x))

simplify68.0ms (3%)

Algorithm

1×	egg-herbie

Rules

800×	`fma-neg_binary64`
465×	`cancel-sign-sub-inv_binary64`
438×	`fma-def_binary64`
410×	`distribute-rgt-out_binary64`
328×	`associate-l_binary64`

Counts

70 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	804
1	210	695
2	687	686
3	2722	684
4	4555	684
5	4959	684

prune45.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
▶	9.6b	(.f64 (sqrt.f64 (fma.f64 x (+.f64 2 x) (.f64 y y))) (sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y))))
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
	38.8b	(+.f64 (/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4)))) (*.f64 y y))

Compiler

Compiled 1129 to 560 computations (50.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y)))
✓	0.0b	(fma.f64 x (+.f64 2 x) (*.f64 y y))
✓	0.1b	(.f64 (sqrt.f64 (fma.f64 x (+.f64 2 x) (.f64 y y))) (sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y))))

series31.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

16.0ms	(sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y)))
9.0ms	(fma.f64 x (+.f64 2 x) (*.f64 y y))
6.0ms	(.f64 (sqrt.f64 (fma.f64 x (+.f64 2 x) (.f64 y y))) (sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y))))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

10.0ms	(.f64 (sqrt.f64 (fma.f64 x (+.f64 2 x) (.f64 y y))) (sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y))))
1.0ms	(sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y)))
0.0ms	(fma.f64 x (+.f64 2 x) (*.f64 y y))

simplify73.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

456×	`fma-def_binary64`
454×	`associate-l_binary64`
297×	`cancel-sign-sub-inv_binary64`
270×	`distribute-rgt-in_binary64`
243×	`distribute-lft-in_binary64`

Counts

150 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2655
1	411	2432
2	1485	2355
3	4973	2355

prune174.0ms (7.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	223	3	226

Error

Counts

226 → 3

Alt Table

Status	Error	Program
✓	9.6b	(.f64 (sqrt.f64 (fma.f64 x (+.f64 2 x) (.f64 y y))) (sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y))))
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	38.8b	(+.f64 (/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4)))) (*.f64 y y))

Compiler

Compiled 6414 to 3744 computations (41.6% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (fma.f64 x (+.f64 x -2) 4))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4)))
✓	3.2b	(fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))
✓	42.0b	(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4))))

series16.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4))))
4.0ms	(.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4)))
4.0ms	(fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))
3.0ms	(*.f64 x (fma.f64 x (+.f64 x -2) 4))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 81

Calls

4 calls:

4.0ms	(/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4))))
4.0ms	(.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4)))
3.0ms	(*.f64 x (fma.f64 x (+.f64 x -2) 4))
0.0ms	(fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6))

simplify83.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-/r*_binary64`
447×	`associate-/l*_binary64`
407×	`distribute-rgt-in_binary64`
394×	`distribute-lft-in_binary64`
205×	`fma-def_binary64`

Counts

129 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2577
1	280	2065
2	1021	2014
3	4723	2012
4	4984	2012

prune118.0ms (5.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	145	3	148

Error

Counts

148 → 3

Alt Table

Status	Error	Program
✓	9.6b	(.f64 (sqrt.f64 (fma.f64 x (+.f64 2 x) (.f64 y y))) (sqrt.f64 (fma.f64 x (+.f64 2 x) (*.f64 y y))))
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	38.8b	(+.f64 (/.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 x 6)) (.f64 x (.f64 x (fma.f64 x (+.f64 x -2) 4)))) (*.f64 y y))

Compiler

Compiled 4272 to 2700 computations (36.8% saved)

regimes300.0ms (13.5%)

Accuracy

Total 0.0b remaining (59%)

Threshold costs 0.0b (59%)

Counts

61 → 1

Compiler

Compiled 4401 to 2956 computations (32.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	10	14
2	10	14

end58.0ms (2.6%)

Compiler: Compiled 83 to 51 computations (38.6% saved)

Details

analyze261.0ms (11.8%)

sample891.0ms (40.1%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

series13.0ms (0.6%)

rewrite9.0ms (0.4%)

simplify68.0ms (3%)

prune45.0ms (2%)

localize7.0ms (0.3%)

series31.0ms (1.4%)

rewrite16.0ms (0.7%)

simplify73.0ms (3.3%)

prune174.0ms (7.8%)

localize14.0ms (0.6%)

series16.0ms (0.7%)

rewrite23.0ms (1%)

simplify83.0ms (3.7%)

prune118.0ms (5.3%)

regimes300.0ms (13.5%)

simplify2.0ms (0.1%)

end58.0ms (2.6%)

Profiling