Details

analyze344.0ms (9.1%)

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 (0.8%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	9×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify98.0ms (2.6%)

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 (/.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)

localize9.0ms (0.2%)

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)))
✓	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series76.0ms (2%)

Counts

4 → 50

Calls

4 calls:

38.0ms	(/.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)))))
9.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite23.0ms (0.6%)

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)

simplify102.0ms (2.7%)

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

prune206.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	156	6	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	6	164

Error

Counts

164 → 6

Alt Table

Status	Error	Program
	2.0b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 a 9 -3)) 3)))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 rand)))))
	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))))))

Compiler

Compiled 3968 to 3073 computations (22.6% saved)

localize10.0ms (0.3%)

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 (-.f64 (*.f64 9 a) 3))))))
✓	0.1b	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))
✓	0.2b	(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
✓	0.5b	(/.f64 1 (-.f64 (*.f64 9 a) 3))

series75.0ms (2%)

Counts

4 → 38

Calls

4 calls:

33.0ms	(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
28.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
11.0ms	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))
3.0ms	(/.f64 1 (-.f64 (*.f64 9 a) 3))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
33×	`sqrt-prod_binary64`
31×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`

Counts

4 → 138

Calls

4 calls:

9.0ms	(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
8.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
4.0ms	(/.f64 1 (-.f64 (*.f64 9 a) 3))
4.0ms	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))

simplify115.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

176 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	3684
1	807	3416
2	2823	3149
3	5251	3149

prune270.0ms (7.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	256	5	261

Error

Counts

261 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	1.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 rand)))))
	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))))))

Compiler

Compiled 6793 to 5541 computations (18.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.1b	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.5b	(/.f64 1 (fma.f64 a 9 -3))

series62.0ms (1.6%)

Counts

4 → 36

Calls

4 calls:

34.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
13.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
11.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
29×	`sqrt-prod_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 117

Calls

4 calls:

10.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
0.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
571×	`times-frac_binary64`
332×	`distribute-rgt-in_binary64`
293×	`distribute-lft-in_binary64`
237×	`fma-neg_binary64`

Counts

153 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3027
1	656	2737
2	1975	2681
3	4916	2673
4	4930	2673

prune243.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

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

Error

Counts

203 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	1.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 rand)))))
	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))))))

Compiler

Compiled 5083 to 4014 computations (21% saved)

localize9.0ms (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))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.8b	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))

series85.0ms (2.2%)

Counts

3 → 50

Calls

3 calls:

34.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
32.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
19.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

rewrite48.0ms (1.3%)

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:

21.0ms	(*.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)

simplify166.0ms (4.4%)

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

prune292.0ms (7.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	292	5	297

Error

Counts

297 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	1.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 rand)))))
	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))))))

Compiler

Compiled 7764 to 6098 computations (21.5% saved)

regimes364.0ms (9.6%)

Accuracy

Total 0.1b remaining (81.3%)

Threshold costs 0.1b (81.3%)

Counts

76 → 1

Compiler

Compiled 5902 to 4750 computations (19.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	14	20
2	14	20

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample1.0s (26.3%)

Algorithm

1×

intervals

Results

623.0ms	8000×	body	128	valid
23.0ms	277×	body	128	nan
19.0ms	237×	body	128	invalid

Compiler

Compiled 133 to 105 computations (21.1% saved)

Details

analyze344.0ms (9.1%)

sample29.0ms (0.8%)

simplify98.0ms (2.6%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series76.0ms (2%)

rewrite23.0ms (0.6%)

simplify102.0ms (2.7%)

prune206.0ms (5.4%)

localize10.0ms (0.3%)

series75.0ms (2%)

rewrite33.0ms (0.9%)

simplify115.0ms (3%)

prune270.0ms (7.1%)

localize11.0ms (0.3%)

series62.0ms (1.6%)

rewrite21.0ms (0.5%)

simplify102.0ms (2.7%)

prune243.0ms (6.4%)

localize9.0ms (0.2%)

series85.0ms (2.2%)

rewrite48.0ms (1.3%)

simplify166.0ms (4.4%)

prune292.0ms (7.7%)

regimes364.0ms (9.6%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.0s (26.3%)

Profiling