Details

analyze128.0ms (2.9%)

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
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)

sample1.5s (33.4%)

Results

1.1s	8256×	body	128	valid
74.0ms	549×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify96.0ms (2.2%)

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

series67.0ms (1.5%)

Counts

4 → 41

Calls

4 calls:

24.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
23.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
11.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
8.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite60.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
26×	`associate-l_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 134

Calls

4 calls:

16.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
14.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
14.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
8.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-in_binary64`
675×	`times-frac_binary64`
199×	`associate-r_binary64`
193×	`cancel-sign-sub-inv_binary64`
178×	`associate-l_binary64`

Counts

175 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	3587
1	771	3326
2	2767	3268
3	5441	3268

prune303.0ms (6.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	245	4	249
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	247	4	251

Error

0.0b

Counts

251 → 4

Alt Table

Status	Error	Program
	7.6b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand) (.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)) (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))))
	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3)))) rand)))
	0.1b	(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
▶	0.1b	(pow.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))) 1)

Compiler

Compiled 7651 to 6452 computations (15.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 a 1/3) 9)
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
✓	0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
✓	0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

series56.0ms (1.3%)

Counts

4 → 49

Calls

4 calls:

24.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
22.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
2.0ms	(*.f64 (-.f64 a 1/3) 9)

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`

Counts

4 → 107

Calls

4 calls:

12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
7.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(*.f64 (-.f64 a 1/3) 9)
4.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify79.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
701×	`distribute-rgt-in_binary64`
517×	`times-frac_binary64`
141×	`cancel-sign-sub-inv_binary64`
130×	`associate-r_binary64`

Counts

156 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	3034
1	695	2620
2	2356	2572
3	5357	2572

prune233.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	211	4	215

Error

0.0b

Counts

215 → 4

Alt Table

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

Compiler

Compiled 5518 to 4417 computations (20% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series25.0ms (0.6%)

Counts

2 → 22

Calls

2 calls:

14.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
11.0ms	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
6×	`sqrt-prod_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

6.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
1.0ms	(fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a)

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

424×	`associate-/l/_binary64`
394×	`fma-neg_binary64`
253×	`associate-l_binary64`
251×	`associate-r_binary64`
244×	`times-frac_binary64`

Counts

60 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	931
1	253	874
2	759	866
3	2627	863
4	4884	859
5	5002	859

prune83.0ms (1.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	79	4	83

Error

0.0b

Counts

83 → 4

Alt Table

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

Compiler

Compiled 1635 to 1245 computations (23.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series54.0ms (1.2%)

Counts

3 → 37

Calls

3 calls:

23.0ms	(*.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3)))) rand)
22.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3)))) rand)))
9.0ms	(/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3))))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
76×	`*-un-lft-identity_binary64`
57×	`sqrt-prod_binary64`
47×	`associate-l_binary64`

Counts

3 → 159

Calls

3 calls:

14.0ms	(*.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3)))) rand)
9.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3)))) rand)))
7.0ms	(/.f64 1/3 (sqrt.f64 (-.f64 a (/.f64 1 3))))

simplify105.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
511×	`times-frac_binary64`
181×	`associate-r_binary64`
178×	`cancel-sign-sub-inv_binary64`
170×	`associate-l_binary64`

Counts

196 → 264

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	4172
1	824	3918
2	2829	3866
3	5375	3866

prune306.0ms (6.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	264	0	264
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	264	4	268

Error

0.0b

Counts

268 → 4

Alt Table

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

Compiler

Compiled 7897 to 6563 computations (16.9% saved)

regimes963.0ms (21.8%)

Accuracy

Total 0.1b remaining (72.3%)

Threshold costs 0.1b (72.3%)

Counts

158 → 1

Compiler

Compiled 16752 to 14233 computations (15% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	24	22
2	25	22
3	22	22

end91.0ms (2.1%)

Compiler: Compiled 134 to 112 computations (16.4% saved)

Details

analyze128.0ms (2.9%)

sample1.5s (33.4%)

simplify96.0ms (2.2%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series67.0ms (1.5%)

rewrite60.0ms (1.4%)

simplify98.0ms (2.2%)

prune303.0ms (6.9%)

localize9.0ms (0.2%)

series56.0ms (1.3%)

rewrite32.0ms (0.7%)

simplify79.0ms (1.8%)

prune233.0ms (5.3%)

localize6.0ms (0.1%)

series25.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify62.0ms (1.4%)

prune83.0ms (1.9%)

localize8.0ms (0.2%)

series54.0ms (1.2%)

rewrite46.0ms (1.1%)

simplify105.0ms (2.4%)

prune306.0ms (6.9%)

regimes963.0ms (21.8%)

simplify2.0ms (0%)

end91.0ms (2.1%)

Profiling