Details

analyze105.0ms (2.2%)

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)

sample274.0ms (5.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid
0.0ms	6×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify101.0ms (2.1%)

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

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize8.0ms (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)))))
✓	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series74.0ms (1.5%)

Counts

4 → 50

Calls

4 calls:

34.0ms	(/.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)))))
11.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite20.0ms (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:

11.0ms	(*.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)

simplify112.0ms (2.3%)

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 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	2971
1	648	2791
2	2198	2639
3	4975	2621
4	4964	2621

prune243.0ms (5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	189	6	195
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	191	6	197

Error

0.0b

Counts

197 → 6

Alt Table

Status	Error	Program
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (fma.f64 a 9 -3)))))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	6.9b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	33.5b	(/.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 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))

Compiler

Compiled 4682 to 3626 computations (22.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
✓	0.9b	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))

series86.0ms (1.8%)

Counts

3 → 50

Calls

3 calls:

36.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
29.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
21.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
100×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
95×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`

Counts

3 → 189

Calls

3 calls:

20.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
6.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

simplify165.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-def_binary64`
625×	`distribute-rgt-in_binary64`
210×	`cancel-sign-sub-inv_binary64`
173×	`fma-neg_binary64`
135×	`associate-r_binary64`

Counts

239 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	5671
1	737	5018
2	2550	4808
3	4887	4790
4	4942	4790

prune383.0ms (7.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	299	6	305

Error

Counts

305 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 1 (-.f64 a 1/3)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)) (-.f64 a 1/3)))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (fma.f64 a 9 -3)))))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	6.9b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	33.5b	(/.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))

Compiler

Compiled 8094 to 6369 computations (21.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
	0.2b	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
	0.9b	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
✓	6.3b	(*.f64 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)) (-.f64 a 1/3))

series41.0ms (0.8%)

Counts

1 → 16

Calls

1 calls:

40.0ms

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

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`times-frac_binary64`
101×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64`
78×	`add-cube-cbrt_binary64`
71×	`associate-l_binary64`

Counts

1 → 135

Calls

1 calls:

20.0ms

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

simplify130.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
515×	`associate-/l*_binary64`
325×	`fma-def_binary64`
236×	`associate-/r/_binary64`
234×	`distribute-rgt-in_binary64`

Counts

151 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3467
1	533	3019
2	1799	3003
3	4846	3003
4	4935	3003

prune593.0ms (12.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	442	0	442
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	442	6	448

Error

Counts

448 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 1 (-.f64 a 1/3)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)) (-.f64 a 1/3)))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (fma.f64 a 9 -3)))))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	6.9b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	33.5b	(/.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))

Compiler

Compiled 14177 to 11121 computations (21.6% 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 (.f64 1 (fma.f64 a 9 -3))))))
✓	0.1b	(sqrt.f64 (*.f64 1 (fma.f64 a 9 -3)))
✓	0.2b	(/.f64 rand (sqrt.f64 (*.f64 1 (fma.f64 a 9 -3))))

series75.0ms (1.6%)

Counts

3 → 38

Calls

3 calls:

36.0ms	(/.f64 rand (sqrt.f64 (*.f64 1 (fma.f64 a 9 -3))))
30.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (fma.f64 a 9 -3))))))
9.0ms	(sqrt.f64 (*.f64 1 (fma.f64 a 9 -3)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`pow1_binary64`

Counts

3 → 79

Calls

3 calls:

13.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (fma.f64 a 9 -3))))))
4.0ms	(/.f64 rand (sqrt.f64 (*.f64 1 (fma.f64 a 9 -3))))
2.0ms	(sqrt.f64 (*.f64 1 (fma.f64 a 9 -3)))

simplify95.0ms (2%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
635×	`distribute-rgt-in_binary64`
486×	`times-frac_binary64`
191×	`cancel-sign-sub-inv_binary64`
155×	`fma-neg_binary64`

Counts

117 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	2600
1	629	2431
2	2160	2275
3	4942	2257
4	4933	2257

prune208.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	185	6	191

Error

Counts

191 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 1 (-.f64 a 1/3)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)) (-.f64 a 1/3)))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (fma.f64 a 9 -3)))))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	6.9b	(/.f64 (.f64 (-.f64 a 1/3) (-.f64 (.f64 1 1) (*.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	33.5b	(/.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))

Compiler

Compiled 4579 to 3614 computations (21.1% saved)

regimes945.0ms (19.5%)

Accuracy

Total 0.1b remaining (77.2%)

Threshold costs 0.1b (77.2%)

Counts

202 → 1

Compiler

Compiled 18258 to 14798 computations (19% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	22	22
2	20	22

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample1.0s (21.4%)

Algorithm

1×

intervals

Results

631.0ms	8000×	body	128	valid
24.0ms	288×	body	128	invalid
20.0ms	293×	body	128	nan

Compiler

Compiled 184 to 149 computations (19% saved)

Details

analyze105.0ms (2.2%)

sample274.0ms (5.7%)

simplify101.0ms (2.1%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series74.0ms (1.5%)

rewrite20.0ms (0.4%)

simplify112.0ms (2.3%)

prune243.0ms (5%)

localize10.0ms (0.2%)

series86.0ms (1.8%)

rewrite47.0ms (1%)

simplify165.0ms (3.4%)

prune383.0ms (7.9%)

localize11.0ms (0.2%)

series41.0ms (0.8%)

rewrite39.0ms (0.8%)

simplify130.0ms (2.7%)

prune593.0ms (12.3%)

localize10.0ms (0.2%)

series75.0ms (1.6%)

rewrite22.0ms (0.5%)

simplify95.0ms (2%)

prune208.0ms (4.3%)

regimes945.0ms (19.5%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.0s (21.4%)

Profiling