Details

analyze120.0ms (2.8%)

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 (34.9%)

Results

1.1s	8256×	body	128	valid
72.0ms	565×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify97.0ms (2.3%)

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)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 9 -3)
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series67.0ms (1.6%)

Counts

4 → 50

Calls

4 calls:

32.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
24.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
9.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 99

Calls

4 calls:

11.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
3.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
1.0ms	(sqrt.f64 (fma.f64 a 9 -3))
0.0ms	(fma.f64 a 9 -3)

simplify105.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-def_binary64`
652×	`distribute-rgt-in_binary64`
401×	`times-frac_binary64`
187×	`cancel-sign-sub-inv_binary64`
151×	`fma-neg_binary64`

Counts

149 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	2971
1	648	2791
2	2198	2639
3	4975	2621
4	4964	2621

prune382.0ms (9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	189	6	195
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	190	7	197

Error

Counts

197 → 7

Alt Table

Status	Error	Program
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))
	48.8b	(.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3)))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	9.3b	(/.f64 (.f64 (+.f64 a -1/3) (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 9 a -3)))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
▶	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))

Compiler

Compiled 4688 to 3632 computations (22.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 9 a -3)
✓	0.1b	(sqrt.f64 (fma.f64 9 a -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
✓	8.4b	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))

series76.0ms (1.8%)

Counts

4 → 48

Calls

4 calls:

33.0ms	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))
31.0ms	(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
9.0ms	(sqrt.f64 (fma.f64 9 a -3))
2.0ms	(fma.f64 9 a -3)

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`

Counts

4 → 115

Calls

4 calls:

9.0ms	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))
3.0ms	(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
1.0ms	(sqrt.f64 (fma.f64 9 a -3))
0.0ms	(fma.f64 9 a -3)

simplify88.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-/l*_binary64`
489×	`fma-def_binary64`
422×	`times-frac_binary64`
321×	`distribute-rgt-in_binary64`
308×	`distribute-lft-in_binary64`

Counts

163 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2948
1	554	2766
2	1907	2703
3	5158	2703

prune275.0ms (6.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	212	6	218

Error

Counts

218 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 9 a -3))))))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	9.3b	(/.f64 (.f64 (+.f64 a -1/3) (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 9 a -3)))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
▶	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	48.8b	(.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3)))

Compiler

Compiled 5318 to 3969 computations (25.4% 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)))
✓	0.1b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
✓	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)))))

series80.0ms (1.9%)

Counts

4 → 41

Calls

4 calls:

30.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
27.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
13.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
9.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite55.0ms (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 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
9.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.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)))))

simplify113.0ms (2.7%)

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 → 249

Iterations

Useful iterations: 2 (0.0ms)

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

prune288.0ms (6.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	250	5	255

Error

Counts

255 → 5

Alt Table

Status	Error	Program
	0.2b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 9 a -3))))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3)))) rand)))
▶	0.1b	(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
✓	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 7606 to 6410 computations (15.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 a 1/3))
✓	0.1b	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a)
✓	0.2b	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))

series40.0ms (1%)

Counts

3 → 26

Calls

3 calls:

17.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
13.0ms	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a)
10.0ms	(sqrt.f64 (-.f64 a 1/3))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 57

Calls

3 calls:

6.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
3.0ms	(sqrt.f64 (-.f64 a 1/3))
0.0ms	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a)

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-neg_binary64`
291×	`times-frac_binary64`
275×	`associate-l_binary64`
262×	`associate-r_binary64`
232×	`fma-def_binary64`

Counts

83 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	134	1213
1	310	1141
2	901	1131
3	3088	1107
4	4829	1105
5	4950	1105

prune128.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	114	5	119

Error

Counts

119 → 5

Alt Table

Status	Error	Program
	0.2b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 9 a -3))))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3)))) rand)))
✓	0.1b	(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
✓	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 2177 to 1665 computations (23.5% saved)

regimes562.0ms (13.3%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

Counts

128 → 1

Compiler

Compiled 9955 to 8003 computations (19.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	17	24
2	18	24
3	17	24

end101.0ms (2.4%)

Compiler: Compiled 133 to 107 computations (19.5% saved)

Details

analyze120.0ms (2.8%)

sample1.5s (34.9%)

simplify97.0ms (2.3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series67.0ms (1.6%)

rewrite20.0ms (0.5%)

simplify105.0ms (2.5%)

prune382.0ms (9%)

localize8.0ms (0.2%)

series76.0ms (1.8%)

rewrite20.0ms (0.5%)

simplify88.0ms (2.1%)

prune275.0ms (6.5%)

localize10.0ms (0.2%)

series80.0ms (1.9%)

rewrite55.0ms (1.3%)

simplify113.0ms (2.7%)

prune288.0ms (6.8%)

localize7.0ms (0.2%)

series40.0ms (1%)

rewrite12.0ms (0.3%)

simplify76.0ms (1.8%)

prune128.0ms (3%)

regimes562.0ms (13.3%)

simplify2.0ms (0.1%)

end101.0ms (2.4%)

Profiling