Details

analyze389.0ms (15.6%)

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)

sample1.2s (50.1%)

Symmetry

(sort x y)

Results

1.2s	8256×	body	128	valid
46.0ms	475×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify7.0ms (0.3%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.2b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize9.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(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 (2.5%)

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 (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Error

0.1b

Counts

25 → 4

Alt Table

Status	Error	Program
	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)))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	18.4b	(.f64 (sqrt.f64 (fma.f64 z (.f64 z 3) (.f64 x y))) (sqrt.f64 (fma.f64 z (.f64 z 3) (*.f64 x y))))

Compiler

Compiled 426 to 224 computations (47.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 z z))

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(*.f64 3 (*.f64 z z))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 21

Calls

1 calls:

4.0ms

(*.f64 3 (*.f64 z z))

simplify58.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
701×	`associate-/l/_binary64`
384×	`distribute-rgt-in_binary64`
347×	`distribute-lft-in_binary64`
212×	`*-commutative_binary64`

Counts

33 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	306
1	76	270
2	175	261
3	419	261
4	633	261
5	1054	261
6	2130	261
7	4875	261
8	4875	261

prune25.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	20	4	24
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	22	6	28

Error

0.0b

Counts

28 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y x (.f64 3 (.f64 z z)))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.3b	(fma.f64 y x (.f64 (sqrt.f64 3) (.f64 z (*.f64 z (sqrt.f64 3)))))
▶	0.2b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
	18.7b	(fma.f64 y x (cbrt.f64 (.f64 (.f64 (.f64 3 3) 3) (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 z z)))))
	18.7b	(fma.f64 y x (cbrt.f64 (*.f64 27 (pow.f64 z 6))))

Compiler

Compiled 467 to 279 computations (40.3% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
✓	0.3b	(.f64 (cbrt.f64 3) (.f64 z z))

series18.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

12.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
5.0ms	(.f64 (cbrt.f64 3) (.f64 z z))

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
7.0ms	(.f64 (cbrt.f64 3) (.f64 z z))

simplify74.0ms (3%)

Algorithm

1×	egg-herbie

Rules

717×	`associate-l_binary64`
475×	`*-commutative_binary64`
434×	`unswap-sqr_binary64`
392×	`associate-/l*_binary64`
339×	`associate-/r/_binary64`

Counts

79 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	895
1	140	727
2	431	697
3	1108	697
4	1725	697
5	3106	697
6	5136	697

prune96.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	2	1	3
Picked	1	0	1
Done	1	1	2
Total	76	6	82

Error

0.0b

Counts

82 → 6

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 3) z) z)))
	0.3b	(fma.f64 y x (.f64 (cbrt.f64 3) (.f64 (cbrt.f64 3) (.f64 (cbrt.f64 3) (.f64 z z)))))
▶	0.1b	(fma.f64 y x (pow.f64 (.f64 (.f64 z z) 3) 1))
	0.3b	(fma.f64 y x (.f64 (sqrt.f64 3) (.f64 z (*.f64 z (sqrt.f64 3)))))
	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))))

Compiler

Compiled 1681 to 1164 computations (30.8% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z z) 3)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 z z) 3)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 21

Calls

1 calls:

6.0ms

(*.f64 (*.f64 z z) 3)

simplify76.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

577×	`associate-/r*_binary64`
286×	`*-commutative_binary64`
270×	`sqr-pow_binary64`
249×	`times-frac_binary64`
248×	`associate-l_binary64`

Counts

33 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	308
1	87	272
2	241	263
3	553	263
4	849	263
5	1501	263
6	2867	263
7	4959	263
8	4934	263

prune35.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	31	6	37

Error

0.0b

Counts

37 → 6

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 3) z) z)))
	0.3b	(fma.f64 y x (.f64 (cbrt.f64 3) (.f64 (cbrt.f64 3) (.f64 (cbrt.f64 3) (.f64 z z)))))
✓	0.1b	(fma.f64 y x (pow.f64 (.f64 (.f64 z z) 3) 1))
	0.3b	(fma.f64 y x (.f64 (sqrt.f64 3) (.f64 z (*.f64 z (sqrt.f64 3)))))
	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))))

Compiler

Compiled 547 to 341 computations (37.7% saved)

regimes205.0ms (8.2%)

Accuracy

Total 0.1b remaining (93.6%)

Threshold costs 0.1b (93.6%)

Counts

30 → 1

Compiler

Compiled 3183 to 2223 computations (30.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	13	11
2	12	11

end94.0ms (3.8%)

Remove: (sort x y)
Compiler: Compiled 142 to 102 computations (28.2% saved)

Details

analyze389.0ms (15.6%)

sample1.2s (50.1%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize9.0ms (0.4%)

series10.0ms (0.4%)

rewrite1.0ms (0%)

simplify63.0ms (2.5%)

prune17.0ms (0.7%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite5.0ms (0.2%)

simplify58.0ms (2.4%)

prune25.0ms (1%)

localize10.0ms (0.4%)

series18.0ms (0.7%)

rewrite20.0ms (0.8%)

simplify74.0ms (3%)

prune96.0ms (3.9%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite7.0ms (0.3%)

simplify76.0ms (3.1%)

prune35.0ms (1.4%)

regimes205.0ms (8.2%)

simplify2.0ms (0.1%)

end94.0ms (3.8%)

Profiling