Details

analyze702.0ms (10.7%)

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
0%	50%	50%	5
0%	37.5%	62.5%	6
0%	37.5%	62.5%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	27.7%	72.3%	10
0%	27.5%	72.5%	11
0%	25.7%	74.3%	12
0%	25.5%	74.5%	13
0%	24.6%	75.4%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample2.1s (31.9%)

Results

1.3s	8256×	body	128	valid
465.0ms	539×	body	8192	exit
62.0ms	437×	body	128	invalid

Compiler

Compiled 45 to 39 computations (13.3% saved)

simplify98.0ms (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

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
	0.2b	(.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)

localize8.0ms (0.1%)

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 (1.2%)

Counts

4 → 50

Calls

4 calls:

40.0ms	(/.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)))))
9.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite22.0ms (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:

13.0ms	(*.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 (1.6%)

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

prune214.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Error

0.0b

Counts

164 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (-.f64 a 1/3) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (.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))))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	11.6b	(-.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))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
▶	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	1.4b	(.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)))))))
	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3)))))))

Compiler

Compiled 4184 to 3253 computations (22.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(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))
✓	6.6b	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))

series37.0ms (0.6%)

Counts

1 → 16

Calls

1 calls:

36.0ms

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
20×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 49

Calls

1 calls:

9.0ms

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

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-l_binary64`
351×	`associate-/l*_binary64`
343×	`fma-def_binary64`
306×	`associate-*r/_binary64`
296×	`associate-*l/_binary64`

Counts

65 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	1455
1	384	1345
2	1345	1327
3	4385	1327
4	4640	1327
5	4988	1327

prune290.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	172	6	178
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	178	8	186

Error

Counts

186 → 8

Alt Table

Status	Error	Program
	0.9b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (+.f64 a -1/3) (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))
▶	0.1b	(+.f64 (+.f64 a -1/3) (.f64 (+.f64 a -1/3) (.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.3b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (.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))))))
	0.4b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (+.f64 a -1/3) (*.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	11.6b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 rand (-.f64 a 1/3)) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.5b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))

Compiler

Compiled 4797 to 3580 computations (25.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(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))
✓	6.6b	(.f64 (+.f64 a -1/3) (.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

series40.0ms (0.6%)

Counts

1 → 16

Calls

1 calls:

40.0ms

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

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
9×	`prod-exp_binary64`
6×	`pow1_binary64`
5×	`cbrt-unprod_binary64`

Counts

1 → 30

Calls

1 calls:

10.0ms

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

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

432×	`times-frac_binary64`
384×	`associate-l_binary64`
350×	`associate-r_binary64`
338×	`fma-def_binary64`
329×	`fma-neg_binary64`

Counts

46 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1065
1	320	922
2	1009	900
3	3837	893
4	4881	893
5	4912	893

prune226.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	146	8	154

Error

Counts

154 → 8

Alt Table

Status	Error	Program
	0.9b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (+.f64 a -1/3) (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))
✓	0.1b	(+.f64 (+.f64 a -1/3) (.f64 (+.f64 a -1/3) (.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.3b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 (/.f64 rand (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (.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))))))
	0.4b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (+.f64 a -1/3) (*.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	11.6b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 rand (-.f64 a 1/3)) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.5b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))

Compiler

Compiled 4126 to 3179 computations (23% 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))
✓	0.5b	(/.f64 1 (fma.f64 a 9 -3))

series61.0ms (0.9%)

Counts

4 → 36

Calls

4 calls:

33.0ms	(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))
12.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite23.0ms (0.3%)

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:

12.0ms	(*.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)

simplify113.0ms (1.7%)

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

prune319.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	199	7	206

Error

Counts

206 → 7

Alt Table

Status	Error	Program
	11.6b	(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 -1/3 a)) -1/3))
✓	0.1b	(+.f64 (+.f64 a -1/3) (.f64 (+.f64 a -1/3) (.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.5b	(+.f64 a (fma.f64 rand (.f64 (sqrt.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 a 2))) (*.f64 1/9 (/.f64 1 a)))) (+.f64 a -1/3)) -1/3))
	0.3b	(+.f64 a (fma.f64 rand (.f64 (.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 (fma.f64 a 9 -3))))) (sqrt.f64 (/.f64 1 (cbrt.f64 (fma.f64 a 9 -3))))) (+.f64 a -1/3)) -1/3))
	0.4b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (+.f64 a -1/3) (*.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.4b	(+.f64 a (fma.f64 rand (.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 (cbrt.f64 (+.f64 a -1/3)) (cbrt.f64 (+.f64 a -1/3)))) (cbrt.f64 (+.f64 a -1/3))) -1/3))
	0.5b	(+.f64 (+.f64 a -1/3) (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))

Compiler

Compiled 5122 to 4048 computations (21% saved)

regimes1.8s (26.9%)

Accuracy

Total 0.1b remaining (81.5%)

Threshold costs 0.1b (81.5%)

Counts

290 → 1

Compiler

Compiled 27018 to 21426 computations (20.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	25	27
2	26	27
3	24	27

end156.0ms (2.4%)

Compiler: Compiled 245 to 194 computations (20.8% saved)

Details

analyze702.0ms (10.7%)

sample2.1s (31.9%)

simplify98.0ms (1.5%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series76.0ms (1.2%)

rewrite22.0ms (0.3%)

simplify102.0ms (1.6%)

prune214.0ms (3.3%)

localize8.0ms (0.1%)

series37.0ms (0.6%)

rewrite14.0ms (0.2%)

simplify82.0ms (1.2%)

prune290.0ms (4.4%)

localize10.0ms (0.1%)

series40.0ms (0.6%)

rewrite12.0ms (0.2%)

simplify75.0ms (1.1%)

prune226.0ms (3.4%)

localize11.0ms (0.2%)

series61.0ms (0.9%)

rewrite23.0ms (0.3%)

simplify113.0ms (1.7%)

prune319.0ms (4.9%)

regimes1.8s (26.9%)

simplify2.0ms (0%)

end156.0ms (2.4%)

Profiling