Details

analyze92.0ms (4.2%)

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)

sample760.0ms (34.6%)

Results

679.0ms	8256×	body	128	valid
16.0ms	197×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify25.0ms (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

prune3.0ms (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))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite11.0ms (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:

7.0ms

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

simplify110.0ms (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

prune63.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Error

Counts

74 → 7

Alt Table

Status	Error	Program
	30.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	29.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
▶	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	10.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	10.6b	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
	7.8b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 1454 to 638 computations (56.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (pow.f64 y 2))
✓	5.0b	(*.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)
3.0ms	(-.f64 y (pow.f64 y 2))

rewrite17.0ms (0.8%)

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:

8.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
5.0ms	(-.f64 y (pow.f64 y 2))

simplify125.0ms (5.7%)

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

prune101.0ms (4.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	124	7	131

Error

Counts

131 → 7

Alt Table

Status	Error	Program
	30.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	29.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
✓	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	10.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
	10.6b	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
▶	7.8b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 2350 to 1307 computations (44.4% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y)))
✓	6.3b	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))

series37.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(/.f64 (.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y))) (+.f64 1 y))
14.0ms	(.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y)))

rewrite23.0ms (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))
9.0ms	(.f64 (.f64 x y) (-.f64 (.f64 1 1) (.f64 y y)))

simplify80.0ms (3.6%)

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

prune94.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	30.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	29.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
▶	5.3b	(/.f64 (.f64 x y) (/.f64 (+.f64 y 1) (-.f64 1 (.f64 y y))))
✓	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	10.6b	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 2364 to 1406 computations (40.5% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 x y) (/.f64 (+.f64 y 1) (-.f64 1 (.f64 y y))))
✓	5.0b	(/.f64 (+.f64 y 1) (-.f64 1 (*.f64 y y)))

series25.0ms (1.1%)

Counts

2 → 36

Calls

2 calls:

22.0ms	(/.f64 (.f64 x y) (/.f64 (+.f64 y 1) (-.f64 1 (.f64 y y))))
3.0ms	(/.f64 (+.f64 y 1) (-.f64 1 (*.f64 y y)))

rewrite27.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
31×	`associate-/r*_binary64`

Counts

2 → 121

Calls

2 calls:

10.0ms	(/.f64 (.f64 x y) (/.f64 (+.f64 y 1) (-.f64 1 (.f64 y y))))
6.0ms	(/.f64 (+.f64 y 1) (-.f64 1 (*.f64 y y)))

simplify132.0ms (6%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-/r/_binary64`
495×	`associate-/r*_binary64`
434×	`associate-*r/_binary64`
364×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`

Counts

157 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	3479
1	517	3094
2	1948	3070
3	4592	3070
4	4994	3070
5	4967	3070

prune230.0ms (10.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	206	6	212

Error

Counts

212 → 6

Alt Table

Status	Error	Program
	30.1b	(.f64 (.f64 x (+.f64 y (pow.f64 y 3/2))) (-.f64 1 (sqrt.f64 y)))
	29.4b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
✓	5.3b	(/.f64 (.f64 x y) (/.f64 (+.f64 y 1) (-.f64 1 (.f64 y y))))
✓	5.3b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	10.6b	(/.f64 (*.f64 x (-.f64 y (pow.f64 y 3))) (+.f64 1 y))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 4589 to 2731 computations (40.5% saved)

regimes120.0ms (5.5%)

Accuracy

Total 0.1b remaining (72.7%)

Threshold costs 0.1b (72.7%)

Counts

41 → 1

Compiler

Compiled 2009 to 1228 computations (38.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	13	10
2	23	10
3	29	10
4	33	10
5	34	10
6	34	10

end74.0ms (3.4%)

Compiler: Compiled 93 to 61 computations (34.4% 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

analyze92.0ms (4.2%)

sample760.0ms (34.6%)

simplify25.0ms (1.1%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite11.0ms (0.5%)

simplify110.0ms (5%)

prune63.0ms (2.9%)

localize4.0ms (0.2%)

series13.0ms (0.6%)

rewrite17.0ms (0.8%)

simplify125.0ms (5.7%)

prune101.0ms (4.6%)

localize8.0ms (0.4%)

series37.0ms (1.7%)

rewrite23.0ms (1%)

simplify80.0ms (3.6%)

prune94.0ms (4.3%)

localize7.0ms (0.3%)

series25.0ms (1.1%)

rewrite27.0ms (1.2%)

simplify132.0ms (6%)

prune230.0ms (10.5%)

regimes120.0ms (5.5%)

simplify3.0ms (0.1%)

end74.0ms (3.4%)

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