Details

analyze86.0ms (3.4%)

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
50%	50%	0.1%	6
68.7%	31.2%	0.1%	7
81.2%	18.7%	0.1%	8
89%	10.9%	0.1%	9
92.1%	7.8%	0.1%	10
95.6%	4.3%	0.1%	11
96.4%	3.5%	0.1%	12
98%	1.9%	0.1%	13
98.2%	1.7%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample954.0ms (37.5%)

Results

802.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify131.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

878×	`div-sub_binary64`
546×	`times-frac_binary64`
500×	`sub-neg_binary64`
408×	`fma-def_binary64`
395×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	16	13
2	40	13
3	81	13
4	153	13
5	248	13
6	435	11
7	1077	11
8	3029	11
9	3558	11
10	3959	11
11	4158	11
12	4377	11
13	4552	11
14	5083	11

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	16.5b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	6.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series18.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
6.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
0.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

simplify104.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
231×	`fma-def_binary64`
198×	`associate-/l*_binary64`
198×	`times-frac_binary64`

Counts

87 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1389
1	226	1308
2	679	1260
3	2411	1246
4	4577	1246
5	4993	1246
6	4941	1246

prune37.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Error

0.0b

Counts

64 → 4

Alt Table

Status	Error	Program
✓	6.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
▶	7.0b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
	16.5b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
	32.7b	(.f64 2 (+.f64 y (/.f64 (.f64 y y) x)))

Compiler

Compiled 1012 to 592 computations (41.5% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
✓	6.9b	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

series22.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
11.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
2.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

simplify137.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-neg_binary64`
408×	`times-frac_binary64`
399×	`cancel-sign-sub-inv_binary64`
256×	`fma-def_binary64`
247×	`associate-/l*_binary64`

Counts

155 → 157

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	3160
1	313	2887
2	929	2794
3	3176	2787
4	4747	2787
5	4935	2787

prune105.0ms (4.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
▶	7.0b	(/.f64 (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)) (/.f64 1 x))
✓	6.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	31.2b	(*.f64 2 (fma.f64 y (/.f64 y x) y))

Compiler

Compiled 3367 to 2109 computations (37.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	0.7b	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))
✓	6.2b	(/.f64 (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)) (/.f64 1 x))

series27.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(/.f64 (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)) (/.f64 1 x))
11.0ms	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))

rewrite136.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

430×	`times-frac_binary64`
206×	`*-un-lft-identity_binary64`
206×	`add-sqr-sqrt_binary64`
206×	`add-cube-cbrt_binary64`
46×	`add-exp-log_binary64`

Counts

2 → 262

Calls

2 calls:

60.0ms	(/.f64 (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)) (/.f64 1 x))
2.0ms	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))

simplify264.0ms (10.4%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
482×	`fma-def_binary64`
404×	`associate-/l*_binary64`
386×	`associate-/r*_binary64`
271×	`associate-*l/_binary64`

Counts

310 → 335

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	8609
1	525	7698
2	1585	7461
3	4507	7444
4	4955	7444

prune232.0ms (9.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	350	3	353

Error

Counts

353 → 3

Alt Table

Status	Error	Program
✓	7.0b	(/.f64 (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)) (/.f64 1 x))
✓	6.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
▶	31.2b	(*.f64 2 (fma.f64 y (/.f64 y x) y))

Compiler

Compiled 8945 to 6212 computations (30.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(fma.f64 y (/.f64 y 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 y (/.f64 y x) y)

simplify91.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
453×	`distribute-rgt-in_binary64`
432×	`distribute-lft-in_binary64`
371×	`sqr-pow_binary64`
327×	`distribute-rgt-out_binary64`

Counts

34 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	295
1	27	278
2	60	278
3	181	278
4	776	278
5	3529	278
6	3992	278
7	4634	278
8	5335	278

prune8.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	17	3	20

Error

Counts

20 → 3

Alt Table

Status	Error	Program
✓	7.0b	(/.f64 (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)) (/.f64 1 x))
✓	6.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	31.2b	(*.f64 2 (fma.f64 y (/.f64 y x) y))

Compiler

Compiled 224 to 97 computations (56.7% saved)

regimes83.0ms (3.2%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Counts

26 → 1

Compiler

Compiled 886 to 664 computations (25.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end53.0ms (2.1%)

Compiler: Compiled 56 to 42 computations (25% saved)

Details

analyze86.0ms (3.4%)

sample954.0ms (37.5%)

simplify131.0ms (5.2%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series18.0ms (0.7%)

rewrite4.0ms (0.2%)

simplify104.0ms (4.1%)

prune37.0ms (1.4%)

localize6.0ms (0.3%)

series22.0ms (0.9%)

rewrite14.0ms (0.5%)

simplify137.0ms (5.4%)

prune105.0ms (4.1%)

localize8.0ms (0.3%)

series27.0ms (1.1%)

rewrite136.0ms (5.3%)

simplify264.0ms (10.4%)

prune232.0ms (9.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite1.0ms (0%)

simplify91.0ms (3.6%)

prune8.0ms (0.3%)

regimes83.0ms (3.2%)

simplify3.0ms (0.1%)

end53.0ms (2.1%)

Profiling