Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	25%	13
75%	0%	25%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample699.0ms (40.1%)

Results

639.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`fma-neg_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	15	8
2	21	8
3	24	8
4	26	8
5	27	8
6	24	8

prune2.0ms (0.1%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (fma.f64 x x -3) 6)

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

(/.f64 (fma.f64 x x -3) 6)

simplify55.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

822×	`distribute-rgt-in_binary64`
507×	`associate-/l*_binary64`
396×	`associate-/l/_binary64`
383×	`fma-def_binary64`
343×	`times-frac_binary64`

Counts

41 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	533
1	103	499
2	216	499
3	434	499
4	1114	499
5	3350	499
6	4886	499

prune70.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Error

Counts

40 → 5

Alt Table

Status	Error	Program
	44.8b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
▶	0.1b	(/.f64 1 (/.f64 6 (fma.f64 x x -3)))
	45.0b	(*.f64 (/.f64 (sqrt.f64 (fma.f64 x x -3)) (sqrt.f64 6)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) (sqrt.f64 6)))

Compiler

Compiled 571 to 426 computations (25.4% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 6 (fma.f64 x x -3))
✓	0.1b	(/.f64 1 (/.f64 6 (fma.f64 x x -3)))

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 6 (fma.f64 x x -3))
3.0ms	(/.f64 1 (/.f64 6 (fma.f64 x x -3)))

rewrite13.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 6 (fma.f64 x x -3)))
2.0ms	(/.f64 6 (fma.f64 x x -3))

simplify115.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-neg_binary64`
527×	`times-frac_binary64`
512×	`fma-def_binary64`
344×	`distribute-rgt-in_binary64`
315×	`distribute-lft-in_binary64`

Counts

131 → 162

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	147	2190
1	284	2011
2	713	1987
3	1761	1987
4	4210	1985
5	4896	1985
6	4877	1985

prune146.0ms (8.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	163	4	167

Error

Counts

167 → 4

Alt Table

Status	Error	Program
	44.8b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
▶	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
	1.0b	(/.f64 1 (*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3))))
✓	0.1b	(/.f64 1 (/.f64 6 (fma.f64 x x -3)))

Compiler

Compiled 2750 to 2192 computations (20.3% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

simplify48.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
474×	`unswap-sqr_binary64`
438×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	214
1	30	197
2	59	197
3	156	197
4	622	197
5	2186	197
6	2781	197
7	5148	197

prune11.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	16	4	20

Error

Counts

20 → 4

Alt Table

Status	Error	Program
	44.8b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
▶	1.0b	(/.f64 1 (*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3))))
✓	0.1b	(/.f64 1 (/.f64 6 (fma.f64 x x -3)))

Compiler

Compiled 218 to 147 computations (32.6% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3))))
✓	0.8b	(/.f64 (sqrt.f64 6) (fma.f64 x x -3))
✓	0.9b	(*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3)))

series37.0ms (2.1%)

Counts

3 → 36

Calls

3 calls:

22.0ms	(/.f64 1 (*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3))))
10.0ms	(*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3)))
5.0ms	(/.f64 (sqrt.f64 6) (fma.f64 x x -3))

rewrite26.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 126

Calls

3 calls:

9.0ms	(*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3)))
7.0ms	(/.f64 1 (*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3))))
3.0ms	(/.f64 (sqrt.f64 6) (fma.f64 x x -3))

simplify117.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary64`
442×	`associate-/l*_binary64`
408×	`fma-def_binary64`
383×	`fma-neg_binary64`
276×	`associate-*l/_binary64`

Counts

162 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	2886
1	486	2523
2	1529	2477
3	4250	2441
4	4690	2441
5	4838	2441

prune136.0ms (7.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	194	4	198

Error

Counts

198 → 4

Alt Table

Status	Error	Program
	44.8b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	1.0b	(/.f64 1 (*.f64 (sqrt.f64 6) (/.f64 (sqrt.f64 6) (fma.f64 x x -3))))
✓	0.1b	(/.f64 1 (/.f64 6 (fma.f64 x x -3)))

Compiler

Compiled 3749 to 3156 computations (15.8% saved)

regimes157.0ms (9%)

Accuracy

Total -0.0b remaining (-2.9%)

Threshold costs -0.0b (-2.9%)

Counts

46 → 1

Compiler

Compiled 2408 to 1898 computations (21.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end60.0ms (3.4%)

Compiler: Compiled 57 to 43 computations (24.6% saved)

Details

analyze4.0ms (0.2%)

sample699.0ms (40.1%)

simplify8.0ms (0.4%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite3.0ms (0.2%)

simplify55.0ms (3.2%)

prune70.0ms (4%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite13.0ms (0.7%)

simplify115.0ms (6.6%)

prune146.0ms (8.4%)

localize3.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0%)

simplify48.0ms (2.8%)

prune11.0ms (0.6%)

localize6.0ms (0.4%)

series37.0ms (2.1%)

rewrite26.0ms (1.5%)

simplify117.0ms (6.7%)

prune136.0ms (7.8%)

regimes157.0ms (9%)

simplify2.0ms (0.1%)

end60.0ms (3.4%)

Profiling