Details

analyze116.0ms (7%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	48.4%	1.7%	7
59.3%	35.9%	4.8%	8
67.1%	25%	7.9%	9
72.6%	18.3%	9.1%	10
76.9%	12.5%	10.6%	11
79.8%	9.3%	10.9%	12
82%	6.2%	11.7%	13
83.6%	4.7%	11.8%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample769.0ms (46.2%)

Symmetry

(sort x y)

Results

723.0ms	8250×	body	128	valid
9.0ms	69×	body	128	invalid
1.0ms	4×	body	512	valid
0.0ms	2×	body	1024	valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify11.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

48×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`distribute-rgt-in_binary64`
4×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	24	8
3	33	8
4	43	8
5	48	8
6	62	8
7	79	8
8	84	8
9	85	8
10	83	8

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 y (fma.f64 x y x))

Compiler

Compiled 31 to 15 computations (51.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (fma.f64 x y x))

series18.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

18.0ms

(+.f64 y (fma.f64 x y x))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(+.f64 y (fma.f64 x y x))

simplify61.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

956×	`fma-def_binary64`
933×	`fma-neg_binary64`
863×	`distribute-rgt-in_binary64`
805×	`distribute-lft-in_binary64`
421×	`associate-l_binary64`

Counts

42 → 35

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	378
1	98	351
2	237	351
3	869	351
4	4044	351
5	4790	351
6	5117	351

prune19.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	3	36

Error

Counts

36 → 3

Alt Table

Status	Error	Program
	0.0b	(fma.f64 x y (+.f64 x y))
▶	0.0b	(+.f64 (fma.f64 x y y) x)
	31.7b	(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x y x))) (sqrt.f64 (+.f64 y (fma.f64 x y x))))

Compiler

Compiled 427 to 121 computations (71.7% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 x y y) x)

series4.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(+.f64 (fma.f64 x y y) x)

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(+.f64 (fma.f64 x y y) x)

simplify98.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
530×	`associate-+l+_binary64`
494×	`associate-+r+_binary64`
444×	`associate-l_binary64`
428×	`cancel-sign-sub-inv_binary64`

Counts

42 → 35

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	379
1	95	358
2	255	350
3	933	350
4	3221	350
5	4503	350
6	4870	350
7	4989	350
8	4955	350

prune15.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Error

Counts

38 → 3

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x y (+.f64 x y))
✓	0.0b	(+.f64 (fma.f64 x y y) x)
	31.7b	(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x y x))) (sqrt.f64 (+.f64 y (fma.f64 x y x))))

Compiler

Compiled 442 to 118 computations (73.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (+.f64 x y))

series5.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(fma.f64 x y (+.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 x y (+.f64 x y))

simplify72.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
568×	`unswap-sqr_binary64`
526×	`distribute-rgt-in_binary64`
515×	`distribute-lft-in_binary64`
481×	`associate-*r/_binary64`

Counts

34 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	298
1	34	277
2	91	273
3	312	273
4	1567	273
5	1830	273
6	2118	273
7	2703	273
8	4352	273
9	5678	273

prune10.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Error

Counts

29 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x y (+.f64 x y))
✓	0.0b	(+.f64 (fma.f64 x y y) x)
▶	31.7b	(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x y x))) (sqrt.f64 (+.f64 y (fma.f64 x y x))))

Compiler

Compiled 285 to 75 computations (73.7% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 y (fma.f64 x y x))
✓	0.0b	(sqrt.f64 (+.f64 y (fma.f64 x y x)))
✓	0.2b	(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x y x))) (sqrt.f64 (+.f64 y (fma.f64 x y x))))

series123.0ms (7.4%)

Counts

2 → 32

Calls

2 calls:

110.0ms	(sqrt.f64 (+.f64 y (fma.f64 x y x)))
4.0ms	(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x y x))) (sqrt.f64 (+.f64 y (fma.f64 x y x))))

rewrite20.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`sqrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`pow1_binary64`
14×	`sqrt-div_binary64`

Counts

2 → 85

Calls

2 calls:

9.0ms	(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x y x))) (sqrt.f64 (+.f64 y (fma.f64 x y x))))
2.0ms	(sqrt.f64 (+.f64 y (fma.f64 x y x)))

simplify81.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
584×	`associate-r_binary64`
469×	`sub-neg_binary64`
350×	`associate--l+_binary64`
335×	`cancel-sign-sub-inv_binary64`

Counts

117 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2076
1	412	1893
2	1401	1803
3	4704	1775
4	5275	1775

prune91.0ms (5.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	236	3	239

Error

Counts

239 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x y (+.f64 x y))
✓	0.0b	(+.f64 (fma.f64 x y y) x)
✓	31.7b	(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x y x))) (sqrt.f64 (+.f64 y (fma.f64 x y x))))

Compiler

Compiled 5786 to 1495 computations (74.2% saved)

regimes72.0ms (4.3%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

Counts

23 → 1

Compiler

Compiled 747 to 402 computations (46.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	6	8
2	6	8

end48.0ms (2.9%)

Remove: (sort x y)
Compiler: Compiled 65 to 30 computations (53.8% saved)

Details

analyze116.0ms (7%)

sample769.0ms (46.2%)

simplify11.0ms (0.6%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series18.0ms (1.1%)

rewrite3.0ms (0.2%)

simplify61.0ms (3.7%)

prune19.0ms (1.2%)

localize5.0ms (0.3%)

series4.0ms (0.2%)

rewrite3.0ms (0.2%)

simplify98.0ms (5.9%)

prune15.0ms (0.9%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite1.0ms (0%)

simplify72.0ms (4.3%)

prune10.0ms (0.6%)

localize5.0ms (0.3%)

series123.0ms (7.4%)

rewrite20.0ms (1.2%)

simplify81.0ms (4.9%)

prune91.0ms (5.5%)

regimes72.0ms (4.3%)

simplify2.0ms (0.1%)

end48.0ms (2.9%)

Profiling