Details

analyze373.0ms (7.3%)

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)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify102.0ms (2%)

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
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.2b	(*.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)

localize10.0ms (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)))
✓	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series74.0ms (1.4%)

Counts

4 → 50

Calls

4 calls:

36.0ms	(/.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)))))
9.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite19.0ms (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:

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)

simplify109.0ms (2.1%)

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

prune224.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	157	5	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	158	6	164

Error

Counts

164 → 6

Alt Table

Status	Error	Program
	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))))))
	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))))))
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	36.0b	(/.f64 (.f64 (-.f64 (.f64 a a) (*.f64 1/3 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (+.f64 a 1/3))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	10.4b	(-.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))

Compiler

Compiled 3987 to 3091 computations (22.5% 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))

series70.0ms (1.4%)

Counts

4 → 36

Calls

4 calls:

33.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
18.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
16.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite21.0ms (0.4%)

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 a 9 -3))) (+.f64 a -1/3))
2.0ms	(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)

simplify108.0ms (2.1%)

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

prune238.0ms (4.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	198	6	204

Error

Counts

204 → 6

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	10.4b	(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 -1/3 a)) -1/3))
▶	0.2b	(*.f64 (-.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))))))
	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))))))
	36.0b	(/.f64 (.f64 (-.f64 (.f64 a a) (*.f64 1/3 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (+.f64 a 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))

Compiler

Compiled 5120 to 4048 computations (20.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.2b	(/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
✓	0.3b	(/.f64 (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series420.0ms (8.2%)

Counts

3 → 52

Calls

3 calls:

379.0ms	(/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
36.0ms	(/.f64 (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
5.0ms	(sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))

rewrite93.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

604×	`sqrt-prod_binary64`
576×	`times-frac_binary64`
315×	`add-sqr-sqrt_binary64`
313×	`*-un-lft-identity_binary64`
313×	`add-cube-cbrt_binary64`

Counts

3 → 410

Calls

3 calls:

13.0ms	(/.f64 (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
4.0ms	(/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
1.0ms	(sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))

simplify516.0ms (10.1%)

Algorithm

1×	egg-herbie

Rules

868×	`times-frac_binary64`
557×	`fma-def_binary64`
382×	`associate-/l/_binary64`
174×	`fma-neg_binary64`
166×	`sub-neg_binary64`

Counts

462 → 478

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	448	18478
1	1063	16817
2	2585	15851
3	4696	15395
4	4689	15395
5	4844	15395

prune775.0ms (15.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	571	1	572
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	572	6	578

Error

Counts

578 → 6

Alt Table

Status	Error	Program
✓	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))))))
	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))))))
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	36.0b	(/.f64 (.f64 (-.f64 (.f64 a a) (*.f64 1/3 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (+.f64 a 1/3))
▶	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))

Compiler

Compiled 20542 to 16505 computations (19.7% saved)

localize11.0ms (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 9 a -3))))))
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
✓	0.2b	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
✓	0.4b	(/.f64 1 (fma.f64 9 a -3))

series75.0ms (1.5%)

Counts

4 → 50

Calls

4 calls:

34.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
27.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))))
12.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
3.0ms	(/.f64 1 (fma.f64 9 a -3))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
29×	`sqrt-prod_binary64`

Counts

4 → 132

Calls

4 calls:

6.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))))
6.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
2.0ms	(/.f64 1 (fma.f64 9 a -3))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))

simplify93.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-in_binary64`
494×	`times-frac_binary64`
251×	`cancel-sign-sub-inv_binary64`
184×	`associate-r_binary64`
177×	`fma-neg_binary64`

Counts

182 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	3720
1	757	3469
2	2694	3204
3	5097	3204

prune293.0ms (5.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	246	6	252

Error

Counts

252 → 6

Alt Table

Status	Error	Program
✓	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))))))
	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))))))
✓	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	36.0b	(/.f64 (.f64 (-.f64 (.f64 a a) (*.f64 1/3 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (+.f64 a 1/3))
✓	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))

Compiler

Compiled 6168 to 4992 computations (19.1% saved)

regimes362.0ms (7.1%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

83 → 1

Compiler

Compiled 6758 to 5358 computations (20.7% 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

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample1.0s (20.2%)

Algorithm

1×

intervals

Results

631.0ms	8000×	body	128	valid
20.0ms	253×	body	128	invalid
16.0ms	240×	body	128	nan

Compiler

Compiled 158 to 128 computations (19% saved)

Details

analyze373.0ms (7.3%)

sample32.0ms (0.6%)

simplify102.0ms (2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series74.0ms (1.4%)

rewrite19.0ms (0.4%)

simplify109.0ms (2.1%)

prune224.0ms (4.4%)

localize10.0ms (0.2%)

series70.0ms (1.4%)

rewrite21.0ms (0.4%)

simplify108.0ms (2.1%)

prune238.0ms (4.7%)

localize11.0ms (0.2%)

series420.0ms (8.2%)

rewrite93.0ms (1.8%)

simplify516.0ms (10.1%)

prune775.0ms (15.2%)

localize11.0ms (0.2%)

series75.0ms (1.5%)

rewrite26.0ms (0.5%)

simplify93.0ms (1.8%)

prune293.0ms (5.7%)

regimes362.0ms (7.1%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.0s (20.2%)

Profiling