Details

analyze261.0ms (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)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	9×	body	128	invalid
0.0ms	7×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify67.0ms (1.5%)

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

rewrite192.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

14.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
10.0ms	(/.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 (1.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

32.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
23.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
10.0ms	(*.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)

simplify100.0ms (2.3%)

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 → 99

Iterations

Useful iterations: 2 (0.0ms)

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

prune133.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

Counts

101 → 7

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
	0.4b	(.f64 (.f64 (-.f64 a 1/3) (.f64 (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))
	34.5b	(/.f64 (.f64 (-.f64 (.f64 a a) 1/9) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))) (+.f64 a 1/3))
	0.6b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
	47.1b	(cbrt.f64 (pow.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))) 3))
	4.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (/.f64 (.f64 9 (-.f64 (*.f64 a a) 1/9)) (+.f64 a 1/3))))))
	0.4b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 2050 to 1609 computations (21.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
0.3b	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
0.3b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 1/3 rand))
0.4b	(*.f64 1/3 rand)

rewrite300.0ms (6.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

60×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
38×	`associate-l_binary64`

Counts

4 → 157

Calls

4 calls:

14.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 1/3 rand))
9.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
6.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(*.f64 1/3 rand)

Compiler

Compiled 3541 to 2928 computations (17.3% saved)

series77.0ms (1.8%)

Error

Counts

4 → 21

Calls

4 calls:

33.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
25.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 1/3 rand))
7.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
7.0ms	(*.f64 1/3 rand)

Compiler

Compiled 757 to 611 computations (19.3% saved)

simplify127.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

648×	`distribute-rgt-in_binary64`
631×	`distribute-lft-in_binary64`
526×	`times-frac_binary64`
224×	`associate-l_binary64`
220×	`associate-r_binary64`

Counts

178 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2819
1	503	2650
2	1727	2580
3	4831	2580
4	5026	2580

prune154.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Error

Counts

143 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
	34.5b	(/.f64 (.f64 (-.f64 (.f64 a a) 1/9) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))) (+.f64 a 1/3))
	0.5b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (+.f64 1 (/.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3))))))
	47.1b	(cbrt.f64 (pow.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))) 3))
	0.4b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))

Compiler

Compiled 2044 to 1656 computations (19% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))
0.1b	(sqrt.f64 (/.f64 1 (-.f64 a 1/3)))
0.2b	(*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3))))
0.3b	(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))

rewrite220.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

56×	`add-sqr-sqrt_binary64`
45×	`sqrt-prod_binary64`
43×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
28×	`associate-r_binary64`

Counts

4 → 128

Calls

4 calls:

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

Compiler

Compiled 2999 to 2470 computations (17.6% saved)

series90.0ms (2.1%)

Error

Counts

4 → 24

Calls

4 calls:

29.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))
25.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))
24.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3))))
7.0ms	(sqrt.f64 (/.f64 1 (-.f64 a 1/3)))

Compiler

Compiled 868 to 694 computations (20% saved)

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

642×	`distribute-rgt-in_binary64`
618×	`distribute-lft-in_binary64`
214×	`associate-l_binary64`
211×	`associate-r_binary64`
185×	`times-frac_binary64`

Counts

152 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2739
1	442	2593
2	1554	2583
3	4453	2583
4	4975	2583

prune107.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
	34.5b	(/.f64 (.f64 (-.f64 (.f64 a a) 1/9) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))) (+.f64 a 1/3))
	0.5b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (+.f64 1 (/.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3))))))
	47.1b	(cbrt.f64 (pow.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))) 3))
▶	0.4b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))

Compiler

Compiled 1940 to 1573 computations (18.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite137.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-sqr-sqrt_binary64`
14×	`-un-lft-identity_binary64` `associate-r/_binary64`
12×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
10×	`add-cube-cbrt_binary64` `sqrt-div_binary64`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
8.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
7.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 1626 to 1244 computations (23.5% saved)

series71.0ms (1.6%)

Error

Counts

4 → 24

Calls

4 calls:

22.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
19.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
18.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
6.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 723 to 561 computations (22.4% saved)

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

389×	`*-commutative_binary64`
380×	`distribute-rgt-in_binary64`
364×	`distribute-lft-in_binary64`
351×	`cancel-sign-sub-inv_binary64`
273×	`distribute-rgt-out_binary64`

Counts

108 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	1670
1	341	1610
2	1105	1570
3	2896	1567
4	4547	1567
5	4927	1567

prune73.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	69	6	75

Error

Counts

75 → 6

Alt Table

Status	Error	Program
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
	34.5b	(/.f64 (.f64 (-.f64 (.f64 a a) 1/9) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))) (+.f64 a 1/3))
	0.5b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (+.f64 1 (/.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3))))))
	47.1b	(cbrt.f64 (pow.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))) 3))
	0.4b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 1/3 (*.f64 rand (sqrt.f64 (/.f64 1 (-.f64 a 1/3)))))))

Compiler

Compiled 1100 to 842 computations (23.5% saved)

regimes962.0ms (22.2%)

Accuracy

Total 0.1b remaining (78%)

Threshold costs 0.1b (78%)

Compiler

Compiled 12722 to 10410 computations (18.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64` `sub-neg_binary64` `*-rgt-identity_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)

sample879.0ms (20.3%)

Algorithm

1×

intervals

Results

465.0ms	8000×	body	128	valid
16.0ms	286×	body	128	invalid
13.0ms	263×	body	128	nan

Compiler

Compiled 158 to 129 computations (18.4% saved)

Details

analyze261.0ms (6%)

sample25.0ms (0.6%)

simplify67.0ms (1.5%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

rewrite192.0ms (4.4%)

series82.0ms (1.9%)

simplify100.0ms (2.3%)

prune133.0ms (3.1%)

localize9.0ms (0.2%)

rewrite300.0ms (6.9%)

series77.0ms (1.8%)

simplify127.0ms (2.9%)

prune154.0ms (3.6%)

localize10.0ms (0.2%)

rewrite220.0ms (5.1%)

series90.0ms (2.1%)

simplify116.0ms (2.7%)

prune107.0ms (2.5%)

localize7.0ms (0.2%)

rewrite137.0ms (3.2%)

series71.0ms (1.6%)

simplify107.0ms (2.5%)

prune73.0ms (1.7%)

regimes962.0ms (22.2%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample879.0ms (20.3%)

Profiling