Details

analyze105.0ms (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
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)

sample272.0ms (7.2%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	12×	body	128	nan
0.0ms	4×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify101.0ms (2.7%)

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)

localize8.0ms (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)))))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.3b	(sqrt.f64 (fma.f64 a 9 -3))

series69.0ms (1.8%)

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)))))
11.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite22.0ms (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:

10.0ms	(*.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 (2.8%)

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 → 162

Iterations

Useful iterations: 3 (0.0ms)

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

prune186.0ms (4.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	156	6	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	6	164

Error

Counts

164 → 6

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -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))))))
	33.7b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))

Compiler

Compiled 3986 to 3085 computations (22.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series94.0ms (2.5%)

Counts

4 → 36

Calls

4 calls:

64.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
16.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
11.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite24.0ms (0.6%)

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 a 9 -3))) (+.f64 a -1/3))
7.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))
0.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)

simplify107.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

153 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3027
1	656	2737
2	1975	2681
3	4916	2673
4	4930	2673

prune237.0ms (6.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	200	4	204

Error

Counts

204 → 4

Alt Table

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

Compiler

Compiled 5065 to 4004 computations (20.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a 9 -3)
✓	0.2b	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)
✓	0.2b	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3)))
	0.3b	(sqrt.f64 (fma.f64 a 9 -3))

series50.0ms (1.3%)

Counts

2 → 20

Calls

2 calls:

37.0ms	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)
13.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
15×	`sqrt-prod_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3)))
0.0ms	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)

simplify132.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-neg_binary64`
465×	`fma-def_binary64`
416×	`times-frac_binary64`
312×	`associate-/l*_binary64`
249×	`associate-+l+_binary64`

Counts

80 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2087
1	422	1851
2	1205	1802
3	4455	1796
4	4984	1796
5	4995	1796
6	4940	1796

prune126.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	119	4	123

Error

Counts

123 → 4

Alt Table

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

Compiler

Compiled 2845 to 2195 computations (22.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series58.0ms (1.5%)

Counts

2 → 34

Calls

2 calls:

32.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
26.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
16×	`sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 69

Calls

2 calls:

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

simplify93.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-def_binary64`
621×	`distribute-rgt-in_binary64`
405×	`times-frac_binary64`
229×	`fma-neg_binary64`
212×	`cancel-sign-sub-inv_binary64`

Counts

103 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2569
1	576	2368
2	2098	2123
3	4832	2123
4	4977	2123

prune253.0ms (6.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	226	4	230

Error

Counts

230 → 4

Alt Table

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

Compiler

Compiled 5675 to 4586 computations (19.2% saved)

regimes517.0ms (13.6%)

Accuracy

Total 0.1b remaining (78.1%)

Threshold costs 0.1b (78.1%)

Counts

111 → 1

Compiler

Compiled 8490 to 6782 computations (20.1% saved)

simplify3.0ms (0.1%)

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	14	21
1	23	21
2	24	21
3	22	21

end1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

sample1.2s (30.8%)

Algorithm

1×

intervals

Results

734.0ms	8000×	body	128	valid
19.0ms	269×	body	128	invalid
18.0ms	271×	body	128	nan

Compiler

Compiled 113 to 92 computations (18.6% saved)

Details

analyze105.0ms (2.8%)

sample272.0ms (7.2%)

simplify101.0ms (2.7%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series69.0ms (1.8%)

rewrite22.0ms (0.6%)

simplify105.0ms (2.8%)

prune186.0ms (4.9%)

localize10.0ms (0.3%)

series94.0ms (2.5%)

rewrite24.0ms (0.6%)

simplify107.0ms (2.8%)

prune237.0ms (6.3%)

localize9.0ms (0.2%)

series50.0ms (1.3%)

rewrite9.0ms (0.2%)

simplify132.0ms (3.5%)

prune126.0ms (3.3%)

localize12.0ms (0.3%)

series58.0ms (1.5%)

rewrite19.0ms (0.5%)

simplify93.0ms (2.4%)

prune253.0ms (6.7%)

regimes517.0ms (13.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.2s (30.8%)

Profiling