Details

analyze128.0ms (2.2%)

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)

sample1.6s (28.1%)

Results

1.3s	8256×	body	128	valid
76.0ms	548×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify95.0ms (1.6%)

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

prune5.0ms (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
	0.2b	(.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 (0.1%)

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)))

series66.0ms (1.1%)

Counts

4 → 50

Calls

4 calls:

31.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
25.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
8.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite33.0ms (0.6%)

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:

23.0ms	(*.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)

simplify103.0ms (1.8%)

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

prune237.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	189	6	195
Fresh	1	0	1
Picked	0	1	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 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	7.6b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	34.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4713 to 3650 computations (22.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series63.0ms (1.1%)

Counts

4 → 36

Calls

4 calls:

34.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
14.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
12.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
3.0ms	(/.f64 1 (fma.f64 9 a -3))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
29×	`sqrt-prod_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 117

Calls

4 calls:

8.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
3.0ms	(/.f64 1 (fma.f64 9 a -3))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
0.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)

simplify142.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
571×	`times-frac_binary64`
332×	`distribute-rgt-in_binary64`
293×	`distribute-lft-in_binary64`
238×	`fma-neg_binary64`

Counts

153 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3027
1	655	2737
2	1975	2681
3	4916	2673
4	4930	2673

prune321.0ms (5.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	220	7	227

Error

Counts

227 → 7

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	7.6b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	34.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 5710 to 4517 computations (20.9% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series88.0ms (1.5%)

Counts

3 → 38

Calls

3 calls:

47.0ms	(*.f64 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))
30.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))))
11.0ms	(/.f64 1 (sqrt.f64 (fma.f64 a 9 -3)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
38×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`

Counts

3 → 128

Calls

3 calls:

8.0ms	(*.f64 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))
7.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))))
4.0ms	(/.f64 1 (sqrt.f64 (fma.f64 a 9 -3)))

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

658×	`distribute-rgt-in_binary64`
512×	`times-frac_binary64`
255×	`fma-neg_binary64`
233×	`cancel-sign-sub-inv_binary64`
174×	`associate-r_binary64`

Counts

166 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	3352
1	693	3123
2	2503	2953
3	4948	2934
4	4989	2934

prune322.0ms (5.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	244	7	251

Error

Counts

251 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))))
▶	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	7.6b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	34.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 6293 to 5101 computations (18.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series511.0ms (8.7%)

Counts

3 → 52

Calls

3 calls:

463.0ms

(/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))

42.0ms

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

5.0ms

(/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))

rewrite66.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`add-sqr-sqrt_binary64`
171×	`sqrt-prod_binary64`
153×	`times-frac_binary64`
97×	`*-un-lft-identity_binary64`
85×	`add-cube-cbrt_binary64`

Counts

3 → 230

Calls

3 calls:

29.0ms

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

4.0ms

(/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))

4.0ms

(/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))

simplify308.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
485×	`associate-/r*_binary64`
428×	`associate-/l/_binary64`
385×	`associate-/r/_binary64`
212×	`fma-neg_binary64`

Counts

282 → 296

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	299	8100
1	750	7013
2	2431	6802
3	4831	5988
4	4661	5844
5	4888	5844
6	4885	5844

prune610.0ms (10.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	356	0	356
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	356	7	363

Error

Counts

363 → 7

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (fma.f64 a 9 -3))))))
✓	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	7.6b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	34.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	7.1b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 11957 to 9874 computations (17.4% saved)

regimes757.0ms (12.9%)

Accuracy

Total 0.1b remaining (81.7%)

Threshold costs 0.1b (81.7%)

Counts

141 → 1

Compiler

Compiled 12722 to 10250 computations (19.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	14	20
2	14	20

end141.0ms (2.4%)

Compiler: Compiled 193 to 153 computations (20.7% saved)

Details

analyze128.0ms (2.2%)

sample1.6s (28.1%)

simplify95.0ms (1.6%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

series66.0ms (1.1%)

rewrite33.0ms (0.6%)

simplify103.0ms (1.8%)

prune237.0ms (4%)

localize12.0ms (0.2%)

series63.0ms (1.1%)

rewrite20.0ms (0.3%)

simplify142.0ms (2.4%)

prune321.0ms (5.5%)

localize19.0ms (0.3%)

series88.0ms (1.5%)

rewrite26.0ms (0.4%)

simplify117.0ms (2%)

prune322.0ms (5.5%)

localize15.0ms (0.3%)

series511.0ms (8.7%)

rewrite66.0ms (1.1%)

simplify308.0ms (5.3%)

prune610.0ms (10.4%)

regimes757.0ms (12.9%)

simplify2.0ms (0%)

end141.0ms (2.4%)

Profiling