Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample1.0s (34%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 84 to 60 computations (28.6% saved)

preprocess32.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

116×	`fma-def_binary64`
43×	`distribute-rgt-in_binary64`
39×	`distribute-lft-in_binary64`
25×	`*-commutative_binary64`
17×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	70
1	88	70
2	184	70
3	289	70
4	343	70
0	4	4
1	4	4

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort b c d)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
10×	`distribute-lft-in_binary64`
10×	`distribute-rgt-in_binary64`
7×	`*-commutative_binary64`
6×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	45	10
3	85	10
4	103	10

Stop Event

1×

saturated

Counts

1 → 2

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 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 40 to 24 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 b (+.f64 c d))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

series14.0ms (0.5%)

Counts

2 → 84

Calls

21 calls:

2.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	b	inf
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	a	-inf
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	b	-inf
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	a	0
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	d	-inf

rewrite57.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

475×	`log-prod_binary64`
429×	`fma-def_binary64`
216×	`fma-neg_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	185	17
2	2889	17

Stop Event

1×	node limit

Counts

2 → 133

simplify21.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

24×	`fma-def_binary64`
7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`distribute-rgt-in_binary64`
4×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	642
1	45	642
2	67	642
3	75	642

Stop Event

1×

saturated

Counts

217 → 149

prune179.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Error

0.0b

Counts

150 → 3

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))
▶	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 1947 to 597 computations (69.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))

series43.0ms (1.4%)

Counts

1 → 48

Calls

12 calls:

32.0ms	(fma.f64 a (+.f64 b c) (*.f64 a d))	d	0
1.0ms	(fma.f64 a (+.f64 b c) (*.f64 a d))	a	-inf
1.0ms	(fma.f64 a (+.f64 b c) (*.f64 a d))	a	inf
1.0ms	(fma.f64 a (+.f64 b c) (*.f64 a d))	d	-inf
1.0ms	(fma.f64 a (+.f64 b c) (*.f64 a d))	a	0

rewrite71.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

850×	`log1p-expm1-u_binary64`
850×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
89×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	168	10
2	2260	10

Stop Event

1×	node limit

Counts

1 → 24

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

27×	`fma-def_binary64`
9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`distribute-rgt-in_binary64`
5×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	437
1	39	435
2	70	435
3	86	435
4	87	435

Stop Event

1×

saturated

Counts

72 → 36

prune16.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	36	3	39

Error

0.0b

Counts

39 → 3

Alt Table

Status	Error	Program
▶	0.5b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))
✓	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 435 to 124 computations (71.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 c d))
✓	0.2b	(*.f64 (sqrt.f64 (+.f64 c d)) a)
✓	0.3b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))

series180.0ms (6%)

Counts

3 → 60

Calls

27 calls:

45.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))	d	0
20.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))	c	0
15.0ms	(*.f64 (sqrt.f64 (+.f64 c d)) a)	c	inf
13.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))	c	inf
13.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))	d	inf

rewrite48.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

646×	`prod-diff_binary64`
223×	`fma-def_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
124×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	208	28
2	2725	26

Stop Event

1×	node limit

Counts

3 → 65

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary64`
419×	`fma-def_binary64`
361×	`associate-l_binary64`
311×	`associate-r_binary64`
283×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	953
1	279	887
2	816	863
3	2765	839
4	4487	839

Stop Event

1×	node limit

Counts

125 → 106

prune87.0ms (2.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	146	4	150

Error

Counts

150 → 4

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))
✓	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))
▶	1.9b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 3021 to 1110 computations (63.3% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c (*.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))
✓	0.1b	(sqrt.f64 (/.f64 1 d))
✓	0.2b	(.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d)))
✓	0.3b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))

series151.0ms (5%)

Counts

4 → 64

Calls

30 calls:

13.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))	d	inf
13.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))	a	-inf
12.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))	d	0
11.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))	d	-inf
10.0ms	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))	c	inf

rewrite80.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`prod-diff_binary64`
171×	`add-sqr-sqrt_binary64`
166×	`*-un-lft-identity_binary64`
166×	`pow1_binary64`
156×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	347	58
2	4218	58

Stop Event

1×	node limit

Counts

4 → 94

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

882×	`times-frac_binary64`
743×	`fma-def_binary64`
667×	`associate-/l*_binary64`
370×	`cancel-sign-sub-inv_binary64`
169×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1391
1	176	1327
2	445	1320
3	1445	1318

Stop Event

1×	node limit

Counts

158 → 120

prune78.0ms (2.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	120	4	124

Error

Counts

124 → 4

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 (sqrt.f64 (+.f64 c d)) a) (.f64 a b))
✓	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))
✓	1.9b	(fma.f64 (sqrt.f64 (+.f64 c d)) (.f64 a (fma.f64 c (.f64 1/2 (sqrt.f64 (/.f64 1 d))) (sqrt.f64 d))) (*.f64 a b))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 2753 to 1106 computations (59.8% saved)

regimes238.0ms (7.9%)

Accuracy

Total 0.0b remaining (80.8%)

Threshold costs 0.0b (80.8%)

Counts

34 → 1

Compiler

Compiled 4161 to 2627 computations (36.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10

Stop Event

1×

saturated

end513.0ms (17.1%)

Stop Event

1×

done

Compiler

Compiled 109 to 67 computations (38.5% saved)

Details

analyze2.0ms (0.1%)

sample1.0s (34%)

preprocess32.0ms (1.1%)

simplify11.0ms (0.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.5%)

rewrite57.0ms (1.9%)

simplify21.0ms (0.7%)

prune179.0ms (6%)

localize5.0ms (0.2%)

series43.0ms (1.4%)

rewrite71.0ms (2.4%)

simplify18.0ms (0.6%)

prune16.0ms (0.5%)

localize9.0ms (0.3%)

series180.0ms (6%)

rewrite48.0ms (1.6%)

simplify55.0ms (1.8%)

prune87.0ms (2.9%)

localize15.0ms (0.5%)

series151.0ms (5%)

rewrite80.0ms (2.7%)

simplify44.0ms (1.5%)

prune78.0ms (2.6%)

regimes238.0ms (7.9%)

simplify2.0ms (0.1%)

end513.0ms (17.1%)

Profiling