Details

analyze165.0ms (4.5%)

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)

sample1.3s (35.9%)

Results

1.2s	8256×	body	128	valid
84.0ms	603×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify69.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
177×	`cancel-sign-sub-inv_binary64`
156×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	82	19
3	199	19
4	510	19
5	969	19
6	1470	19
7	2421	19
8	3626	19
9	4073	19
10	4231	19
11	4272	19
12	4275	19
13	4828	19
14	4828	19

Stop Event

1×

saturated

Counts

1 → 2

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)

localize11.0ms (0.3%)

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))

series53.0ms (1.5%)

Counts

4 → 50

Calls

4 calls:

25.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
21.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
6.0ms	(sqrt.f64 (fma.f64 a 9 -3))
1.0ms	(fma.f64 a 9 -3)

rewrite61.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`prod-diff_binary64`
237×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	288	40
2	3706	40

Stop Event

1×	node limit

Counts

4 → 127

Calls

4 calls:

59.0ms	(fma.f64 a 9 -3)
59.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
59.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
59.0ms	(sqrt.f64 (fma.f64 a 9 -3))

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

374×	`fma-def_binary64`
347×	`associate-+l+_binary64`
282×	`associate-/l*_binary64`
276×	`times-frac_binary64`
231×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1065
1	321	1019
2	1143	867

Stop Event

1×	node limit

Counts

177 → 164

prune167.0ms (4.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	4	166

Error

Counts

166 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (.f64 9 a) 3)))))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
▶	0.1b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))
	8.6b	(-.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))

Compiler

Compiled 3568 to 2783 computations (22% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.2b	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.4b	(/.f64 1 (fma.f64 a 9 -3))

series46.0ms (1.3%)

Counts

4 → 36

Calls

4 calls:

27.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))
10.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
7.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite56.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
209×	`prod-diff_binary64`
194×	`log-pow_binary64`
156×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	280	45
2	3417	45

Stop Event

1×	node limit

Counts

4 → 140

Calls

4 calls:

54.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
54.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))
54.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
54.0ms	(/.f64 1 (fma.f64 a 9 -3))

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-def_binary64`
457×	`times-frac_binary64`
358×	`associate-+l+_binary64`
317×	`associate-/l*_binary64`
179×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	861
1	380	818
2	1291	769

Stop Event

1×	node limit

Counts

176 → 178

prune181.0ms (5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	178	4	182

Error

Counts

182 → 4

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (.f64 9 a) 3)))))
	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
✓	0.1b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))
	8.6b	(-.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))

Compiler

Compiled 4386 to 3422 computations (22% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (*.f64 9 a) 3))))
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (.f64 9 a) 3)))))
✓	0.2b	(/.f64 rand (sqrt.f64 (-.f64 (*.f64 9 a) 3)))
✓	0.4b	(sqrt.f64 (-.f64 (*.f64 9 a) 3))

series73.0ms (2%)

Counts

4 → 54

Calls

4 calls:

26.0ms	(/.f64 rand (sqrt.f64 (-.f64 (*.f64 9 a) 3)))
23.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (.f64 9 a) 3)))))
18.0ms	(+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (*.f64 9 a) 3))))
6.0ms	(sqrt.f64 (-.f64 (*.f64 9 a) 3))

rewrite85.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`
146×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	318	47
2	4180	47

Stop Event

1×	node limit

Counts

4 → 134

Calls

4 calls:

83.0ms	(+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (*.f64 9 a) 3))))
83.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (.f64 9 a) 3)))))
83.0ms	(/.f64 rand (sqrt.f64 (-.f64 (*.f64 9 a) 3)))
83.0ms	(sqrt.f64 (-.f64 (*.f64 9 a) 3))

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

397×	`fma-def_binary64`
368×	`associate-+l+_binary64`
282×	`associate-/l*_binary64`
276×	`times-frac_binary64`
220×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1359
1	338	1298
2	1212	1099

Stop Event

1×	node limit

Counts

188 → 177

prune219.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	177	4	181

Error

Counts

181 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (.f64 9 a) 3)))))
▶	0.1b	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1))
✓	0.1b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))
	8.6b	(-.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))

Compiler

Compiled 4007 to 3104 computations (22.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 9 a -3)
✓	0.1b	(fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1)
✓	0.1b	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1))
✓	0.3b	(pow.f64 (fma.f64 9 a -3) -1/2)

series199.0ms (5.5%)

Counts

4 → 72

Calls

4 calls:

131.0ms	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1))
62.0ms	(fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1)
4.0ms	(pow.f64 (fma.f64 9 a -3) -1/2)
1.0ms	(fma.f64 9 a -3)

rewrite51.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log-prod_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
184×	`log-pow_binary64`
129×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	275	43
2	3073	43

Stop Event

1×	node limit

Counts

4 → 102

Calls

4 calls:

50.0ms	(fma.f64 9 a -3)
50.0ms	(fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1)
50.0ms	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1))
50.0ms	(pow.f64 (fma.f64 9 a -3) -1/2)

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-l_binary64`
352×	`times-frac_binary64`
343×	`associate-r_binary64`
237×	`fma-neg_binary64`
221×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2325
1	548	2209
2	1753	1855

Stop Event

1×	node limit

Counts

174 → 189

prune192.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	189	4	193

Error

Counts

193 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (-.f64 (.f64 9 a) 3)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 9 a -3) -1/2) 1))
✓	0.1b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))
	8.6b	(-.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))

Compiler

Compiled 4539 to 3633 computations (20% saved)

regimes410.0ms (11.3%)

Accuracy

Total 0.1b remaining (74.1%)

Threshold costs 0.1b (74.1%)

Counts

95 → 1

Compiler

Compiled 7018 to 5570 computations (20.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	14	21

Stop Event

1×

saturated

end82.0ms (2.3%)

Compiler: Compiled 115 to 91 computations (20.9% saved)

Details

analyze165.0ms (4.5%)

sample1.3s (35.9%)

simplify69.0ms (1.9%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

series53.0ms (1.5%)

rewrite61.0ms (1.7%)

simplify30.0ms (0.8%)

prune167.0ms (4.6%)

localize11.0ms (0.3%)

series46.0ms (1.3%)

rewrite56.0ms (1.5%)

simplify28.0ms (0.8%)

prune181.0ms (5%)

localize10.0ms (0.3%)

series73.0ms (2%)

rewrite85.0ms (2.3%)

simplify63.0ms (1.7%)

prune219.0ms (6%)

localize11.0ms (0.3%)

series199.0ms (5.5%)

rewrite51.0ms (1.4%)

simplify55.0ms (1.5%)

prune192.0ms (5.3%)

regimes410.0ms (11.3%)

simplify2.0ms (0.1%)

end82.0ms (2.3%)

Profiling