Details

analyze431.0ms (14.4%)

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)

sample889.0ms (29.7%)

Symmetry

(sort x y)

Results

815.0ms	8256×	body	128	valid
41.0ms	457×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify11.0ms (0.4%)

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))

series10.0ms (0.3%)

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))

simplify62.0ms (2.1%)

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

prune16.0ms (0.5%)

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

0.0b

Counts

25 → 4

Alt Table

Status	Error	Program
	17.1b	(.f64 (sqrt.f64 (fma.f64 y x (.f64 3 (.f64 z z)))) (sqrt.f64 (fma.f64 y x (.f64 3 (*.f64 z z)))))
	1.2b	(.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))

Compiler

Compiled 426 to 224 computations (47.4% saved)

localize7.0ms (0.2%)

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 (0.5%)

Counts

2 → 48

Calls

2 calls:

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

rewrite5.0ms (0.2%)

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:

4.0ms	(.f64 3 (.f64 z z))
0.0ms	(fma.f64 y x (.f64 3 (.f64 z z)))

simplify69.0ms (2.3%)

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

prune34.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	44	4	48

Error

0.0b

Counts

48 → 4

Alt Table

Status	Error	Program
	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 y x (.f64 3 (.f64 z z)))
✓	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 (cbrt.f64 3) (.f64 z z))))

Compiler

Compiled 666 to 350 computations (47.4% saved)

localize11.0ms (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 (1.9%)

Counts

3 → 60

Calls

3 calls:

38.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z))))
13.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 z z)))
6.0ms	(.f64 (cbrt.f64 3) (.f64 z z))

rewrite22.0ms (0.7%)

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:

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

simplify115.0ms (3.8%)

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

prune94.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	95	5	100

Error

Counts

100 → 5

Alt Table

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

Compiler

Compiled 1991 to 1338 computations (32.8% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series435.0ms (14.5%)

Counts

4 → 72

Calls

4 calls:

377.0ms	(.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z))
39.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z)))))
13.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z))))
6.0ms	(.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z)))

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
50×	`pow1_binary64`
33×	`cbrt-unprod_binary64`
33×	`prod-exp_binary64`
33×	`pow-prod-down_binary64`

Counts

4 → 99

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z))))
8.0ms	(.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z)))
5.0ms	(.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z))
0.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (cbrt.f64 (cbrt.f64 3)) (.f64 z z)))))

simplify148.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

476×	`*-commutative_binary64`
429×	`unswap-sqr_binary64`
294×	`associate-+l+_binary64`
278×	`sqr-pow_binary64`
233×	`fma-def_binary64`

Counts

171 → 142

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	124	4211
1	254	3189
2	889	3180
3	1784	2838
4	3610	2649
5	4984	2649
6	4958	2649

prune177.0ms (5.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	142	5	147

Error

Counts

147 → 5

Alt Table

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

Compiler

Compiled 4290 to 3373 computations (21.4% saved)

regimes246.0ms (8.2%)

Accuracy

Total 0.1b remaining (88.7%)

Threshold costs 0.1b (88.7%)

Counts

36 → 1

Compiler

Compiled 4586 to 3413 computations (25.6% 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

end80.0ms (2.7%)

Remove: (sort x y)
Compiler: Compiled 129 to 90 computations (30.2% saved)

Details

analyze431.0ms (14.4%)

sample889.0ms (29.7%)

simplify11.0ms (0.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series10.0ms (0.3%)

rewrite1.0ms (0%)

simplify62.0ms (2.1%)

prune16.0ms (0.5%)

localize7.0ms (0.2%)

series15.0ms (0.5%)

rewrite5.0ms (0.2%)

simplify69.0ms (2.3%)

prune34.0ms (1.1%)

localize11.0ms (0.4%)

series56.0ms (1.9%)

rewrite22.0ms (0.7%)

simplify115.0ms (3.8%)

prune94.0ms (3.1%)

localize14.0ms (0.5%)

series435.0ms (14.5%)

rewrite37.0ms (1.2%)

simplify148.0ms (4.9%)

prune177.0ms (5.9%)

regimes246.0ms (8.2%)

simplify2.0ms (0.1%)

end80.0ms (2.7%)

Profiling