Details

analyze458.0ms (5.8%)

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
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)

sample99.0ms (1.3%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
1.0ms	10×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify115.0ms (1.5%)

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)

localize15.0ms (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)))))
✓	0.1b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

rewrite41.0ms (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:

26.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
4.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
1.0ms	(sqrt.f64 (fma.f64 a 9 -3))
1.0ms	(fma.f64 a 9 -3)

series199.0ms (2.5%)

Counts

4 → 50

Calls

4 calls:

100.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
78.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
12.0ms	(sqrt.f64 (fma.f64 a 9 -3))
9.0ms	(fma.f64 a 9 -3)

simplify172.0ms (2.2%)

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 → 281

Iterations

Useful iterations: 3 (0.0ms)

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

prune476.0ms (6.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	275	6	281
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	276	7	283

Error

Counts

283 → 7

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 rand (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	7.9b	(-.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))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))

Compiler

Compiled 4716 to 3658 computations (22.4% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
✓	0.1b	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
✓	0.3b	(/.f64 1 (fma.f64 9 a -3))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))

rewrite34.0ms (0.4%)

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:

15.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
5.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
4.0ms	(/.f64 1 (fma.f64 9 a -3))
1.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)

series124.0ms (1.6%)

Counts

4 → 36

Calls

4 calls:

81.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
20.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
16.0ms	(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
5.0ms	(/.f64 1 (fma.f64 9 a -3))

simplify174.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

153 → 286

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3027
1	655	2737
2	1975	2681
3	4916	2673
4	4930	2673

prune636.0ms (8.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	286	7	293

Error

Counts

293 → 7

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 rand (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	7.9b	(-.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))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))

Compiler

Compiled 5699 to 4515 computations (20.8% saved)

localize17.0ms (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)
✓	1.0b	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))

rewrite74.0ms (0.9%)

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:

34.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
11.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
5.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

series222.0ms (2.8%)

Counts

3 → 50

Calls

3 calls:

92.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
76.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
53.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

simplify293.0ms (3.7%)

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 → 442

Iterations

Useful iterations: 3 (0.0ms)

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

prune773.0ms (9.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	475	0	475
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	475	7	482

Error

Counts

482 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 rand (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	7.9b	(-.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))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))

Compiler

Compiled 8068 to 6353 computations (21.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 9 a -3)
✓	0.1b	(sqrt.f64 (fma.f64 9 a -3))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
✓	8.1b	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`

Counts

4 → 115

Calls

4 calls:

14.0ms	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))
9.0ms	(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
2.0ms	(sqrt.f64 (fma.f64 9 a -3))
1.0ms	(fma.f64 9 a -3)

series223.0ms (2.8%)

Counts

4 → 48

Calls

4 calls:

103.0ms	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3))))
98.0ms	(/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))
13.0ms	(sqrt.f64 (fma.f64 9 a -3))
8.0ms	(fma.f64 9 a -3)

simplify139.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-/l*_binary64`
489×	`fma-def_binary64`
422×	`times-frac_binary64`
321×	`distribute-rgt-in_binary64`
308×	`distribute-lft-in_binary64`

Counts

163 → 311

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2948
1	554	2766
2	1907	2703
3	5158	2703

prune542.0ms (6.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	309	2	311
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	311	7	318

Error

Counts

318 → 7

Alt Table

Status	Error	Program
	0.2b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (cbrt.f64 (fma.f64 9 a -3))))))
	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 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 9 a -3)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	7.8b	(+.f64 (+.f64 a -1/3) (/.f64 (*.f64 (+.f64 a -1/3) rand) (sqrt.f64 (fma.f64 9 a -3))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
	0.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 9 a -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))

Compiler

Compiled 5210 to 3883 computations (25.5% saved)

regimes1.3s (16.1%)

Accuracy

Total 0.1b remaining (86.1%)

Threshold costs 0.1b (86.1%)

Compiler

Compiled 13234 to 10534 computations (20.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	16	21
2	16	21

end1.0ms (0%)

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

sample1.7s (21.2%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
33.0ms	257×	body	128	invalid
32.0ms	288×	body	128	nan

Compiler

Compiled 181 to 147 computations (18.8% saved)

Details

analyze458.0ms (5.8%)

sample99.0ms (1.3%)

simplify115.0ms (1.5%)

prune7.0ms (0.1%)

localize15.0ms (0.2%)

rewrite41.0ms (0.5%)

series199.0ms (2.5%)

simplify172.0ms (2.2%)

prune476.0ms (6.1%)

localize24.0ms (0.3%)

rewrite34.0ms (0.4%)

series124.0ms (1.6%)

simplify174.0ms (2.2%)

prune636.0ms (8.1%)

localize17.0ms (0.2%)

rewrite74.0ms (0.9%)

series222.0ms (2.8%)

simplify293.0ms (3.7%)

prune773.0ms (9.9%)

localize17.0ms (0.2%)

rewrite37.0ms (0.5%)

series223.0ms (2.8%)

simplify139.0ms (1.8%)

prune542.0ms (6.9%)

regimes1.3s (16.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.7s (21.2%)

Profiling