Details

analyze48.0ms (2.5%)

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
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)

sample880.0ms (45.5%)

Results

724.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify134.0ms (6.9%)

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
▶	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	14.9b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series11.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

rewrite3.0ms (0.2%)

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))

simplify62.0ms (3.2%)

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

prune30.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Error

Counts

49 → 5

Alt Table

Status	Error	Program
	32.2b	(*.f64 2 y)
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
▶	7.4b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
	32.4b	(.f64 -2 (+.f64 x (.f64 (/.f64 x y) (+.f64 x (/.f64 (*.f64 x x) y)))))
	14.9b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 862 to 506 computations (41.3% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
✓	7.3b	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

series19.0ms (1%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
8.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

rewrite16.0ms (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:

7.0ms	(/.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)

simplify122.0ms (6.3%)

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

prune119.0ms (6.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	32.4b	(.f64 -2 (+.f64 x (.f64 (/.f64 x y) (+.f64 x (/.f64 (*.f64 x x) y)))))
	14.9b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 3195 to 1997 computations (37.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 -1/2 x) (/.f64 1/2 y))
✓	0.1b	(/.f64 1 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))

series17.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 1 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))
6.0ms	(+.f64 (/.f64 -1/2 x) (/.f64 1/2 y))

rewrite54.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 73

Calls

2 calls:

40.0ms	(/.f64 1 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))
11.0ms	(+.f64 (/.f64 -1/2 x) (/.f64 1/2 y))

simplify72.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-neg_binary64`
549×	`cancel-sign-sub-inv_binary64`
339×	`fma-def_binary64`
229×	`associate-l_binary64`
209×	`times-frac_binary64`

Counts

121 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1757
1	291	1647
2	841	1598
3	3402	1595
4	5077	1595

prune112.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	97	4	101

Error

Counts

101 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	32.4b	(.f64 -2 (+.f64 x (.f64 (/.f64 x y) (+.f64 x (/.f64 (*.f64 x x) y)))))
▶	14.9b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 1669 to 1276 computations (23.5% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	14.6b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

series13.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

6.0ms

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

simplify60.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-l_binary64`
479×	`associate-*l/_binary64`
433×	`associate-/r*_binary64`
421×	`associate-/l/_binary64`
317×	`associate-*r/_binary64`

Counts

55 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1110
1	320	982
2	1370	939
3	4937	936
4	5014	936

prune33.0ms (1.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	59	4	63

Error

Counts

63 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	7.1b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
✓	14.9b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 1005 to 524 computations (47.9% saved)

regimes40.0ms (2.1%)

Accuracy

Total 0.2b remaining (97.5%)

Threshold costs 0.2b (97.5%)

Counts

14 → 1

Compiler

Compiled 421 to 298 computations (29.2% saved)

simplify2.0ms (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

end54.0ms (2.8%)

Compiler: Compiled 65 to 48 computations (26.2% saved)

Details

analyze48.0ms (2.5%)

sample880.0ms (45.5%)

simplify134.0ms (6.9%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

series11.0ms (0.6%)

rewrite3.0ms (0.2%)

simplify62.0ms (3.2%)

prune30.0ms (1.5%)

localize9.0ms (0.4%)

series19.0ms (1%)

rewrite16.0ms (0.8%)

simplify122.0ms (6.3%)

prune119.0ms (6.2%)

localize5.0ms (0.3%)

series17.0ms (0.9%)

rewrite54.0ms (2.8%)

simplify72.0ms (3.7%)

prune112.0ms (5.8%)

localize5.0ms (0.3%)

series13.0ms (0.7%)

rewrite8.0ms (0.4%)

simplify60.0ms (3.1%)

prune33.0ms (1.7%)

regimes40.0ms (2.1%)

simplify2.0ms (0.1%)

end54.0ms (2.8%)

Profiling