Details

analyze45.0ms (1.5%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.2s (41.3%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify198.0ms (6.7%)

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 (0.1%)

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
▶	6.1b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	16.1b	(/.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 1 expressions with local error:

New	Error	Program
✓	6.1b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series13.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

12.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

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

simplify88.0ms (3%)

Algorithm

1×	egg-herbie

Rules

539×	`associate-/r/_binary64`
418×	`fma-neg_binary64`
375×	`cancel-sign-sub-inv_binary64`
232×	`fma-def_binary64`
195×	`times-frac_binary64`

Counts

53 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1094
1	218	1030
2	655	982
3	2331	968
4	4993	968

prune72.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
▶	6.2b	(*.f64 x (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))
	6.3b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
	7.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
	37.3b	(.f64 2 (+.f64 y (/.f64 (.f64 y y) x)))

Compiler

Compiled 900 to 531 computations (41% saved)

localize17.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))
✓	5.7b	(*.f64 x (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))

series137.0ms (4.6%)

Counts

2 → 48

Calls

2 calls:

116.0ms	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))
21.0ms	(*.f64 x (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))

rewrite39.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 71

Calls

2 calls:

26.0ms	(*.f64 x (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))
5.0ms	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))

simplify160.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-neg_binary64`
510×	`times-frac_binary64`
465×	`fma-def_binary64`
305×	`associate-/l*_binary64`
235×	`associate-/r*_binary64`

Counts

119 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2199
1	346	2027
2	1101	1874
3	3903	1857
4	5056	1857

prune98.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	136	3	139

Error

Counts

139 → 3

Alt Table

Status	Error	Program
✓	6.2b	(*.f64 x (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))
▶	6.3b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
	36.1b	(*.f64 2 (fma.f64 y (/.f64 y x) y))

Compiler

Compiled 2491 to 1602 computations (35.7% saved)

localize16.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
✓	6.1b	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

series42.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
19.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

rewrite23.0ms (0.8%)

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:

6.0ms	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
5.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

simplify224.0ms (7.6%)

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

prune171.0ms (5.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	157	3	160

Error

Counts

160 → 3

Alt Table

Status	Error	Program
✓	6.2b	(*.f64 x (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	6.3b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
▶	36.1b	(*.f64 2 (fma.f64 y (/.f64 y x) y))

Compiler

Compiled 3151 to 1968 computations (37.5% saved)

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series17.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

17.0ms

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

rewrite2.0ms (0.1%)

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 y (/.f64 y x) y)

simplify150.0ms (5.1%)

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

prune10.0ms (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
✓	6.2b	(*.f64 x (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	6.3b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
✓	36.1b	(*.f64 2 (fma.f64 y (/.f64 y x) y))

Compiler

Compiled 224 to 97 computations (56.7% saved)

regimes80.0ms (2.7%)

Accuracy

Total 0.2b remaining (94.9%)

Threshold costs 0.2b (94.9%)

Counts

24 → 1

Compiler

Compiled 982 to 676 computations (31.2% saved)

simplify5.0ms (0.2%)

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

end107.0ms (3.6%)

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

Details

analyze45.0ms (1.5%)

sample1.2s (41.3%)

simplify198.0ms (6.7%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

series13.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify88.0ms (3%)

prune72.0ms (2.4%)

localize17.0ms (0.6%)

series137.0ms (4.6%)

rewrite39.0ms (1.3%)

simplify160.0ms (5.4%)

prune98.0ms (3.3%)

localize16.0ms (0.6%)

series42.0ms (1.4%)

rewrite23.0ms (0.8%)

simplify224.0ms (7.6%)

prune171.0ms (5.8%)

localize11.0ms (0.4%)

series17.0ms (0.6%)

rewrite2.0ms (0.1%)

simplify150.0ms (5.1%)

prune10.0ms (0.3%)

regimes80.0ms (2.7%)

simplify5.0ms (0.2%)

end107.0ms (3.6%)

Profiling