Details

analyze91.0ms (4.4%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample794.0ms (38.3%)

Results

720.0ms	8256×	body	128	valid
13.0ms	161×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify23.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
148×	`fma-neg_binary64`
84×	`distribute-rgt-in_binary64`
50×	`distribute-lft-in_binary64`
50×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

series8.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 51

Calls

1 calls:

6.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

simplify103.0ms (5%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-neg_binary64`
433×	`exp-prod_binary64`
400×	`*-commutative_binary64`
343×	`fma-def_binary64`
288×	`associate-+r+_binary64`

Counts

75 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1085
1	223	985
2	948	871
3	2323	814
4	4186	814
5	4991	814
6	4915	814
7	4901	814

prune60.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	6	74

Error

0.0b

Counts

74 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	36.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
▶	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	16.1b	(/.f64 (.f64 x (-.f64 y (pow.f64 y 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 y y) (.f64 1 y))))
	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	8.1b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))

Compiler

Compiled 1440 to 630 computations (56.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (pow.f64 y 2))
✓	5.5b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

series13.0ms (0.6%)

Counts

2 → 15

Calls

2 calls:

10.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
2.0ms	(-.f64 y (pow.f64 y 2))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
24×	`prod-diff_binary64`
21×	`add-cube-cbrt_binary64`
14×	`unpow-prod-down_binary64`

Counts

2 → 82

Calls

2 calls:

6.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
5.0ms	(-.f64 y (pow.f64 y 2))

simplify93.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

967×	`fma-neg_binary64`
456×	`fma-def_binary64`
377×	`exp-prod_binary64`
263×	`cancel-sign-sub-inv_binary64`
232×	`difference-of-squares_binary64`

Counts

97 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1889
1	261	1074
2	791	924
3	2087	924
4	3779	924
5	4661	924
6	4794	924

prune97.0ms (4.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	124	6	130

Error

0.0b

Counts

130 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	36.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	16.1b	(/.f64 (.f64 x (-.f64 y (pow.f64 y 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 y y) (.f64 1 y))))
	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
▶	8.1b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))

Compiler

Compiled 2336 to 1299 computations (44.4% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.5b	(.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y)))
✓	6.1b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))

series35.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))
13.0ms	(.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y)))

rewrite20.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64`
7×	`pow1_binary64`
6×	`cbrt-unprod_binary64`

Counts

2 → 60

Calls

2 calls:

10.0ms	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))
7.0ms	(.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y)))

simplify77.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

549×	`associate-/r*_binary64`
469×	`associate-/r/_binary64`
352×	`fma-def_binary64`
307×	`distribute-rgt-in_binary64`
272×	`distribute-lft-in_binary64`

Counts

108 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	1834
1	369	1468
2	1552	1453
3	4606	1452
4	4971	1452

prune92.0ms (4.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	107	6	113

Error

0.0b

Counts

113 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	36.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	16.1b	(/.f64 (.f64 x (-.f64 y (pow.f64 y 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 y y) (.f64 1 y))))
▶	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	8.1b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))

Compiler

Compiled 2367 to 1412 computations (40.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 y))
✓	0.1b	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
✓	0.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

series31.0ms (1.5%)

Counts

3 → 44

Calls

3 calls:

15.0ms	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
8.0ms	(sqrt.f64 (-.f64 1 y))
8.0ms	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

rewrite28.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-prod_binary64`
18×	`associate-r_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 85

Calls

3 calls:

10.0ms	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
7.0ms	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
5.0ms	(sqrt.f64 (-.f64 1 y))

simplify91.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

524×	`*-commutative_binary64`
460×	`fma-def_binary64`
361×	`associate-l_binary64`
333×	`fma-neg_binary64`
321×	`cancel-sign-sub-inv_binary64`

Counts

129 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1853
1	373	1689
2	1352	1668
3	2949	1656
4	4698	1656
5	4966	1656

prune145.0ms (7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	165	7	172

Error

Counts

172 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))
	36.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
✓	5.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	16.1b	(/.f64 (.f64 x (-.f64 y (pow.f64 y 4))) (+.f64 (.f64 1 1) (+.f64 (.f64 y y) (.f64 1 y))))
	9.2b	(.f64 (.f64 x y) (*.f64 (sqrt.f64 (-.f64 1 y)) (sqrt.f64 (-.f64 1 y))))
✓	9.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	8.1b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))

Compiler

Compiled 3366 to 2190 computations (34.9% saved)

regimes135.0ms (6.5%)

Accuracy

Total 0.1b remaining (77.9%)

Threshold costs 0.1b (77.9%)

Counts

50 → 1

Compiler

Compiled 2535 to 1595 computations (37.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	17	10
3	19	10
4	20	10
5	19	10

end87.0ms (4.2%)

Compiler: Compiled 118 to 83 computations (29.7% saved)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Details

analyze91.0ms (4.4%)

sample794.0ms (38.3%)

simplify23.0ms (1.1%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite10.0ms (0.5%)

simplify103.0ms (5%)

prune60.0ms (2.9%)

localize4.0ms (0.2%)

series13.0ms (0.6%)

rewrite16.0ms (0.7%)

simplify93.0ms (4.5%)

prune97.0ms (4.7%)

localize8.0ms (0.4%)

series35.0ms (1.7%)

rewrite20.0ms (1%)

simplify77.0ms (3.7%)

prune92.0ms (4.4%)

localize6.0ms (0.3%)

series31.0ms (1.5%)

rewrite28.0ms (1.3%)

simplify91.0ms (4.4%)

prune145.0ms (7%)

regimes135.0ms (6.5%)

simplify2.0ms (0.1%)

end87.0ms (4.2%)

Profiling

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10