Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample656.0ms (40%)

Infinites

34.2% of outputs are infinite.

Symmetry

(sort x y)

Results

601.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify7.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
5×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	54	11
4	68	11
5	72	11
6	70	11

prune3.0ms (0.2%)

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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(fma.f64 z (.f64 z 3) (.f64 x y))
	1.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(fma.f64 z (.f64 z 3) (.f64 x y))

series12.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

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 z (*.f64 z 3) (*.f64 x y))

simplify60.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
483×	`distribute-rgt-out_binary64`
466×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
301×	`*-commutative_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	508
1	34	485
2	65	485
3	184	485
4	750	485
5	2905	485
6	3790	485
7	4921	485

prune17.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Error

0.0b

Counts

25 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 z (.f64 z 3) (.f64 x y))
	14.7b	(.f64 (sqrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (sqrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))))
▶	0.6b	(fma.f64 y x (.f64 3 (.f64 z z)))

Compiler

Compiled 362 to 188 computations (48.1% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 3 (.f64 z z))
✓	0.5b	(fma.f64 y x (.f64 3 (.f64 z z)))

series15.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 y x (.f64 3 (.f64 z z)))
2.0ms	(.f64 3 (.f64 z z))

rewrite8.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-l_binary64`

Counts

2 → 31

Calls

2 calls:

7.0ms	(.f64 3 (.f64 z z))
0.0ms	(fma.f64 y x (.f64 3 (.f64 z z)))

simplify71.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

744×	`distribute-rgt-in_binary64`
732×	`distribute-lft-in_binary64`
709×	`associate-/l/_binary64`
476×	`fma-def_binary64`
374×	`*-commutative_binary64`

Counts

79 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	811
1	93	752
2	216	743
3	554	743
4	1006	743
5	2364	743
6	3846	743
7	5210	743

prune41.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	44	3	47

Error

0.0b

Counts

47 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 z (.f64 z 3) (.f64 x y))
	1.1b	(fma.f64 3 (.f64 z z) (.f64 y x))
▶	0.6b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))

Compiler

Compiled 635 to 327 computations (48.5% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 3 (.f64 z z))
✓	0.2b	(.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z))))
✓	0.5b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))
✓	28.1b	(sqrt.f64 (.f64 3 (.f64 z z)))

series40.0ms (2.4%)

Counts

3 → 60

Calls

3 calls:

28.0ms	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))
9.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z))))
3.0ms	(sqrt.f64 (.f64 3 (.f64 z z)))

rewrite21.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`pow1_binary64`
74×	`pow-prod-down_binary64`
63×	`sqrt-pow1_binary64`
17×	`pow-prod-up_binary64`
13×	`pow1/2_binary64`

Counts

3 → 92

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z))))
3.0ms	(sqrt.f64 (.f64 3 (.f64 z z)))
0.0ms	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))

simplify106.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-l_binary64`
485×	`distribute-rgt-in_binary64`
476×	`distribute-lft-in_binary64`
362×	`associate-+l+_binary64`
323×	`associate-r_binary64`

Counts

152 → 93

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	72	1363
1	114	1228
2	353	1216
3	1287	1203
4	2498	1134
5	4617	1134
6	4824	1132
7	4926	1132

prune126.0ms (7.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	154	3	157

Error

0.0b

Counts

157 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	1.1b	(fma.f64 3 (.f64 z z) (.f64 y x))
✓	0.6b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))

Compiler

Compiled 3085 to 1732 computations (43.9% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 3 (.f64 z z) (.f64 y x))

series13.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(fma.f64 3 (*.f64 z z) (*.f64 y x))

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 3 (*.f64 z z) (*.f64 y x))

simplify61.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
483×	`distribute-rgt-out_binary64`
466×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
302×	`*-commutative_binary64`

Counts

46 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	508
1	32	485
2	64	485
3	184	485
4	750	485
5	2905	485
6	3790	485
7	4921	485

prune17.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	22	3	25

Error

0.0b

Counts

25 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	1.1b	(fma.f64 3 (.f64 z z) (.f64 y x))
✓	0.6b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))

Compiler

Compiled 317 to 148 computations (53.3% saved)

regimes286.0ms (17.4%)

Accuracy

Total 0.7b remaining (97.9%)

Threshold costs 0.7b (97.9%)

Counts

51 → 1

Compiler

Compiled 4866 to 3444 computations (29.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end51.0ms (3.1%)

Remove: (sort x y)
Compiler: Compiled 85 to 54 computations (36.5% saved)

Details

analyze2.0ms (0.1%)

sample656.0ms (40%)

simplify7.0ms (0.5%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series12.0ms (0.8%)

rewrite1.0ms (0%)

simplify60.0ms (3.7%)

prune17.0ms (1%)

localize5.0ms (0.3%)

series15.0ms (0.9%)

rewrite8.0ms (0.5%)

simplify71.0ms (4.3%)

prune41.0ms (2.5%)

localize7.0ms (0.4%)

series40.0ms (2.4%)

rewrite21.0ms (1.3%)

simplify106.0ms (6.5%)

prune126.0ms (7.7%)

localize5.0ms (0.3%)

series13.0ms (0.8%)

rewrite1.0ms (0%)

simplify61.0ms (3.7%)

prune17.0ms (1%)

regimes286.0ms (17.4%)

simplify2.0ms (0.1%)

end51.0ms (3.1%)

Profiling