Details

analyze324.0ms (7%)

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)

sample29.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
0.0ms	4×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify66.0ms (1.4%)

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

prune4.0ms (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)))
0.6b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite217.0ms (4.7%)

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:

31.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
6.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(*.f64 (-.f64 a 1/3) 9)

Compiler

Compiled 2230 to 1765 computations (20.9% saved)

series76.0ms (1.6%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

25.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
21.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
9.0ms	(*.f64 (-.f64 a 1/3) 9)
8.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 783 to 624 computations (20.3% saved)

simplify105.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

686×	`distribute-rgt-in_binary64`
671×	`distribute-lft-in_binary64`
299×	`associate-*l/_binary64`
277×	`associate-*r/_binary64`
200×	`times-frac_binary64`

Counts

123 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2238
1	447	2076
2	1360	2067
3	4770	2067
4	4968	2067

prune103.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	5	106

Error

0.0b

Counts

106 → 5

Alt Table

Status	Error	Program
	7.6b	(.f64 (.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))
▶	0.1b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
	8.0b	(.f64 (.f64 (sqrt.f64 (+.f64 -1/3 a)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))) (.f64 (sqrt.f64 (+.f64 -1/3 a)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))))))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))

Compiler

Compiled 2071 to 1628 computations (21.4% saved)

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

rewrite90.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

7.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
6.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
4.0ms	(+.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)

series88.0ms (1.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

51.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
16.0ms	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a)))))
13.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
5.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 720 to 562 computations (21.9% saved)

simplify104.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

497×	`distribute-rgt-in_binary64`
483×	`distribute-lft-in_binary64`
323×	`*-commutative_binary64`
277×	`distribute-rgt-out_binary64`
263×	`distribute-rgt-neg-in_binary64`

Counts

96 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1198
1	256	1146
2	712	1143
3	1444	1143
4	3458	1143
5	4503	1143
6	4914	1143

prune56.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	64	6	70

Error

0.0b

Counts

70 → 6

Alt Table

Status	Error	Program
	0.4b	(+.f64 -1/3 (+.f64 a (.f64 (.f64 (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))) (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))
	7.6b	(.f64 (.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))
✓	0.1b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
	8.0b	(.f64 (.f64 (sqrt.f64 (+.f64 -1/3 a)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))) (.f64 (sqrt.f64 (+.f64 -1/3 a)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))))))
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))

Compiler

Compiled 1162 to 903 computations (22.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite478.0ms (10.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

330×	`times-frac_binary64`
233×	`*-un-lft-identity_binary64`
188×	`sqrt-prod_binary64`
182×	`add-sqr-sqrt_binary64`
177×	`add-cube-cbrt_binary64`

Counts

4 → 302

Calls

4 calls:

38.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
12.0ms	(/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))
5.0ms	(/.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 6333 to 5015 computations (20.8% saved)

series72.0ms (1.5%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

24.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
20.0ms	(/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))
18.0ms	(/.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
5.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 905 to 730 computations (19.3% saved)

simplify261.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-*l/_binary64`
559×	`associate-*r/_binary64`
469×	`associate-/r*_binary64`
416×	`times-frac_binary64`
358×	`associate-/l*_binary64`

Counts

326 → 298

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	358	7875
1	821	7703
2	2257	7703
3	4990	7703
4	4958	7703

prune220.0ms (4.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	298	6	304

Error

0.0b

Counts

304 → 6

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 -1/3 (+.f64 a (.f64 (.f64 (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))) (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))
	7.6b	(.f64 (.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))
✓	0.1b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
	8.0b	(.f64 (.f64 (sqrt.f64 (+.f64 -1/3 a)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))) (.f64 (sqrt.f64 (+.f64 -1/3 a)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))

Compiler

Compiled 4476 to 3486 computations (22.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (cbrt.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
0.6b	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
0.6b	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
0.6b	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))

rewrite138.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
18×	`sqrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
6.0ms	(.f64 (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (cbrt.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
6.0ms	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
5.0ms	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 2928 to 2326 computations (20.6% saved)

series277.0ms (5.9%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

63.0ms	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
60.0ms	(.f64 (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (cbrt.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))))))
53.0ms	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
52.0ms	(cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 4053 to 3379 computations (16.6% saved)

simplify107.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

728×	`times-frac_binary64`
501×	`unswap-sqr_binary64`
359×	`*-commutative_binary64`
142×	`sub-neg_binary64`
136×	`sqr-pow_binary64`

Counts

108 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	3084
1	427	2828
2	1169	2514
3	2780	2448
4	5114	2448

prune92.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	80	6	86

Error

Counts

86 → 6

Alt Table

Status	Error	Program
	0.4b	(+.f64 -1/3 (+.f64 a (.f64 (.f64 (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))) (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))
	0.5b	(+.f64 -1/3 (+.f64 a (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))) 6) 1) (cbrt.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))
	7.6b	(.f64 (.f64 (+.f64 -1/3 a) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))))
	0.1b	(+.f64 -1/3 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))

Compiler

Compiled 2405 to 1883 computations (21.7% saved)

regimes705.0ms (15.2%)

Accuracy

Total 0.2b remaining (90.4%)

Threshold costs 0.2b (90.4%)

Compiler

Compiled 12882 to 10458 computations (18.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	16	18
2	16	18

end1.0ms (0%)

Compiler: Compiled 14 to 11 computations (21.4% saved)

sample996.0ms (21.4%)

Algorithm

1×

intervals

Results

594.0ms	8000×	body	128	valid
19.0ms	288×	body	128	nan
17.0ms	244×	body	128	invalid

Compiler

Compiled 186 to 153 computations (17.7% saved)

Details

analyze324.0ms (7%)

sample29.0ms (0.6%)

simplify66.0ms (1.4%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite217.0ms (4.7%)

series76.0ms (1.6%)

simplify105.0ms (2.3%)

prune103.0ms (2.2%)

localize9.0ms (0.2%)

rewrite90.0ms (1.9%)

series88.0ms (1.9%)

simplify104.0ms (2.2%)

prune56.0ms (1.2%)

localize11.0ms (0.2%)

rewrite478.0ms (10.3%)

series72.0ms (1.5%)

simplify261.0ms (5.6%)

prune220.0ms (4.7%)

localize14.0ms (0.3%)

rewrite138.0ms (3%)

series277.0ms (5.9%)

simplify107.0ms (2.3%)

prune92.0ms (2%)

regimes705.0ms (15.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample996.0ms (21.4%)

Profiling