Details

analyze143.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
0%	50%	50%	5
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	9.8%	72.7%	10
18.1%	8.8%	73.1%	11
19.6%	5.2%	75.2%	12
20%	4.5%	75.5%	13
20.7%	2.7%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.5s (33.6%)

Results

1.2s	8256×	body	128	valid
78.0ms	536×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify101.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
173×	`cancel-sign-sub-inv_binary64`
156×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	75	19
3	168	19
4	358	19
5	678	19
6	901	19
7	1446	19
8	1914	19
9	1873	19
10	1916	19
11	1915	19
12	1912	19
13	2465	19
14	2465	19
15	2321	19

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
✓	0.3b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
✓	0.4b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

series83.0ms (1.8%)

Counts

4 → 41

Calls

4 calls:

29.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
28.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
16.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
10.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite58.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
26×	`associate-l_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 134

Calls

4 calls:

18.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
12.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
11.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
8.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

simplify101.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-in_binary64`
675×	`times-frac_binary64`
199×	`associate-r_binary64`
193×	`cancel-sign-sub-inv_binary64`
178×	`associate-l_binary64`

Counts

175 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	3587
1	771	3326
2	2767	3268
3	5441	3268

prune359.0ms (7.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	247	5	252
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	248	6	254

Error

Counts

254 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) (cbrt.f64 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))))) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))) rand))))
	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
	0.6b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9)))))

Compiler

Compiled 7756 to 6544 computations (15.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 -1/3 a) 9)
✓	0.2b	(/.f64 rand (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9)))
✓	0.4b	(sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))
✓	8.8b	(.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9))))

series98.0ms (2.1%)

Counts

4 → 48

Calls

4 calls:

64.0ms	(/.f64 rand (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9)))
23.0ms	(.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9))))
10.0ms	(sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))
2.0ms	(*.f64 (+.f64 -1/3 a) 9)

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

4 → 117

Calls

4 calls:

13.0ms	(.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9))))
5.0ms	(/.f64 rand (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9)))
4.0ms	(*.f64 (+.f64 -1/3 a) 9)
3.0ms	(sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

587×	`times-frac_binary64`
430×	`fma-def_binary64`
389×	`distribute-rgt-in_binary64`
376×	`distribute-lft-in_binary64`
134×	`associate-l_binary64`

Counts

165 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	2968
1	587	2552
2	2070	2504
3	4894	2504
4	4972	2504

prune278.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	229	4	233

Error

Counts

233 → 4

Alt Table

Status	Error	Program
	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9))) (+.f64 -1/3 a)))
▶	0.1b	(+.f64 (+.f64 -1/3 a) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9))))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Compiler

Compiled 5628 to 4237 computations (24.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 -1/3 a) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9))))
✓	0.0b	(sqrt.f64 (+.f64 -1/3 a))
✓	0.4b	(*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9)))
✓	0.5b	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a)))

series65.0ms (1.4%)

Counts

4 → 41

Calls

4 calls:

23.0ms	(+.f64 (+.f64 -1/3 a) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9))))
22.0ms	(*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9)))
11.0ms	(sqrt.f64 (+.f64 -1/3 a))
9.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a)))

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`*-un-lft-identity_binary64`
86×	`times-frac_binary64`
86×	`add-sqr-sqrt_binary64`
55×	`sqrt-prod_binary64`
53×	`add-cube-cbrt_binary64`

Counts

4 → 190

Calls

4 calls:

20.0ms	(*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9)))
7.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a)))
5.0ms	(+.f64 (+.f64 -1/3 a) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9))))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))

simplify147.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
604×	`distribute-rgt-in_binary64`
189×	`*-commutative_binary64`
185×	`associate-*l/_binary64`
173×	`associate-*r/_binary64`

Counts

231 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4954
1	772	4098
2	2454	4070
3	4958	4070

prune321.0ms (7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	261	4	265

Error

Counts

265 → 4

Alt Table

Status	Error	Program
	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
▶	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9))) (+.f64 -1/3 a)))
✓	0.1b	(+.f64 (+.f64 -1/3 a) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9))))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Compiler

Compiled 6782 to 5278 computations (22.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 -1/3 a) 9)
	0.2b	(/.f64 rand (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9)))
	0.4b	(sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))
✓	8.8b	(.f64 (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9))) (+.f64 -1/3 a))

series25.0ms (0.5%)

Counts

1 → 16

Calls

1 calls:

24.0ms

(*.f64 (/.f64 rand (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))) (+.f64 -1/3 a))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-l_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`times-frac_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 46

Calls

1 calls:

12.0ms

(*.f64 (/.f64 rand (sqrt.f64 (*.f64 (+.f64 -1/3 a) 9))) (+.f64 -1/3 a))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-def_binary64`
538×	`associate-l_binary64`
370×	`associate-*l/_binary64`
361×	`associate-/l*_binary64`
308×	`distribute-rgt-in_binary64`

Counts

62 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1343
1	452	1219
2	1198	1127
3	4236	1127
4	4987	1127

prune228.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	233	4	237

Error

Counts

237 → 4

Alt Table

Status	Error	Program
	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
✓	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (/.f64 rand (sqrt.f64 (.f64 (+.f64 -1/3 a) 9))) (+.f64 -1/3 a)))
✓	0.1b	(+.f64 (+.f64 -1/3 a) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9))))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Compiler

Compiled 5717 to 4303 computations (24.7% saved)

regimes625.0ms (13.7%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

125 → 1

Compiler

Compiled 11800 to 9722 computations (17.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	16	24
2	15	24

end84.0ms (1.8%)

Compiler: Compiled 109 to 87 computations (20.2% saved)

Details

analyze143.0ms (3.1%)

sample1.5s (33.6%)

simplify101.0ms (2.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series83.0ms (1.8%)

rewrite58.0ms (1.3%)

simplify101.0ms (2.2%)

prune359.0ms (7.9%)

localize8.0ms (0.2%)

series98.0ms (2.1%)

rewrite32.0ms (0.7%)

simplify109.0ms (2.4%)

prune278.0ms (6.1%)

localize8.0ms (0.2%)

series65.0ms (1.4%)

rewrite52.0ms (1.1%)

simplify147.0ms (3.2%)

prune321.0ms (7%)

localize8.0ms (0.2%)

series25.0ms (0.5%)

rewrite16.0ms (0.3%)

simplify68.0ms (1.5%)

prune228.0ms (5%)

regimes625.0ms (13.7%)

simplify2.0ms (0%)

end84.0ms (1.8%)

Profiling