Details

analyze272.0ms (6.5%)

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)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
0.0ms	7×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

189×	`distribute-rgt-in_binary64`
173×	`cancel-sign-sub-inv_binary64`
159×	`sub-neg_binary64`
156×	`distribute-lft-in_binary64`
149×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	71	21
3	150	21
4	266	21
5	460	21
6	618	21
7	987	21
8	1185	21
9	1148	21
10	1191	21
11	1190	21
12	1187	21
13	1049	21

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 2

Alt Table

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

Compiler

Compiled 92 to 77 computations (16.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite206.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`

Counts

4 → 99

Calls

4 calls:

17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
7.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 2230 to 1765 computations (20.9% saved)

series82.0ms (2%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

29.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
24.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
9.0ms	(*.f64 (-.f64 a 1/3) 9)
7.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 783 to 624 computations (20.3% saved)

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-in_binary64`
667×	`distribute-lft-in_binary64`
297×	`associate-*l/_binary64`
279×	`associate-*r/_binary64`
216×	`times-frac_binary64`

Counts

123 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2238
1	454	2076
2	1357	2067
3	4811	2067
4	5007	2067

prune137.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Error

Counts

106 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (.f64 3 (sqrt.f64 (+.f64 -1/3 a))))))))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))))
	12.6b	(/.f64 (.f64 (+.f64 -1/3 a) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))) 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))
	9.6b	(/.f64 (.f64 (+.f64 -1/3 a) (-.f64 1 (.f64 rand (/.f64 rand (+.f64 -3 (.f64 a 9)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
	0.4b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))

Compiler

Compiled 2123 to 1669 computations (21.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))
0.3b	(*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))
0.4b	(sqrt.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))))
0.5b	(.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 3 (sqrt.f64 (+.f64 -1/3 a))))

rewrite251.0ms (6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

87×	`pow1_binary64`
36×	`sqrt-div_binary64`
36×	`pow-prod-down_binary64`
32×	`associate-*r/_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 126

Calls

4 calls:

13.0ms	(.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 3 (sqrt.f64 (+.f64 -1/3 a))))
12.0ms	(sqrt.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))))
10.0ms	(*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))
7.0ms	(*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))

Compiler

Compiled 2934 to 2414 computations (17.7% saved)

series39.0ms (0.9%)

Error

Counts

4 → 14

Calls

4 calls:

9.0ms	(.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 3 (sqrt.f64 (+.f64 -1/3 a))))
8.0ms	(*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))
8.0ms	(*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))
8.0ms	(sqrt.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (*.f64 3 (sqrt.f64 (+.f64 -1/3 a)))))

Compiler

Compiled 657 to 541 computations (17.7% saved)

simplify149.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

572×	`associate-l_binary64`
479×	`times-frac_binary64`
327×	`associate-r_binary64`
324×	`*-commutative_binary64`
296×	`associate-*r/_binary64`

Counts

140 → 114

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	124	1648
1	244	1456
2	576	1456
3	1330	1456
4	1517	1456
5	1850	1456
6	3412	1456
7	4917	1456
8	4845	1456

prune125.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Error

Counts

120 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (.f64 3 (sqrt.f64 (+.f64 -1/3 a))))))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))))
	12.6b	(/.f64 (.f64 (+.f64 -1/3 a) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))) 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))
	9.6b	(/.f64 (.f64 (+.f64 -1/3 a) (-.f64 1 (.f64 rand (/.f64 rand (+.f64 -3 (.f64 a 9)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
	0.4b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))

Compiler

Compiled 1790 to 1458 computations (18.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))))
0.1b	(sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand)
0.3b	(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))

rewrite438.0ms (10.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`sqrt-prod_binary64`
29×	`associate-l_binary64`
28×	`times-frac_binary64`

Counts

4 → 122

Calls

4 calls:

12.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand)
11.0ms	(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))
8.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))))
6.0ms	(sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))

Compiler

Compiled 2823 to 2330 computations (17.5% saved)

series86.0ms (2%)

Error

Counts

4 → 24

Calls

4 calls:

29.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))))
24.0ms	(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))
21.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand)
7.0ms	(sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))

Compiler

Compiled 880 to 704 computations (20% saved)

simplify142.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

260×	`associate-/l*_binary64`
243×	`cancel-sign-sub-inv_binary64`
210×	`associate-r_binary64`
206×	`distribute-rgt-neg-in_binary64`
201×	`associate-l_binary64`

Counts

146 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2676
1	467	2524
2	1567	2517
3	2823	2517
4	4749	2517
5	5046	2517

prune158.0ms (3.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	125	6	131

Error

Counts

131 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (.f64 3 (sqrt.f64 (+.f64 -1/3 a))))))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))))
	12.6b	(/.f64 (.f64 (+.f64 -1/3 a) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))) 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))
	9.6b	(/.f64 (.f64 (+.f64 -1/3 a) (-.f64 1 (.f64 rand (/.f64 rand (+.f64 -3 (.f64 a 9)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
▶	0.4b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))

Compiler

Compiled 2175 to 1780 computations (18.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 -1/3 a))
0.0b	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a)))))
0.2b	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
0.6b	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))

rewrite129.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
12×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
7.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
3.0ms	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a)))))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 1255 to 960 computations (23.5% saved)

series71.0ms (1.7%)

Error

Counts

4 → 24

Calls

4 calls:

20.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
19.0ms	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a)))))
16.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
8.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 732 to 571 computations (22% saved)

simplify110.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

532×	`distribute-rgt-in_binary64`
517×	`distribute-lft-in_binary64`
353×	`*-commutative_binary64`
321×	`distribute-rgt-neg-in_binary64`
301×	`unsub-neg_binary64`

Counts

96 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	1198
1	259	1146
2	754	1143
3	1574	1143
4	3936	1143
5	4565	1143
6	4965	1143

prune78.0ms (1.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	67	6	73

Error

Counts

73 → 6

Alt Table

Status	Error	Program
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 (+.f64 -1/3 a))) (.f64 3 (sqrt.f64 (+.f64 -1/3 a))))))))
	0.5b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 (*.f64 rand (fabs.f64 (cbrt.f64 (-.f64 a 1/3)))) (sqrt.f64 (cbrt.f64 (+.f64 -1/3 a)))))))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 -1/3 a))) rand))))
	9.6b	(/.f64 (.f64 (+.f64 -1/3 a) (-.f64 1 (.f64 rand (/.f64 rand (+.f64 -3 (.f64 a 9)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
	0.4b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))

Compiler

Compiled 1005 to 773 computations (23.1% saved)

regimes631.0ms (15%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Compiler

Compiled 9558 to 7850 computations (17.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	22	24
2	23	24
3	21	24

end1.0ms (0%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

sample850.0ms (20.2%)

Algorithm

1×

intervals

Results

444.0ms	8000×	body	128	valid
16.0ms	244×	body	128	nan
13.0ms	239×	body	128	invalid

Compiler

Compiled 164 to 134 computations (18.3% saved)

Details

analyze272.0ms (6.5%)

sample24.0ms (0.6%)

simplify68.0ms (1.6%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

rewrite206.0ms (4.9%)

series82.0ms (2%)

simplify104.0ms (2.5%)

prune137.0ms (3.3%)

localize12.0ms (0.3%)

rewrite251.0ms (6%)

series39.0ms (0.9%)

simplify149.0ms (3.5%)

prune125.0ms (3%)

localize13.0ms (0.3%)

rewrite438.0ms (10.4%)

series86.0ms (2%)

simplify142.0ms (3.4%)

prune158.0ms (3.8%)

localize8.0ms (0.2%)

rewrite129.0ms (3.1%)

series71.0ms (1.7%)

simplify110.0ms (2.6%)

prune78.0ms (1.8%)

regimes631.0ms (15%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample850.0ms (20.2%)

Profiling