Details

analyze117.0ms (1.8%)

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
25%	25%	50%	4
25%	25%	50%	5
25%	12.5%	62.5%	6
25%	12.5%	62.5%	7
25%	6.2%	68.8%	8
25%	6.2%	68.8%	9
25%	3.1%	71.9%	10
25%	3.1%	71.9%	11
25%	1.6%	73.5%	12
25%	1.6%	73.5%	13
25%	0.8%	74.2%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.8s (27.9%)

Results

1.4s	8256×	body	128	valid
38.0ms	232×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify124.0ms (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

prune7.0ms (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)))
▶	0.1b	(*.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)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)))
✓	0.6b	(sqrt.f64 (fma.f64 a 9 -3))

series89.0ms (1.4%)

Counts

4 → 50

Calls

4 calls:

46.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
26.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
15.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite21.0ms (0.3%)

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:

12.0ms	(*.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)

simplify111.0ms (1.7%)

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

prune234.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Error

Counts

164 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (cbrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (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))))))
	7.9b	(/.f64 (*.f64 (+.f64 a -1/3) (-.f64 1 (/.f64 rand (/.f64 (fma.f64 a 9 -3) rand)))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))

Compiler

Compiled 4054 to 3141 computations (22.5% saved)

localize10.0ms (0.1%)

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)))
✓	0.3b	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
✓	0.6b	(/.f64 1 (fma.f64 a 9 -3))

series80.0ms (1.3%)

Counts

4 → 50

Calls

4 calls:

37.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
27.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
12.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite26.0ms (0.4%)

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:

8.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
7.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))

simplify141.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

182 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	3720
1	758	3469
2	2694	3204
3	5097	3204

prune419.0ms (6.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	208	3	211
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	212	6	218

Error

Counts

218 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 a 2))) (.f64 1/9 (/.f64 1 a)))))))
	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))))))
	7.4b	(+.f64 (+.f64 -1/3 a) (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (.f64 rand (+.f64 -1/3 a))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (cbrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))

Compiler

Compiled 5498 to 4433 computations (19.4% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a 9 -3)
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.2b	(/.f64 (*.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))
	0.6b	(sqrt.f64 (fma.f64 a 9 -3))

series217.0ms (3.4%)

Counts

2 → 34

Calls

2 calls:

150.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))))
67.0ms	(/.f64 (*.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 62

Calls

2 calls:

11.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))))
10.0ms	(/.f64 (*.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))

simplify139.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
631×	`distribute-rgt-in_binary64`
565×	`times-frac_binary64`
193×	`fma-neg_binary64`
182×	`cancel-sign-sub-inv_binary64`

Counts

96 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	2261
1	576	2102
2	2058	1950
3	4909	1932
4	4936	1932

prune333.0ms (5.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	164	6	170

Error

Counts

170 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 a 2))) (.f64 1/9 (/.f64 1 a)))))))
	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))))))
	7.4b	(+.f64 (+.f64 -1/3 a) (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (.f64 rand (+.f64 -1/3 a))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (cbrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))

Compiler

Compiled 4324 to 3483 computations (19.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series132.0ms (2.1%)

Counts

2 → 20

Calls

2 calls:

109.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
22.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`associate-l_binary64`
16×	`sqrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`

Counts

2 → 54

Calls

2 calls:

19.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
1.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)

simplify130.0ms (2%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-def_binary64`
505×	`times-frac_binary64`
452×	`fma-neg_binary64`
308×	`associate-/l*_binary64`
270×	`distribute-rgt-in_binary64`

Counts

74 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	1874
1	463	1634
2	1382	1601
3	4883	1595
4	5171	1595

prune586.0ms (9.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	198	5	203

Error

Counts

203 → 5

Alt Table

Status	Error	Program
	0.8b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 a 2))) (.f64 1/9 (/.f64 1 a)))))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 rand (sqrt.f64 1)) (sqrt.f64 (fma.f64 a 9 -3)))))
	7.4b	(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 -1/3 a)) -1/3))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (cbrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3))

Compiler

Compiled 4983 to 3939 computations (21% saved)

regimes1.4s (22.6%)

Accuracy

Total 0.1b remaining (86%)

Threshold costs 0.1b (86%)

Counts

180 → 1

Compiler

Compiled 13734 to 11118 computations (19% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	21	19
2	22	19
3	20	19

end123.0ms (1.9%)

Compiler: Compiled 129 to 101 computations (21.7% saved)

Details

analyze117.0ms (1.8%)

sample1.8s (27.9%)

simplify124.0ms (2%)

prune7.0ms (0.1%)

localize19.0ms (0.3%)

series89.0ms (1.4%)

rewrite21.0ms (0.3%)

simplify111.0ms (1.7%)

prune234.0ms (3.7%)

localize10.0ms (0.1%)

series80.0ms (1.3%)

rewrite26.0ms (0.4%)

simplify141.0ms (2.2%)

prune419.0ms (6.6%)

localize22.0ms (0.3%)

series217.0ms (3.4%)

rewrite27.0ms (0.4%)

simplify139.0ms (2.2%)

prune333.0ms (5.2%)

localize11.0ms (0.2%)

series132.0ms (2.1%)

rewrite27.0ms (0.4%)

simplify130.0ms (2%)

prune586.0ms (9.2%)

regimes1.4s (22.6%)

simplify4.0ms (0.1%)

end123.0ms (1.9%)

Profiling