Details

analyze352.0ms (7.1%)

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)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	8×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify103.0ms (2.1%)

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
✓	0.1b	(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))

rewrite22.0ms (0.4%)

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:

13.0ms	(*.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)

series119.0ms (2.4%)

Counts

4 → 50

Calls

4 calls:

60.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
46.0ms	(*.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))
5.0ms	(fma.f64 a 9 -3)

simplify118.0ms (2.4%)

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 → 245

Iterations

Useful iterations: 3 (0.0ms)

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

prune201.0ms (4.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	241	6	247

Error

Counts

247 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	9.1b	(/.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)))))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
	2.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 a 9 -3)) (sqrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (fma.f64 a 9 -3)))))))
	44.5b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))

Compiler

Compiled 4005 to 3107 computations (22.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.1b	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.4b	(/.f64 1 (fma.f64 a 9 -3))

rewrite26.0ms (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:

15.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))
2.0ms	(sqrt.f64 (/.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)

series83.0ms (1.7%)

Counts

4 → 36

Calls

4 calls:

56.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
14.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
9.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

simplify121.0ms (2.5%)

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 → 265

Iterations

Useful iterations: 3 (0.0ms)

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

prune274.0ms (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	265	6	271

Error

Counts

271 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	9.1b	(/.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)))))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
	2.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 a 9 -3)) (sqrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (fma.f64 a 9 -3)))))))
	44.5b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))

Compiler

Compiled 5163 to 4086 computations (20.9% saved)

localize9.0ms (0.2%)

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))

rewrite18.0ms (0.4%)

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:

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

series102.0ms (2.1%)

Counts

2 → 34

Calls

2 calls:

58.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
44.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))

simplify104.0ms (2.1%)

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 → 198

Iterations

Useful iterations: 2 (0.0ms)

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

prune302.0ms (6.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	323	6	329

Error

Counts

329 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	9.1b	(/.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)))))
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
	2.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 a 9 -3)) (sqrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (fma.f64 a 9 -3)))))))
	44.5b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))

Compiler

Compiled 5805 to 4692 computations (19.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
	0.3b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.6b	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
100×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
95×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`

Counts

3 → 189

Calls

3 calls:

23.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
8.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

series142.0ms (2.9%)

Counts

3 → 50

Calls

3 calls:

59.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
47.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
34.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

simplify202.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-def_binary64`
625×	`distribute-rgt-in_binary64`
210×	`cancel-sign-sub-inv_binary64`
173×	`fma-neg_binary64`
135×	`associate-r_binary64`

Counts

239 → 442

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	5671
1	737	5018
2	2550	4808
3	4887	4790
4	4942	4790

prune370.0ms (7.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	468	6	474

Error

Counts

474 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	9.1b	(/.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)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
	2.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 a 9 -3)) (sqrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (fma.f64 a 9 -3)))))))
	44.5b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))

Compiler

Compiled 7789 to 6121 computations (21.4% saved)

regimes991.0ms (20.1%)

Accuracy

Total 0.3b remaining (92.5%)

Threshold costs 0.3b (92.5%)

Compiler

Compiled 17714 to 14206 computations (19.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	46
1	31	46
2	31	46

end1.0ms (0%)

Compiler: Compiled 33 to 25 computations (24.2% saved)

sample1.2s (23.6%)

Algorithm

1×

intervals

Results

783.0ms	8000×	body	128	valid
18.0ms	260×	body	128	invalid
16.0ms	247×	body	128	nan

Compiler

Compiled 202 to 163 computations (19.3% saved)

Details

analyze352.0ms (7.1%)

sample28.0ms (0.6%)

simplify103.0ms (2.1%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite22.0ms (0.4%)

series119.0ms (2.4%)

simplify118.0ms (2.4%)

prune201.0ms (4.1%)

localize10.0ms (0.2%)

rewrite26.0ms (0.5%)

series83.0ms (1.7%)

simplify121.0ms (2.5%)

prune274.0ms (5.6%)

localize9.0ms (0.2%)

rewrite18.0ms (0.4%)

series102.0ms (2.1%)

simplify104.0ms (2.1%)

prune302.0ms (6.1%)

localize10.0ms (0.2%)

rewrite48.0ms (1%)

series142.0ms (2.9%)

simplify202.0ms (4.1%)

prune370.0ms (7.5%)

regimes991.0ms (20.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (23.6%)

Profiling