Details

analyze420.0ms (17.3%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample938.0ms (38.6%)

Symmetry

(sort x y)

Results

847.0ms	8256×	body	128	valid
58.0ms	489×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify15.0ms (0.6%)

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 (0.1%)

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
▶	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.1b	(+.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 (0.2%)

Local error

Found 1 expressions with local error:

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

series19.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

19.0ms

(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))

simplify63.0ms (2.6%)

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

prune19.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Error

0.0b

Counts

25 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
	17.1b	(.f64 (sqrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (sqrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y)))) (cbrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))))
▶	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))

Compiler

Compiled 462 to 240 computations (48.1% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y x (.f64 3 (.f64 z z)))
✓	0.2b	(.f64 3 (.f64 z z))

series15.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 y x (.f64 3 (.f64 z z)))
3.0ms	(.f64 3 (.f64 z z))

rewrite8.0ms (0.3%)

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)))

simplify73.0ms (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

prune39.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	45	4	49

Error

0.0b

Counts

49 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.1b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
	0.2b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))
▶	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))

Compiler

Compiled 677 to 357 computations (47.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series15.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(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))

simplify64.0ms (2.6%)

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

prune14.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	22	4	26

Error

0.0b

Counts

26 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.1b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
	0.2b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))
✓	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))

Compiler

Compiled 372 to 188 computations (49.5% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
✓	0.1b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
✓	0.3b	(.f64 (cbrt.f64 3) (.f64 z z))

series56.0ms (2.3%)

Counts

3 → 60

Calls

3 calls:

36.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
14.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
6.0ms	(.f64 (cbrt.f64 3) (.f64 z z))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
29×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 65

Calls

3 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
6.0ms	(.f64 (cbrt.f64 3) (.f64 z z))
0.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))

simplify113.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

489×	`fma-def_binary64`
409×	`times-frac_binary64`
328×	`sqr-pow_binary64`
280×	`*-commutative_binary64`
267×	`associate-/l*_binary64`

Counts

125 → 96

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	86	1400
1	157	1209
2	474	1179
3	831	1179
4	1275	1179
5	2695	1179
6	4063	1174
7	4683	1174
8	4862	1174

prune98.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	96	4	100

Error

Counts

100 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.2b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) z) (*.f64 (cbrt.f64 (sqrt.f64 3)) z))))
	0.2b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))
✓	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))

Compiler

Compiled 1925 to 1287 computations (33.1% saved)

regimes333.0ms (13.7%)

Accuracy

Total 0.1b remaining (86.4%)

Threshold costs 0.1b (86.4%)

Counts

52 → 1

Compiler

Compiled 5733 to 4115 computations (28.2% 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

end75.0ms (3.1%)

Remove: (sort x y)
Compiler: Compiled 108 to 73 computations (32.4% saved)

Details

analyze420.0ms (17.3%)

sample938.0ms (38.6%)

simplify15.0ms (0.6%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series19.0ms (0.8%)

rewrite1.0ms (0%)

simplify63.0ms (2.6%)

prune19.0ms (0.8%)

localize6.0ms (0.3%)

series15.0ms (0.6%)

rewrite8.0ms (0.3%)

simplify73.0ms (3%)

prune39.0ms (1.6%)

localize5.0ms (0.2%)

series15.0ms (0.6%)

rewrite1.0ms (0%)

simplify64.0ms (2.6%)

prune14.0ms (0.6%)

localize9.0ms (0.4%)

series56.0ms (2.3%)

rewrite21.0ms (0.9%)

simplify113.0ms (4.6%)

prune98.0ms (4%)

regimes333.0ms (13.7%)

simplify2.0ms (0.1%)

end75.0ms (3.1%)

Profiling