Details

analyze153.0ms (4%)

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 (33.6%)

Results

1.1s	8256×	body	128	valid
77.0ms	556×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify66.0ms (1.7%)

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 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)

localize10.0ms (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))

series58.0ms (1.5%)

Counts

4 → 50

Calls

4 calls:

27.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
24.0ms	(*.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))
2.0ms	(fma.f64 a 9 -3)

rewrite85.0ms (2.2%)

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:

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

simplify32.0ms (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

prune228.0ms (6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	157	7	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Error

0.0b

Counts

166 → 7

Alt Table

Status	Error	Program
	30.6b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 (sqrt.f64 rand) 1) (/.f64 (sqrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a 9 -3)) (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2))))))
	0.1b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))
	10.8b	(-.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 1/3) (+.f64 1 (.f64 (/.f64 1 (pow.f64 (fma.f64 a 9 -3) 1/4)) (/.f64 rand (pow.f64 (fma.f64 a 9 -3) 1/4)))))
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1)))))
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 3)

Compiler

Compiled 3714 to 2903 computations (21.8% saved)

localize10.0ms (0.3%)

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 (pow.f64 (fma.f64 a 9 -3) 1)))))
✓	0.2b	(/.f64 rand (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1)))
✓	0.4b	(sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1))

series61.0ms (1.6%)

Counts

3 → 38

Calls

3 calls:

30.0ms	(/.f64 rand (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1)))
25.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1)))))
6.0ms	(sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1))

rewrite59.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`prod-diff_binary64`
238×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`
135×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	299	35
2	3749	35

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

57.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1)))))
57.0ms	(/.f64 rand (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1)))
57.0ms	(sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1))

simplify31.0ms (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	1011
1	321	965
2	1143	813

Stop Event

1×	node limit

Counts

137 → 131

prune184.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	164	7	171

Error

0.0b

Counts

171 → 7

Alt Table

Status	Error	Program
	30.6b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 (sqrt.f64 rand) 1) (/.f64 (sqrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a 9 -3)) (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2))))))
▶	0.1b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))
	10.8b	(-.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 1/3) (+.f64 1 (.f64 (/.f64 1 (pow.f64 (fma.f64 a 9 -3) 1/4)) (/.f64 rand (pow.f64 (fma.f64 a 9 -3) 1/4)))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 1)))))
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 3)

Compiler

Compiled 3763 to 2962 computations (21.3% saved)

localize12.0ms (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))
✓	0.5b	(/.f64 1 (fma.f64 a 9 -3))

series49.0ms (1.3%)

Counts

4 → 36

Calls

4 calls:

30.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))
9.0ms	(*.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))

rewrite63.0ms (1.7%)

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:

58.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
58.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))
58.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
58.0ms	(/.f64 1 (fma.f64 a 9 -3))

simplify31.0ms (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

prune239.0ms (6.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	174	4	178
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	179	6	185

Error

Counts

185 → 6

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 -1/3 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (*.f64 a (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (-.f64 1/3 a))
	0.3b	(-.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) rand)) 3) (-.f64 1/3 a))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (pow.f64 (fma.f64 a 9 -3) 1/4)) (/.f64 rand (pow.f64 (fma.f64 a 9 -3) 1/4)))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a 9 -3)) (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2))))))
	0.1b	(-.f64 (.f64 rand (.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))) (-.f64 1/3 a))
	10.8b	(-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (.f64 rand (+.f64 -1/3 a))) (-.f64 1/3 a))

Compiler

Compiled 4501 to 3513 computations (22% 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))
✓	7.5b	(*.f64 a (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))

series28.0ms (0.7%)

Counts

1 → 16

Calls

1 calls:

28.0ms

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

rewrite36.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`log1p-expm1-u_binary64`
848×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`
85×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	189	13
2	2292	13

Stop Event

1×	node limit

Counts

1 → 24

Calls

1 calls:

35.0ms

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

simplify29.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

927×	`cancel-sign-sub-inv_binary64`
300×	`fma-neg_binary64`
233×	`distribute-rgt-neg-in_binary64`
218×	`distribute-neg-in_binary64`
188×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	396
1	156	387
2	536	355
3	2638	353

Stop Event

1×	node limit

Counts

40 → 33

prune326.0ms (8.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	243	6	249

Error

Counts

249 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 -1/3 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (*.f64 a (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (-.f64 1/3 a))
	0.3b	(-.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 a 9 -3))) rand)) 3) (-.f64 1/3 a))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (pow.f64 (fma.f64 a 9 -3) 1/4)) (/.f64 rand (pow.f64 (fma.f64 a 9 -3) 1/4)))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a 9 -3)) (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2))))))
	0.1b	(-.f64 (.f64 rand (.f64 (pow.f64 (fma.f64 a 9 -3) -1/2) (+.f64 a -1/3))) (-.f64 1/3 a))
	10.8b	(-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (.f64 rand (+.f64 -1/3 a))) (-.f64 1/3 a))

Compiler

Compiled 7048 to 5295 computations (24.9% saved)

regimes608.0ms (16%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

Counts

127 → 1

Compiler

Compiled 9806 to 7818 computations (20.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	27	21
2	29	21

Stop Event

1×

saturated

end117.0ms (3.1%)

Compiler: Compiled 162 to 130 computations (19.8% saved)

Details

analyze153.0ms (4%)

sample1.3s (33.6%)

simplify66.0ms (1.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series58.0ms (1.5%)

rewrite85.0ms (2.2%)

simplify32.0ms (0.8%)

prune228.0ms (6%)

localize10.0ms (0.3%)

series61.0ms (1.6%)

rewrite59.0ms (1.6%)

simplify31.0ms (0.8%)

prune184.0ms (4.8%)

localize12.0ms (0.3%)

series49.0ms (1.3%)

rewrite63.0ms (1.7%)

simplify31.0ms (0.8%)

prune239.0ms (6.3%)

localize10.0ms (0.3%)

series28.0ms (0.7%)

rewrite36.0ms (0.9%)

simplify29.0ms (0.8%)

prune326.0ms (8.5%)

regimes608.0ms (16%)

simplify2.0ms (0.1%)

end117.0ms (3.1%)

Profiling