Details

analyze38.0ms (0.9%)

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)

sample1.2s (30%)

Results

934.0ms	8256×	body	128	valid
35.0ms	249×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify95.0ms (2.3%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	0.3b	(.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)

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

series67.0ms (1.6%)

Counts

4 → 50

Calls

4 calls:

31.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
25.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
10.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite20.0ms (0.5%)

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)

simplify109.0ms (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

prune188.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	156	8	164

Error

0.3b

Counts

164 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3)))))))
✓	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))
	0.8b	(.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))))))
	7.6b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
▶	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.5b	(.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 4111 to 3189 computations (22.4% 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 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
✓	0.2b	(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))

series72.0ms (1.8%)

Counts

4 → 38

Calls

4 calls:

33.0ms	(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
25.0ms	(.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 (0.8%)

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))))
7.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
5.0ms	(/.f64 1 (-.f64 (*.f64 9 a) 3))
5.0ms	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))

simplify92.0ms (2.2%)

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

prune351.0ms (8.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	252	3	255
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	256	7	263

Error

0.0b

Counts

263 → 7

Alt Table

Status	Error	Program
	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.8b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (fma.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) 1) (sqrt.f64 (+.f64 -1/3 a))))
▶	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	7.6b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3)))))))
	0.8b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (fma.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
	0.5b	(.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 6915 to 5641 computations (18.4% saved)

localize8.0ms (0.2%)

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 1/9 a)))))
✓	0.2b	(sqrt.f64 (/.f64 1/9 a))
✓	0.2b	(*.f64 rand (sqrt.f64 (/.f64 1/9 a)))
✓	0.4b	(/.f64 1/9 a)

series54.0ms (1.3%)

Counts

4 → 26

Calls

4 calls:

25.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
16.0ms	(*.f64 rand (sqrt.f64 (/.f64 1/9 a)))
6.0ms	(sqrt.f64 (/.f64 1/9 a))
6.0ms	(/.f64 1/9 a)

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

8.0ms	(*.f64 rand (sqrt.f64 (/.f64 1/9 a)))
6.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
2.0ms	(/.f64 1/9 a)
2.0ms	(sqrt.f64 (/.f64 1/9 a))

simplify116.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

635×	`distribute-rgt-in_binary64`
620×	`distribute-lft-in_binary64`
540×	`fma-def_binary64`
191×	`fma-neg_binary64`
167×	`associate-l_binary64`

Counts

150 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2299
1	451	2080
2	1486	2070
3	4864	2043
4	4954	2043

prune296.0ms (7.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	176	7	183

Error

0.0b

Counts

183 → 7

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	7.6b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
	0.4b	(+.f64 a (fma.f64 rand (fma.f64 1/3 (sqrt.f64 a) (*.f64 (sqrt.f64 (/.f64 1 a)) -1/9)) -1/3))
	0.5b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (.f64 (cbrt.f64 rand) (sqrt.f64 (/.f64 1/9 a))))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 1/3 rand) (sqrt.f64 a))))
	0.8b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (fma.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
▶	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))

Compiler

Compiled 3730 to 2794 computations (25.1% saved)

localize12.0ms (0.3%)

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))
✓	1.0b	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))

series80.0ms (2%)

Counts

3 → 50

Calls

3 calls:

36.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
26.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
18.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

rewrite46.0ms (1.1%)

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:

21.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
8.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

simplify180.0ms (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

prune341.0ms (8.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	293	6	299

Error

0.0b

Counts

299 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 -1/3 a)) -1/3))
	0.4b	(+.f64 a (fma.f64 rand (fma.f64 1/3 (sqrt.f64 a) (*.f64 (sqrt.f64 (/.f64 1 a)) -1/9)) -1/3))
	0.5b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (.f64 (cbrt.f64 rand) (sqrt.f64 (/.f64 1/9 a))))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 1/3 rand) (sqrt.f64 a))))
	0.8b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 (fma.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) 1) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
✓	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))

Compiler

Compiled 7783 to 6112 computations (21.5% saved)

regimes506.0ms (12.3%)

Accuracy

Total 0.2b remaining (91.6%)

Threshold costs 0.2b (91.6%)

Counts

113 → 1

Compiler

Compiled 9118 to 7294 computations (20% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	29	27
2	31	27
3	28	27

end111.0ms (2.7%)

Compiler: Compiled 151 to 117 computations (22.5% saved)

Details

analyze38.0ms (0.9%)

sample1.2s (30%)

simplify95.0ms (2.3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series67.0ms (1.6%)

rewrite20.0ms (0.5%)

simplify109.0ms (2.7%)

prune188.0ms (4.6%)

localize10.0ms (0.2%)

series72.0ms (1.8%)

rewrite33.0ms (0.8%)

simplify92.0ms (2.2%)

prune351.0ms (8.6%)

localize8.0ms (0.2%)

series54.0ms (1.3%)

rewrite24.0ms (0.6%)

simplify116.0ms (2.8%)

prune296.0ms (7.2%)

localize12.0ms (0.3%)

series80.0ms (2%)

rewrite46.0ms (1.1%)

simplify180.0ms (4.4%)

prune341.0ms (8.3%)

regimes506.0ms (12.3%)

simplify2.0ms (0.1%)

end111.0ms (2.7%)

Profiling