Details

analyze133.0ms (3.3%)

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
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	9.8%	72.7%	10
18.1%	8.8%	73.1%	11
19.6%	5.2%	75.2%	12
20%	4.5%	75.5%	13
20.7%	2.7%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.6s (39.7%)

Results

1.2s	8256×	body	128	valid
81.0ms	552×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify97.0ms (2.4%)

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)))))
	0.1b	(.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)))))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series131.0ms (3.2%)

Counts

4 → 50

Calls

4 calls:

88.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
29.0ms	(*.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))
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:

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)

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

prune181.0ms (4.4%)

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

0.0b

Counts

164 → 6

Alt Table

Status	Error	Program
	0.3b	(.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)))))))
	33.4b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (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))
	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 (cbrt.f64 rand) (cbrt.f64 rand)) (/.f64 (cbrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))

Compiler

Compiled 3974 to 3073 computations (22.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
✓	0.2b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.4b	(/.f64 1 (fma.f64 a 9 -3))

series101.0ms (2.5%)

Counts

4 → 36

Calls

4 calls:

69.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
18.0ms	(*.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:

9.0ms	(*.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 (2.5%)

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

prune266.0ms (6.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	198	6	204

Error

Counts

204 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3))
	0.3b	(.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)))))))
	16.9b	(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 -1/3 a)) 3)) -1/3))
	0.2b	(+.f64 a (fma.f64 rand (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) (+.f64 a -1/3))) -1/3))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))

Compiler

Compiled 5163 to 4084 computations (20.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a 9 -3)
✓	0.1b	(fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3)
✓	0.2b	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
✓	0.4b	(pow.f64 (fma.f64 a 9 -3) -1/2)

series54.0ms (1.3%)

Counts

3 → 32

Calls

3 calls:

34.0ms	(fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3)
14.0ms	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
5.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-l_binary64`

Counts

3 → 61

Calls

3 calls:

6.0ms	(*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))
1.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)
0.0ms	(fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3)

simplify126.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-def_binary64`
449×	`times-frac_binary64`
308×	`associate-/l*_binary64`
296×	`distribute-rgt-in_binary64`
287×	`distribute-lft-in_binary64`

Counts

93 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	216	2279
1	592	2026
2	1823	1894
3	4876	1866
4	4966	1866

prune227.0ms (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	150	6	156

Error

Counts

156 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3))
	0.3b	(.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)))))))
	16.9b	(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 -1/3 a)) 3)) -1/3))
	0.2b	(+.f64 a (fma.f64 rand (.f64 (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) -1/2)) (.f64 (pow.f64 (fma.f64 a 9 -3) -1/4) (+.f64 -1/3 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 3918 to 3073 computations (21.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(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))
✓	7.6b	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))

series35.0ms (0.9%)

Counts

1 → 16

Calls

1 calls:

35.0ms

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

rewrite13.0ms (0.3%)

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))))

simplify86.0ms (2.1%)

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

prune203.0ms (5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	178	6	184

Error

Counts

184 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3)) -1/3))
	0.3b	(.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)))))))
	0.1b	(+.f64 (+.f64 a -1/3) (.f64 (+.f64 a -1/3) (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))))
	16.9b	(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 -1/3 a)) 3)) -1/3))
	0.2b	(+.f64 a (fma.f64 rand (.f64 (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) -1/2)) (.f64 (pow.f64 (fma.f64 a 9 -3) -1/4) (+.f64 -1/3 a))) -1/3))

Compiler

Compiled 4472 to 3328 computations (25.6% saved)

regimes367.0ms (9%)

Accuracy

Total 0.1b remaining (82.5%)

Threshold costs 0.1b (82.5%)

Counts

79 → 1

Compiler

Compiled 6422 to 5082 computations (20.9% saved)

simplify2.0ms (0.1%)

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

end123.0ms (3%)

Compiler: Compiled 163 to 130 computations (20.2% saved)

Details

analyze133.0ms (3.3%)

sample1.6s (39.7%)

simplify97.0ms (2.4%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series131.0ms (3.2%)

rewrite23.0ms (0.6%)

simplify109.0ms (2.7%)

prune181.0ms (4.4%)

localize10.0ms (0.2%)

series101.0ms (2.5%)

rewrite21.0ms (0.5%)

simplify102.0ms (2.5%)

prune266.0ms (6.5%)

localize11.0ms (0.3%)

series54.0ms (1.3%)

rewrite10.0ms (0.2%)

simplify126.0ms (3.1%)

prune227.0ms (5.6%)

localize10.0ms (0.3%)

series35.0ms (0.9%)

rewrite13.0ms (0.3%)

simplify86.0ms (2.1%)

prune203.0ms (5%)

regimes367.0ms (9%)

simplify2.0ms (0.1%)

end123.0ms (3%)

Profiling