Details

analyze122.0ms (3.7%)

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
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)

sample1.2s (36.1%)

Results

1.1s	8256×	body	128	valid
67.0ms	541×	body	128	invalid

Compiler

Compiled 46 to 40 computations (13% saved)

preprocess41.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

692×	`fma-def_binary64`
438×	`fma-neg_binary64`
227×	`sub-neg_binary64`
210×	`distribute-rgt-neg-in_binary64`
204×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	52	42
2	141	38
3	395	38
4	1005	38
5	1898	38
6	2873	38
7	4197	38
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify66.0ms (2%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.3b	(*.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 (0.2%)

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))

series58.0ms (1.8%)

Counts

4 → 50

Calls

18 calls:

6.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))	rand	-inf
6.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))	a	-inf
5.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))	rand	inf
4.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))	rand	0
4.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))	rand	inf

rewrite65.0ms (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

simplify32.0ms (1%)

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

prune176.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	159	5	164
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	160	6	166

Error

0.2b

Counts

166 → 6

Alt Table

Status	Error	Program
	2.7b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2)))))
	0.6b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) 3))))
✓	0.3b	(*.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 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	0.4b	(.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)))))
▶	0.3b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))

Compiler

Compiled 3611 to 2821 computations (21.9% saved)

localize10.0ms (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))

series45.0ms (1.4%)

Counts

4 → 36

Calls

15 calls:

6.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))	rand	0
5.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))	rand	-inf
4.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))	rand	inf
4.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))	a	-inf
4.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))	a	inf

rewrite59.0ms (1.8%)

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

simplify30.0ms (0.9%)

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 (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	179	5	184

Error

Counts

184 → 5

Alt Table

Status	Error	Program
	2.7b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2)))))
✓	0.3b	(*.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 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
	0.8b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3))) (-.f64 1/3 a))
✓	0.3b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))

Compiler

Compiled 4375 to 3412 computations (22% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.8b	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)

series81.0ms (2.5%)

Counts

3 → 48

Calls

18 calls:

7.0ms	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)	rand	inf
6.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))	a	-inf
6.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)	a	inf
6.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))	a	0
6.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))	a	inf

rewrite63.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`prod-diff_binary64`
154×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`
149×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	330	39
2	4126	39

Stop Event

1×	node limit

Counts

3 → 120

simplify37.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

375×	`times-frac_binary64`
313×	`associate-/l*_binary64`
286×	`fma-def_binary64`
277×	`associate--r+_binary64`
246×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1192
1	310	1112
2	1088	974

Stop Event

1×	node limit

Counts

168 → 152

prune166.0ms (5.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	182	5	187

Error

Counts

187 → 5

Alt Table

Status	Error	Program
	2.7b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2)))))
✓	0.3b	(*.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 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
▶	0.8b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3))) (-.f64 1/3 a))
✓	0.3b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))

Compiler

Compiled 4146 to 3273 computations (21.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series36.0ms (1.1%)

Counts

4 → 12

Calls

15 calls:

4.0ms	(*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3))	a	-inf
4.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)))	a	-inf
3.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)))	a	0
3.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)))	a	inf
3.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)))	rand	0

rewrite60.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
218×	`prod-diff_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
164×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	227	37
2	2988	37

Stop Event

1×	node limit

Counts

4 → 155

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-def_binary64`
467×	`fma-neg_binary64`
268×	`distribute-rgt-neg-in_binary64`
264×	`cancel-sign-sub-inv_binary64`
206×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	224
1	39	216
2	92	216
3	278	216
4	553	200
5	755	200
6	1057	200
7	1648	200
8	2852	200
9	3886	200
10	4326	200
11	4400	200
12	4406	200
13	4409	200

Stop Event

1×	node limit

Counts

167 → 159

prune199.0ms (6.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
	2.7b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2)))))
✓	0.3b	(*.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 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
✓	0.8b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3))) (-.f64 1/3 a))
✓	0.3b	(-.f64 (.f64 rand (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (-.f64 1/3 a))

Compiler

Compiled 3240 to 2233 computations (31.1% saved)

regimes384.0ms (11.7%)

Accuracy

Total 0.1b remaining (73.1%)

Threshold costs 0.1b (73.1%)

Counts

87 → 1

Compiler

Compiled 6174 to 4886 computations (20.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
11×	`+-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`
10×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	22	23
2	33	23
3	45	23
4	64	23
5	84	23
6	105	23
7	116	23
8	122	23
9	124	23

Stop Event

1×

saturated

end84.0ms (2.6%)

Stop Event

1×

fuel

Compiler

Compiled 120 to 95 computations (20.8% saved)

Details

analyze122.0ms (3.7%)

sample1.2s (36.1%)

preprocess41.0ms (1.3%)

simplify66.0ms (2%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series58.0ms (1.8%)

rewrite65.0ms (2%)

simplify32.0ms (1%)

prune176.0ms (5.3%)

localize10.0ms (0.3%)

series45.0ms (1.4%)

rewrite59.0ms (1.8%)

simplify30.0ms (0.9%)

prune181.0ms (5.5%)

localize9.0ms (0.3%)

series81.0ms (2.5%)

rewrite63.0ms (1.9%)

simplify37.0ms (1.1%)

prune166.0ms (5.1%)

localize8.0ms (0.2%)

series36.0ms (1.1%)

rewrite60.0ms (1.8%)

simplify68.0ms (2.1%)

prune199.0ms (6.1%)

regimes384.0ms (11.7%)

simplify3.0ms (0.1%)

end84.0ms (2.6%)

Profiling