Details

analyze101.0ms (2.6%)

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)

sample253.0ms (6.6%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid
1.0ms	8×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify90.0ms (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 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

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)))))
✓	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series145.0ms (3.8%)

Counts

4 → 50

Calls

4 calls:

57.0ms	(fma.f64 a 9 -3)
52.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
27.0ms	(*.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))

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:

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)

simplify96.0ms (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

prune249.0ms (6.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	190	5	195
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	191	6	197

Error

Counts

197 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -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))))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	8.4b	(-.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))
	0.2b	(*.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))))))

Compiler

Compiled 4667 to 3616 computations (22.5% saved)

localize10.0ms (0.3%)

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 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
✓	0.3b	(/.f64 1 (fma.f64 9 a -3))

series68.0ms (1.8%)

Counts

4 → 36

Calls

4 calls:

36.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
16.0ms	(*.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))

rewrite19.0ms (0.5%)

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:

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

simplify100.0ms (2.6%)

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

prune288.0ms (7.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	217	3	220
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	221	5	226

Error

Counts

226 → 5

Alt Table

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

Compiler

Compiled 5598 to 4426 computations (20.9% saved)

localize9.0ms (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	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3))) -1/3)
✓	0.3b	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3)))

series66.0ms (1.7%)

Counts

4 → 36

Calls

4 calls:

35.0ms	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3))) -1/3)
16.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3)))
13.0ms	(sqrt.f64 (fma.f64 9 a -3))
2.0ms	(fma.f64 9 a -3)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`sqrt-prod_binary64`

Counts

4 → 85

Calls

4 calls:

5.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3)))
1.0ms	(sqrt.f64 (fma.f64 9 a -3))
0.0ms	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 9 a -3))) -1/3)
0.0ms	(fma.f64 9 a -3)

simplify88.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
501×	`fma-def_binary64`
467×	`times-frac_binary64`
366×	`associate-/l*_binary64`
246×	`associate-l_binary64`

Counts

121 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2461
1	482	2204
2	1392	2155
3	4732	2149
4	5098	2149

prune171.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	162	4	166

Error

Counts

166 → 4

Alt Table

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

Compiler

Compiled 3767 to 2901 computations (23% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series62.0ms (1.6%)

Counts

3 → 24

Calls

3 calls:

34.0ms	(fma.f64 rand (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 9 a -3)) (+.f64 -1/3 a))) -1/3)
15.0ms	(/.f64 (sqrt.f64 (fma.f64 9 a -3)) (+.f64 -1/3 a))
13.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 9 a -3)) (+.f64 -1/3 a)))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
173×	`*-un-lft-identity_binary64`
111×	`add-sqr-sqrt_binary64`
111×	`add-cube-cbrt_binary64`
63×	`sqrt-prod_binary64`

Counts

3 → 206

Calls

3 calls:

8.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 9 a -3)) (+.f64 -1/3 a)))
6.0ms	(/.f64 (sqrt.f64 (fma.f64 9 a -3)) (+.f64 -1/3 a))
0.0ms	(fma.f64 rand (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 9 a -3)) (+.f64 -1/3 a))) -1/3)

simplify168.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-def_binary64`
656×	`times-frac_binary64`
314×	`fma-neg_binary64`
197×	`distribute-rgt-in_binary64`
168×	`distribute-lft-in_binary64`

Counts

230 → 270

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	270	6188
1	663	5596
2	2091	5457
3	4772	5453
4	4951	5453

prune343.0ms (8.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	300	4	304

Error

Counts

304 → 4

Alt Table

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

Compiler

Compiled 8355 to 6652 computations (20.4% saved)

regimes494.0ms (12.9%)

Accuracy

Total 0.1b remaining (63.4%)

Threshold costs 0.1b (63.4%)

Counts

115 → 1

Compiler

Compiled 9402 to 7402 computations (21.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	15	22
2	15	22

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample939.0ms (24.4%)

Algorithm

1×

intervals

Results

610.0ms	8000×	body	128	valid
19.0ms	271×	body	128	invalid
17.0ms	261×	body	128	nan

Compiler

Compiled 120 to 97 computations (19.2% saved)

Details

analyze101.0ms (2.6%)

sample253.0ms (6.6%)

simplify90.0ms (2.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series145.0ms (3.8%)

rewrite20.0ms (0.5%)

simplify96.0ms (2.5%)

prune249.0ms (6.5%)

localize10.0ms (0.3%)

series68.0ms (1.8%)

rewrite19.0ms (0.5%)

simplify100.0ms (2.6%)

prune288.0ms (7.5%)

localize9.0ms (0.2%)

series66.0ms (1.7%)

rewrite10.0ms (0.3%)

simplify88.0ms (2.3%)

prune171.0ms (4.5%)

localize10.0ms (0.3%)

series62.0ms (1.6%)

rewrite32.0ms (0.8%)

simplify168.0ms (4.4%)

prune343.0ms (8.9%)

regimes494.0ms (12.9%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample939.0ms (24.4%)

Profiling