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 (53.7%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 84 to 60 computations (28.6% saved)

preprocess36.0ms (1.9%)

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)

simplify7.0ms (0.3%)

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)))

series18.0ms (0.9%)

Counts

2 → 84

Calls

21 calls:

5.0ms	(+.f64 b (+.f64 c d))	c	0
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	a	-inf
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	a	0
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	c	-inf
1.0ms	(*.f64 a (+.f64 b (+.f64 c d)))	b	-inf

rewrite55.0ms (2.9%)

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	2845	17

Stop Event

1×	node limit

Counts

2 → 133

simplify21.0ms (1.1%)

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

prune72.0ms (3.7%)

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

Counts

150 → 3

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))
	8.4b	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 1953 to 605 computations (69% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.5%)

Counts

1 → 48

Calls

12 calls:

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

rewrite37.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

850×	`expm1-log1p-u_binary64`
631×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	168	10
2	2246	10

Stop Event

1×	node limit

Counts

1 → 24

simplify14.0ms (0.7%)

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

prune15.0ms (0.8%)

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

Counts

39 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))
▶	8.4b	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 441 to 130 computations (70.5% saved)

localize13.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 b (+.f64 c d))
✓	0.0b	(pow.f64 (+.f64 c d) 2)
✓	0.4b	(.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a)
✓	7.9b	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))

series129.0ms (6.7%)

Counts

4 → 129

Calls

39 calls:

11.0ms	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))	a	-inf
10.0ms	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))	a	0
8.0ms	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))	b	0
8.0ms	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))	a	inf
8.0ms	(.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a)	a	-inf

rewrite76.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	301	40
2	4469	40

Stop Event

1×	node limit

Counts

4 → 144

simplify75.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

337×	`cancel-sign-sub-inv_binary64`
249×	`associate-+r+_binary64`
245×	`times-frac_binary64`
213×	`sub-neg_binary64`
202×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	3994
1	749	3763
2	3386	3760

Stop Event

1×	node limit

Counts

273 → 219

prune124.0ms (6.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	219	3	222

Error

Counts

222 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 a (+.f64 b c) (*.f64 a d))
✓	8.4b	(/.f64 (.f64 (-.f64 (.f64 b b) (pow.f64 (+.f64 c d) 2)) a) (-.f64 b (+.f64 c d)))
✓	0.0b	(*.f64 a (+.f64 b (+.f64 c d)))

Compiler

Compiled 6543 to 2474 computations (62.2% saved)

regimes109.0ms (5.7%)

Accuracy

Total 0.0b remaining (50.5%)

Threshold costs 0.0b (50.5%)

Counts

16 → 1

Compiler

Compiled 1592 to 1006 computations (36.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11

Stop Event

1×

saturated

end60.0ms (3.1%)

Stop Event

1×

done

Remove

(sort b c d)

Compiler

Compiled 92 to 54 computations (41.3% saved)

Details

analyze2.0ms (0.1%)

sample1.0s (53.7%)

preprocess36.0ms (1.9%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series18.0ms (0.9%)

rewrite55.0ms (2.9%)

simplify21.0ms (1.1%)

prune72.0ms (3.7%)

localize5.0ms (0.3%)

series10.0ms (0.5%)

rewrite37.0ms (1.9%)

simplify14.0ms (0.7%)

prune15.0ms (0.8%)

localize13.0ms (0.7%)

series129.0ms (6.7%)

rewrite76.0ms (3.9%)

simplify75.0ms (3.9%)

prune124.0ms (6.5%)

regimes109.0ms (5.7%)

simplify2.0ms (0.1%)

end60.0ms (3.1%)

Profiling