Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample1.0s (52.1%)

Results

961.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify59.0ms (3%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
83×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	32	14
2	69	12
3	160	12
4	298	9
5	418	9
6	666	9
7	960	9
8	1262	9
9	1473	9
10	1531	9
11	1530	9
12	1536	9
13	1536	9
14	1401	9

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 65 to 50 computations (23.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)
1.0ms	(fma.f64 x 9 -12)

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)
0.0ms	(fma.f64 x 9 -12)

simplify62.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-+l+_binary64`
415×	`fma-neg_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

44 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	431
1	63	344
2	120	342
3	378	342
4	1764	342
5	4979	342
6	5271	342

prune54.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Error

0.0b

Counts

39 → 5

Alt Table

Status	Error	Program
	0.8b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
	0.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3))) (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 509 to 392 computations (23% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series5.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

2.0ms	(*.f64 9 (pow.f64 x 2))
2.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`

Counts

2 → 51

Calls

2 calls:

4.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
4.0ms	(*.f64 9 (pow.f64 x 2))

simplify68.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-l_binary64`
410×	`associate-r_binary64`
379×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`
252×	`fma-def_binary64`

Counts

57 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	880
1	216	651
2	609	587
3	2814	561
4	4082	561
5	4830	561

prune73.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	89	4	93

Error

Counts

93 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 1566 to 1257 computations (19.7% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
✓	0.2b	(*.f64 (cbrt.f64 9) (pow.f64 x 2))
✓	0.2b	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))

series24.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))

6.0ms

(-.f64 (+.f64 3 (*.f64 (*.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))) (*.f64 12 x))

5.0ms

(*.f64 (cbrt.f64 9) (pow.f64 x 2))

rewrite22.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`prod-exp_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-r_binary64`

Counts

3 → 84

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))

5.0ms

(-.f64 (+.f64 3 (*.f64 (*.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))) (*.f64 12 x))

4.0ms

(*.f64 (cbrt.f64 9) (pow.f64 x 2))

simplify63.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

910×	`distribute-rgt-in_binary64`
820×	`distribute-lft-in_binary64`
337×	`fma-def_binary64`
301×	`*-commutative_binary64`
162×	`fma-neg_binary64`

Counts

108 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1482
1	285	1210
2	919	1119
3	2365	1087
4	5043	1087

prune124.0ms (6.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
▶	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 3209 to 2756 computations (14.1% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.4b	(.f64 (.f64 3 x) (*.f64 3 x))

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(.f64 (.f64 3 x) (*.f64 3 x))
2.0ms	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))

rewrite14.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
17×	`pow-prod-down_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

2 → 58

Calls

2 calls:

6.0ms	(.f64 (.f64 3 x) (*.f64 3 x))
4.0ms	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))

simplify70.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-r_binary64`
631×	`associate-+l+_binary64`
287×	`fma-def_binary64`
272×	`distribute-rgt-out_binary64`
228×	`fma-neg_binary64`

Counts

82 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	947
1	208	778
2	679	638
3	2522	638
4	5058	638

prune62.0ms (3.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	80	4	84

Error

Counts

84 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
✓	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 1513 to 1168 computations (22.8% saved)

regimes138.0ms (6.9%)

Accuracy

Total 0.1b remaining (85.5%)

Threshold costs 0.1b (85.5%)

Counts

37 → 1

Compiler

Compiled 1904 to 1513 computations (20.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end64.0ms (3.2%)

Compiler: Compiled 69 to 56 computations (18.8% saved)

Details

analyze5.0ms (0.2%)

sample1.0s (52.1%)

simplify59.0ms (3%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify62.0ms (3.1%)

prune54.0ms (2.7%)

localize7.0ms (0.4%)

series5.0ms (0.2%)

rewrite11.0ms (0.6%)

simplify68.0ms (3.4%)

prune73.0ms (3.6%)

localize10.0ms (0.5%)

series24.0ms (1.2%)

rewrite22.0ms (1.1%)

simplify63.0ms (3.2%)

prune124.0ms (6.2%)

localize6.0ms (0.3%)

series4.0ms (0.2%)

rewrite14.0ms (0.7%)

simplify70.0ms (3.5%)

prune62.0ms (3.1%)

regimes138.0ms (6.9%)

simplify2.0ms (0.1%)

end64.0ms (3.2%)

Profiling