Details

analyze684.0ms (23.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample990.0ms (33.8%)

Results

977.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

preprocess29.0ms (1%)

Algorithm

2×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`+-commutative_binary64`
4×	`associate-+l+_binary64`
1×	`swap-x-z`
1×	`swap-x-y`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	29	56
2	34	56
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y z)

Compiler

Compiled 15 to 9 computations (40% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	14
2	26	14
3	32	14

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

37.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.1b	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 z z))
✓	34.6b	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))

series49.0ms (1.7%)

Counts

2 → 60

Calls

15 calls:

9.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	x	-inf
4.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	x	0
4.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	y	inf
4.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	x	inf
4.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	y	0

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`log1p-expm1-u_binary64`
642×	`expm1-log1p-u_binary64`
135×	`expm1-udef_binary64`
135×	`log1p-udef_binary64`
132×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	157	14
2	1821	14

Stop Event

1×	node limit

Counts

2 → 51

simplify51.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

704×	`cancel-sign-sub-inv_binary64`
324×	`sub-neg_binary64`
295×	`fma-neg_binary64`
203×	`fma-def_binary64`
180×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	2181
1	730	1989
2	3012	1987

Stop Event

1×	node limit

Counts

111 → 126

prune94.0ms (3.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Error

Counts

127 → 2

Alt Table

Status	Error	Program
▶	0.0b	(hypot.f64 x (hypot.f64 y z))
	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)

Compiler

Compiled 3375 to 2089 computations (38.1% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 y z)
✓	0.0b	(hypot.f64 x (hypot.f64 y z))

series59.0ms (2%)

Counts

2 → 60

Calls

15 calls:

8.0ms	(hypot.f64 x (hypot.f64 y z))	z	0
8.0ms	(hypot.f64 x (hypot.f64 y z))	x	0
5.0ms	(hypot.f64 x (hypot.f64 y z))	z	-inf
5.0ms	(hypot.f64 x (hypot.f64 y z))	z	inf
5.0ms	(hypot.f64 x (hypot.f64 y z))	x	-inf

rewrite48.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log1p-expm1-u_binary64`
494×	`expm1-log1p-u_binary64`
317×	`unpow-prod-down_binary64`
264×	`log-prod_binary64`
156×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	119	11
2	1385	11

Stop Event

1×	node limit

Counts

2 → 68

simplify63.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

729×	`cancel-sign-sub-inv_binary64`
366×	`fma-neg_binary64`
364×	`sub-neg_binary64`
221×	`fma-def_binary64`
155×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	2471
1	797	2291
2	3239	2289

Stop Event

1×	node limit

Counts

128 → 161

prune162.0ms (5.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	161	2	163

Error

Counts

163 → 2

Alt Table

Status	Error	Program
✓	0.0b	(hypot.f64 x (hypot.f64 y z))
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)

Compiler

Compiled 4064 to 2436 computations (40.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 y z)
	0.0b	(hypot.f64 x (hypot.f64 y z))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)

series75.0ms (2.6%)

Counts

1 → 12

Calls

9 calls:

24.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)	z	0
10.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)	x	0
9.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)	y	0
8.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)	x	-inf
5.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)	y	-inf

rewrite61.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

631×	`log1p-expm1-u_binary64`
631×	`expm1-log1p-u_binary64`
321×	`log-prod_binary64`
137×	`expm1-udef_binary64`
137×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	7
1	183	7
2	1825	7

Stop Event

1×	node limit

Counts

1 → 23

simplify43.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
399×	`cancel-sign-sub-inv_binary64`
303×	`fma-def_binary64`
225×	`associate-r_binary64`
195×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	629
1	221	487
2	666	471
3	2382	471
4	4506	471

Stop Event

1×	node limit

Counts

35 → 47

prune135.0ms (4.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	208	2	210

Error

Counts

210 → 2

Alt Table

Status	Error	Program
✓	0.0b	(hypot.f64 x (hypot.f64 y z))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)

Compiler

Compiled 5553 to 3444 computations (38% saved)

regimes253.0ms (8.6%)

Accuracy

Total 0.0b remaining (31%)

Threshold costs 0.0b (31%)

Counts

25 → 1

Compiler

Compiled 3150 to 2089 computations (33.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7

Stop Event

1×

saturated

end57.0ms (1.9%)

Stop Event

1×

done

Remove

(sort x y z)

Compiler

Compiled 51 to 33 computations (35.3% saved)

Details

analyze684.0ms (23.3%)

sample990.0ms (33.8%)

preprocess29.0ms (1%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series49.0ms (1.7%)

rewrite52.0ms (1.8%)

simplify51.0ms (1.7%)

prune94.0ms (3.2%)

localize4.0ms (0.1%)

series59.0ms (2%)

rewrite48.0ms (1.6%)

simplify63.0ms (2.1%)

prune162.0ms (5.5%)

localize6.0ms (0.2%)

series75.0ms (2.6%)

rewrite61.0ms (2.1%)

simplify43.0ms (1.5%)

prune135.0ms (4.6%)

regimes253.0ms (8.6%)

simplify2.0ms (0.1%)

end57.0ms (1.9%)

Profiling