Details

analyze8.0ms (0.4%)

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)

sample998.0ms (50.1%)

Results

986.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 42 to 32 computations (23.8% saved)

preprocess34.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

598×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
403×	`associate-/l*_binary64`
348×	`distribute-lft-in_binary64`
224×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	89	27
3	238	27
4	710	27
5	1695	25
6	2919	25
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 15 computations (25% saved)

simplify22.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
403×	`associate-/l*_binary64`
348×	`distribute-lft-in_binary64`
224×	`fma-neg_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	89	27
3	238	27
4	710	27
5	1695	25
6	2919	25

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.2%)

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

Compiler

Compiled 73 to 56 computations (23.3% saved)

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.9%)

Counts

2 → 24

Calls

6 calls:

4.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))	v	-inf
4.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))	v	inf
4.0ms	(.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1)))	v	0
2.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))	v	0
2.0ms	(.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1)))	v	-inf

rewrite46.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	294	36
2	3185	36

Stop Event

1×	node limit

Counts

2 → 40

simplify41.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

831×	`times-frac_binary64`
389×	`fma-def_binary64`
358×	`cancel-sign-sub-inv_binary64`
309×	`associate-l_binary64`
285×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	805
1	234	749
2	926	631
3	4725	631

Stop Event

1×	node limit

Counts

64 → 67

prune56.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Error

Counts

68 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))
▶	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))))
	1.0b	(pow.f64 (sqrt.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))) 2)

Compiler

Compiled 1780 to 1488 computations (16.4% saved)

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1)))
✓	0.0b	(log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))))
✓	0.0b	(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1)))))

series39.0ms (1.9%)

Counts

3 → 36

Calls

9 calls:

12.0ms	(log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))	v	0
5.0ms	(log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))	v	inf
5.0ms	(log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))	v	-inf
4.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))))	v	inf
4.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))))	v	-inf

rewrite55.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

352×	`prod-diff_binary64`
246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
216×	`log-pow_binary64`
141×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	53
1	313	53
2	3333	53

Stop Event

1×	node limit

Counts

3 → 77

simplify52.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
616×	`times-frac_binary64`
429×	`cancel-sign-sub-inv_binary64`
224×	`distribute-neg-in_binary64`
201×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	1551
1	551	1409
2	2163	1368

Stop Event

1×	node limit

Counts

113 → 128

prune139.0ms (7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))))
▶	1.0b	(pow.f64 (sqrt.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))) 2)

Compiler

Compiled 4510 to 3757 computations (16.7% saved)

localize12.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2))
✓	0.0b	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))
✓	1.0b	(pow.f64 (sqrt.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))) 2)

series65.0ms (3.3%)

Counts

3 → 28

Calls

9 calls:

28.0ms	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))	v	-inf
11.0ms	(pow.f64 (sqrt.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))) 2)	v	inf
10.0ms	(pow.f64 (sqrt.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))) 2)	v	-inf
4.0ms	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))	v	inf
3.0ms	(pow.f64 (sqrt.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))) 2)	v	0

rewrite88.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`log-prod_binary64`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`
204×	`log-pow_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	59
1	315	59
2	3211	59

Stop Event

1×	node limit

Counts

3 → 88

simplify33.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

574×	`fma-def_binary64`
466×	`cancel-sign-sub-inv_binary64`
375×	`associate-l_binary64`
357×	`associate-r_binary64`
258×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1118
1	323	1054
2	1275	921

Stop Event

1×	node limit

Counts

116 → 120

prune98.0ms (4.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	120	3	123

Error

Counts

123 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 2) (.f64 -1/4 (fma.f64 v v -1))))))
✓	1.0b	(pow.f64 (sqrt.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 (fma.f64 v (.f64 v -3) 1) 2)))) 2)

Compiler

Compiled 3467 to 2760 computations (20.4% saved)

regimes74.0ms (3.7%)

Accuracy

Total 0.0b remaining (67.4%)

Threshold costs 0.0b (67.4%)

Counts

22 → 1

Compiler

Compiled 1265 to 1001 computations (20.9% 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	17	29
1	23	29

Stop Event

1×

saturated

end82.0ms (4.1%)

Stop Event

1×

done

Compiler

Compiled 98 to 78 computations (20.4% saved)

Details

analyze8.0ms (0.4%)

sample998.0ms (50.1%)

preprocess34.0ms (1.7%)

simplify22.0ms (1.1%)

prune5.0ms (0.2%)

localize10.0ms (0.5%)

series18.0ms (0.9%)

rewrite46.0ms (2.3%)

simplify41.0ms (2.1%)

prune56.0ms (2.8%)

localize14.0ms (0.7%)

series39.0ms (1.9%)

rewrite55.0ms (2.8%)

simplify52.0ms (2.6%)

prune139.0ms (7%)

localize12.0ms (0.6%)

series65.0ms (3.3%)

rewrite88.0ms (4.4%)

simplify33.0ms (1.7%)

prune98.0ms (4.9%)

regimes74.0ms (3.7%)

simplify2.0ms (0.1%)

end82.0ms (4.1%)

Profiling