Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 15 to 12 computations (20% saved)

sample938.0ms (32.5%)

Results

825.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify78.0ms (2.7%)

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 (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 65 to 50 computations (23.1% saved)

localize4.0ms (0.1%)

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 (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite1.0ms (0%)

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)

simplify70.0ms (2.4%)

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

prune34.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	36	3	39

Error

Counts

39 → 3

Alt Table

Status	Error	Program
	0.7b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 447 to 344 computations (23% saved)

localize9.0ms (0.3%)

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))
✓	0.1b	(*.f64 9 (pow.f64 x 2))

series6.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(*.f64 9 (pow.f64 x 2))
3.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

rewrite12.0ms (0.4%)

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:

6.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
4.0ms	(*.f64 9 (pow.f64 x 2))

simplify113.0ms (3.9%)

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

prune150.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	88	3	91

Error

Counts

91 → 3

Alt Table

Status	Error	Program
	0.7b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
▶	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 1556 to 1245 computations (20% saved)

localize15.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(.f64 (.f64 x 3) x)

series17.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
6.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
5.0ms	(.f64 (.f64 x 3) x)

rewrite39.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

3 → 61

Calls

3 calls:

18.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
8.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
8.0ms	(.f64 (.f64 x 3) x)

simplify129.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary64`
363×	`fma-def_binary64`
281×	`+-commutative_binary64`
278×	`distribute-rgt-in_binary64`
273×	`distribute-lft-in_binary64`

Counts

97 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1328
1	302	1147
2	889	982
3	2422	980
4	4233	980
5	5064	980

prune84.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Error

Counts

115 → 3

Alt Table

Status	Error	Program
▶	0.7b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 2114 to 1634 computations (22.7% saved)

localize7.0ms (0.3%)

Local error

Found 4 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)
✓	0.7b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
✓	11.7b	(sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3))

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3))
4.0ms	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

9.0ms	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
2.0ms	(sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3))

simplify154.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

663×	`times-frac_binary64`
476×	`fma-neg_binary64`
206×	`associate-l_binary64`
193×	`sub-neg_binary64`
178×	`associate-r_binary64`

Counts

92 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	1484
1	248	1225
2	691	1163
3	2490	1111
4	4830	1087
5	4940	1087
6	4997	1087
7	4920	1087

prune302.0ms (10.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	220	3	223

Error

Counts

223 → 3

Alt Table

Status	Error	Program
✓	0.7b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 4642 to 3674 computations (20.9% saved)

regimes560.0ms (19.4%)

Accuracy

Total 0.1b remaining (82.7%)

Threshold costs 0.1b (82.7%)

Counts

101 → 1

Compiler

Compiled 5072 to 4065 computations (19.9% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	28	16
3	32	16
4	35	16
5	36	16
6	35	16

end118.0ms (4.1%)

Compiler: Compiled 68 to 55 computations (19.1% saved)

Details

analyze1.0ms (0%)

sample938.0ms (32.5%)

simplify78.0ms (2.7%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify70.0ms (2.4%)

prune34.0ms (1.2%)

localize9.0ms (0.3%)

series6.0ms (0.2%)

rewrite12.0ms (0.4%)

simplify113.0ms (3.9%)

prune150.0ms (5.2%)

localize15.0ms (0.5%)

series17.0ms (0.6%)

rewrite39.0ms (1.3%)

simplify129.0ms (4.5%)

prune84.0ms (2.9%)

localize7.0ms (0.3%)

series11.0ms (0.4%)

rewrite19.0ms (0.7%)

simplify154.0ms (5.3%)

prune302.0ms (10.5%)

regimes560.0ms (19.4%)

simplify6.0ms (0.2%)

end118.0ms (4.1%)

Profiling