Details

analyze9.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample1.4s (49.2%)

Results

1.3s	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 62 to 47 computations (24.2% saved)

simplify76.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

750×	`div-sub_binary64`
748×	`fma-neg_binary64`
599×	`fma-def_binary64`
502×	`associate-/l*_binary64`
423×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	27
3	201	27
4	526	27
5	991	25
6	1614	25
7	3273	25
8	3653	25
9	4694	25
10	4942	25

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

Compiler

Compiled 73 to 56 computations (23.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

series23.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

11.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))))

7.0ms

(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

5.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))

rewrite60.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

629×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
202×	`log-pow_binary64`
134×	`add-sqr-sqrt_binary64`

Counts

3 → 71

Calls

3 calls:

58.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))

58.0ms

(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

58.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	55
1	292	53
2	3049	53
3	4979	53
0	0	0
1	0	0

simplify65.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
690×	`fma-neg_binary64`
569×	`cancel-sign-sub-inv_binary64`
444×	`times-frac_binary64`
381×	`associate-/r*_binary64`

Counts

107 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1310
1	444	1257
2	1628	1102
3	4372	1098
4	5183	1098

prune165.0ms (5.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	3	136

Error

Counts

136 → 3

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
▶	0.0b	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))

Compiler

Compiled 3581 to 2977 computations (16.9% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))
✓	0.0b	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))

series16.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))
6.0ms	(sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))

rewrite121.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

578×	`log-prod_binary64`
219×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`
198×	`pow3_binary64`
187×	`log-pow_binary64`

Counts

2 → 48

Calls

2 calls:

120.0ms	(sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))
120.0ms	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	273	36
2	2845	36
3	4989	36
4	4834	36
0	0	0
1	0	0

simplify58.0ms (2%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-def_binary64`
466×	`cancel-sign-sub-inv_binary64`
382×	`associate-l_binary64`
363×	`associate-r_binary64`
258×	`associate-/r*_binary64`

Counts

72 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1016
1	322	968
2	1220	849
3	4538	849
4	5098	849

prune184.0ms (6.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	91	3	94

Error

Counts

94 → 3

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.0b	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))

Compiler

Compiled 2456 to 2052 computations (16.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.1b	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))
✓	0.2b	(*.f64 (pow.f64 v 2) (sqrt.f64 2))

series15.0ms (0.5%)

Counts

3 → 3

Calls

3 calls:

6.0ms	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
5.0ms	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))
4.0ms	(*.f64 (pow.f64 v 2) (sqrt.f64 2))

rewrite98.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

982×	`prod-diff_binary64`
238×	`egg-rr`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
113×	`add-sqr-sqrt_binary64`

Counts

3 → 238

Calls

3 calls:

90.0ms	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
90.0ms	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))
90.0ms	(*.f64 (pow.f64 v 2) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	245	36
2	2739	36
3	4980	36
0	0	0
1	0	0

simplify134.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
661×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
611×	`cube-prod_binary64`
310×	`cube-mult_binary64`

Counts

241 → 241

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	20	30
2	38	30
3	74	30
4	176	30
5	500	30
6	631	30
7	868	30
8	893	30
9	1003	30
10	1121	30
11	1288	30
12	1452	30
13	1680	30
14	2014	30
15	2409	30
16	2967	30
17	3651	30
18	3876	30
19	4141	30
20	4233	30
21	4267	30
22	4288	30
23	4971	30

prune251.0ms (8.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	241	3	244

Error

Counts

244 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.0b	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))

Compiler

Compiled 8421 to 6566 computations (22% saved)

regimes77.0ms (2.7%)

Accuracy

Total 0.0b remaining (65.8%)

Threshold costs 0.0b (65.8%)

Counts

26 → 1

Compiler

Compiled 1360 to 1127 computations (17.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	21	25
2	20	25

end66.0ms (2.3%)

Compiler: Compiled 85 to 68 computations (20% saved)

Details

analyze9.0ms (0.3%)

sample1.4s (49.2%)

simplify76.0ms (2.7%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series23.0ms (0.8%)

rewrite60.0ms (2.1%)

simplify65.0ms (2.3%)

prune165.0ms (5.8%)

localize10.0ms (0.4%)

series16.0ms (0.6%)

rewrite121.0ms (4.2%)

simplify58.0ms (2%)

prune184.0ms (6.5%)

localize8.0ms (0.3%)

series15.0ms (0.5%)

rewrite98.0ms (3.4%)

simplify134.0ms (4.7%)

prune251.0ms (8.8%)

regimes77.0ms (2.7%)

simplify2.0ms (0.1%)

end66.0ms (2.3%)

Profiling