Details

analyze142.0ms (2.7%)

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
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample267.0ms (5.2%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify96.0ms (1.9%)

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)

localize11.0ms (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)
✓	0.2b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

series88.0ms (1.7%)

Counts

4 → 41

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
29.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
15.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
12.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite58.0ms (1.1%)

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))))
13.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
11.0ms	(.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)))))

simplify97.0ms (1.9%)

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

prune452.0ms (8.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	241	8	249
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	243	8	251

Error

Counts

251 → 8

Alt Table

Status	Error	Program
	0.1b	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (sqrt.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)
	0.3b	(.f64 (.f64 (-.f64 a 1/3) (.f64 (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))) (cbrt.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand))))
	6.1b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 1 (.f64 rand (.f64 rand (/.f64 1/9 (-.f64 a 1/3)))))) (-.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))) (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))) (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))
	0.5b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
▶	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))

Compiler

Compiled 7919 to 6672 computations (15.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 9 (-.f64 a (/.f64 1 3)))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
✓	0.1b	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
✓	0.2b	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

series67.0ms (1.3%)

Counts

4 → 58

Calls

4 calls:

33.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)
26.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
6.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
2.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))

rewrite92.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`add-sqr-sqrt_binary64`
101×	`*-un-lft-identity_binary64`
93×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`
76×	`times-frac_binary64`

Counts

4 → 212

Calls

4 calls:

48.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
11.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))
8.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
5.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

simplify198.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

489×	`times-frac_binary64`
225×	`associate-r_binary64`
219×	`associate-l_binary64`
216×	`*-commutative_binary64`
207×	`fma-neg_binary64`

Counts

270 → 325

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	406	5155
1	970	4157
2	3088	4026
3	4759	3857
4	4986	3857
5	4832	3857

prune580.0ms (11.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	322	3	325
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	325	8	333

Error

Counts

333 → 8

Alt Table

Status	Error	Program
	0.3b	(.f64 (.f64 (+.f64 -1/3 a) (.f64 (cbrt.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (cbrt.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))) (cbrt.f64 (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand))))
	0.1b	(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
	6.1b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 1 (.f64 rand (.f64 rand (/.f64 1/9 (-.f64 a 1/3)))))) (-.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))) -1/2) rand)))
▶	0.1b	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))) (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))) (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))
	0.5b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))

Compiler

Compiled 11669 to 10002 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
✓	0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
✓	0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
✓	10.4b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

series85.0ms (1.6%)

Counts

4 → 53

Calls

4 calls:

29.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
23.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
22.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
11.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`associate-r_binary64`

Counts

4 → 138

Calls

4 calls:

13.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
7.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
6.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
4.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify137.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

603×	`times-frac_binary64`
205×	`fma-neg_binary64`
176×	`fma-def_binary64`
154×	`distribute-rgt-in_binary64`
153×	`*-commutative_binary64`

Counts

191 → 277

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	316	4358
1	825	4055
2	2994	3998
3	4756	3997
4	4905	3997

prune341.0ms (6.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	274	3	277
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	280	5	285

Error

Counts

285 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
	0.1b	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 -1/3 a))) (/.f64 rand (sqrt.f64 9))))
	0.1b	(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
	0.1b	(+.f64 (-.f64 a 1/3) (.f64 (.f64 (-.f64 a 1/3) (/.f64 1 (sqrt.f64 (-.f64 a 1/3)))) (/.f64 rand (sqrt.f64 9))))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))

Compiler

Compiled 7661 to 5776 computations (24.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
✓	0.2b	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
✓	0.8b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
✓	10.4b	(.f64 (-.f64 a 1/3) (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand)))

series80.0ms (1.5%)

Counts

3 → 48

Calls

3 calls:

30.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
26.0ms	(.f64 (-.f64 a 1/3) (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand)))
24.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)

rewrite57.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`times-frac_binary64`
119×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`
103×	`add-cube-cbrt_binary64`
53×	`associate-r_binary64`

Counts

3 → 215

Calls

3 calls:

20.0ms	(.f64 (-.f64 a 1/3) (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand)))
8.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
8.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)

simplify177.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-/r/_binary64`
355×	`fma-def_binary64`
235×	`distribute-rgt-in_binary64`
234×	`associate-/l/_binary64`
225×	`distribute-lft-in_binary64`

Counts

263 → 373

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	6007
1	644	5414
2	2316	4883
3	4736	4883
4	4987	4883

prune430.0ms (8.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	404	1	405
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	406	4	410

Error

Counts

410 → 4

Alt Table

Status	Error	Program
	0.1b	(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
	0.1b	(+.f64 (-.f64 a 1/3) (.f64 (.f64 (-.f64 a 1/3) (/.f64 1 (sqrt.f64 (-.f64 a 1/3)))) (/.f64 rand (sqrt.f64 9))))
	0.1b	(+.f64 (-.f64 a 1/3) (/.f64 (-.f64 a 1/3) (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)))
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))

Compiler

Compiled 11496 to 8846 computations (23.1% saved)

regimes693.0ms (13.4%)

Accuracy

Total 0.1b remaining (88.9%)

Threshold costs 0.1b (88.9%)

Counts

141 → 1

Compiler

Compiled 13656 to 11191 computations (18.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	22
1	25	22
2	22	22

end1.0ms (0%)

Compiler: Compiled 17 to 14 computations (17.6% saved)

sample968.0ms (18.6%)

Algorithm

1×

intervals

Results

619.0ms	8000×	body	128	valid
21.0ms	251×	body	128	nan
17.0ms	245×	body	128	invalid

Compiler

Compiled 115 to 95 computations (17.4% saved)

Details

analyze142.0ms (2.7%)

sample267.0ms (5.2%)

simplify96.0ms (1.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series88.0ms (1.7%)

rewrite58.0ms (1.1%)

simplify97.0ms (1.9%)

prune452.0ms (8.7%)

localize11.0ms (0.2%)

series67.0ms (1.3%)

rewrite92.0ms (1.8%)

simplify198.0ms (3.8%)

prune580.0ms (11.2%)

localize8.0ms (0.2%)

series85.0ms (1.6%)

rewrite40.0ms (0.8%)

simplify137.0ms (2.6%)

prune341.0ms (6.6%)

localize9.0ms (0.2%)

series80.0ms (1.5%)

rewrite57.0ms (1.1%)

simplify177.0ms (3.4%)

prune430.0ms (8.3%)

regimes693.0ms (13.4%)

simplify2.0ms (0%)

end1.0ms (0%)

sample968.0ms (18.6%)

Profiling