Details

analyze4.0ms (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)

sample1.0s (31.4%)

Symmetry

(sort x y)

Results

949.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify15.0ms (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

prune6.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.3b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize11.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series23.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

23.0ms

(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:

1.0ms

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

simplify100.0ms (3.1%)

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

prune41.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	18	5	23
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	20	5	25

Error

0.0b

Counts

25 → 5

Alt Table

Status	Error	Program
	15.8b	(.f64 (sqrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (sqrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))))
	1.1b	(.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))))
	27.7b	(cbrt.f64 (pow.f64 (fma.f64 y x (.f64 3 (.f64 z z))) 3))
	0.3b	(+.f64 (.f64 z (.f64 z 3)) (*.f64 x y))
▶	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))

Compiler

Compiled 467 to 253 computations (45.8% saved)

localize11.0ms (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))

series28.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(fma.f64 y x (.f64 3 (.f64 z z)))
5.0ms	(.f64 3 (.f64 z z))

rewrite24.0ms (0.8%)

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:

8.0ms	(.f64 3 (.f64 z z))
1.0ms	(fma.f64 y x (.f64 3 (.f64 z z)))

simplify138.0ms (4.2%)

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

prune97.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	39	5	44
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Error

0.0b

Counts

49 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y x (.f64 (.f64 3 z) z))
	0.1b	(fma.f64 y x (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z)))))
	0.4b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 z z))) (cbrt.f64 (.f64 3 (.f64 z z)))) (cbrt.f64 (.f64 3 (.f64 z z)))))
	13.8b	(fma.f64 y x (cbrt.f64 (*.f64 27 (pow.f64 z 6))))
	0.3b	(fma.f64 3 (.f64 z z) (.f64 y x))

Compiler

Compiled 728 to 386 computations (47% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series27.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(fma.f64 y x (.f64 (.f64 3 z) z))
7.0ms	(.f64 (.f64 3 z) z)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

7.0ms	(.f64 (.f64 3 z) z)
1.0ms	(fma.f64 y x (.f64 (.f64 3 z) z))

simplify124.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
363×	`associate-l_binary64`
300×	`associate-*l/_binary64`
277×	`distribute-rgt-in_binary64`
271×	`distribute-lft-in_binary64`

Counts

78 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	801
1	111	742
2	343	733
3	728	731
4	1239	731
5	2892	731
6	4704	731
7	4973	731

prune69.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Error

Counts

54 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y x (.f64 (.f64 3 z) z))
▶	0.3b	(fma.f64 y x (.f64 (.f64 (.f64 3 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
	13.8b	(fma.f64 y x (cbrt.f64 (*.f64 27 (pow.f64 z 6))))
	0.3b	(fma.f64 3 (.f64 z z) (.f64 y x))

Compiler

Compiled 722 to 393 computations (45.6% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (.f64 3 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
✓	0.2b	(.f64 (.f64 3 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series556.0ms (17.1%)

Counts

4 → 48

Calls

4 calls:

236.0ms	(.f64 (.f64 3 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
221.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
64.0ms	(cbrt.f64 z)
34.0ms	(.f64 (.f64 (.f64 3 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))

rewrite69.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
36×	`add-exp-log_binary64`
23×	`pow-prod-down_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-unprod_binary64`

Counts

4 → 111

Calls

4 calls:

29.0ms	(.f64 (.f64 (.f64 3 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
13.0ms	(.f64 (.f64 3 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
9.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify214.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

525×	`*-commutative_binary64`
397×	`sqr-pow_binary64`
313×	`cube-prod_binary64`
300×	`log-prod_binary64`
293×	`exp-prod_binary64`

Counts

159 → 149

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	127	1693
1	261	1383
2	1053	1258
3	1809	1215
4	3643	1091
5	4505	1087
6	4831	1087

prune225.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y x (.f64 (.f64 3 z) z))
✓	0.3b	(fma.f64 y x (.f64 (.f64 (.f64 3 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z)))
	13.8b	(fma.f64 y x (cbrt.f64 (*.f64 27 (pow.f64 z 6))))
	0.3b	(fma.f64 3 (.f64 z z) (.f64 y x))

Compiler

Compiled 3580 to 1506 computations (57.9% saved)

regimes327.0ms (10.1%)

Accuracy

Total 0.0b remaining (14.3%)

Threshold costs 0.0b (14.3%)

Counts

35 → 1

Compiler

Compiled 3651 to 2400 computations (34.3% saved)

simplify3.0ms (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

end76.0ms (2.3%)

Remove: (sort x y)
Compiler: Compiled 96 to 61 computations (36.5% saved)

Details

analyze4.0ms (0.1%)

sample1.0s (31.4%)

simplify15.0ms (0.5%)

prune6.0ms (0.2%)

localize11.0ms (0.3%)

series23.0ms (0.7%)

rewrite1.0ms (0%)

simplify100.0ms (3.1%)

prune41.0ms (1.3%)

localize11.0ms (0.3%)

series28.0ms (0.9%)

rewrite24.0ms (0.8%)

simplify138.0ms (4.2%)

prune97.0ms (3%)

localize10.0ms (0.3%)

series27.0ms (0.8%)

rewrite9.0ms (0.3%)

simplify124.0ms (3.8%)

prune69.0ms (2.1%)

localize16.0ms (0.5%)

series556.0ms (17.1%)

rewrite69.0ms (2.1%)

simplify214.0ms (6.6%)

prune225.0ms (6.9%)

regimes327.0ms (10.1%)

simplify3.0ms (0.1%)

end76.0ms (2.3%)

Profiling