Details

analyze646.0ms (15.8%)

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)

sample1.0s (25%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

preprocess31.0ms (0.8%)

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)

simplify8.0ms (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

prune5.0ms (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

39.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.2b	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))

Compiler

Compiled 51 to 26 computations (49% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 z z))
✓	36.5b	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))

series56.0ms (1.4%)

Counts

2 → 60

Calls

15 calls:

16.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	x	-inf
5.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	z	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))))	z	-inf
4.0ms	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))	y	inf

rewrite43.0ms (1.1%)

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

simplify57.0ms (1.4%)

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

prune92.0ms (2.3%)

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

0.0b

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)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series45.0ms (1.1%)

Counts

1 → 36

Calls

9 calls:

6.0ms	(hypot.f64 x (hypot.f64 y z))	x	inf
5.0ms	(hypot.f64 x (hypot.f64 y z))	y	-inf
5.0ms	(hypot.f64 x (hypot.f64 y z))	z	0
5.0ms	(hypot.f64 x (hypot.f64 y z))	z	-inf
5.0ms	(hypot.f64 x (hypot.f64 y z))	z	inf

rewrite33.0ms (0.8%)

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	7
1	119	7
2	1385	7

Stop Event

1×	node limit

Counts

1 → 34

simplify50.0ms (1.2%)

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	1977
1	730	1821
2	3012	1819

Stop Event

1×	node limit

Counts

70 → 103

prune76.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	102	3	105

Error

Counts

105 → 3

Alt Table

Status	Error	Program
	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3))
✓	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 3208 to 1975 computations (38.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series135.0ms (3.3%)

Counts

2 → 24

Calls

18 calls:

34.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 2)	y	0
14.0ms	(sqrt.f64 (hypot.f64 x (hypot.f64 y z)))	x	-inf
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)	z	0
7.0ms	(sqrt.f64 (hypot.f64 x (hypot.f64 y z)))	z	0

rewrite41.0ms (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	16
1	183	16
2	1825	16

Stop Event

1×	node limit

Counts

2 → 50

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

606×	`associate-r_binary64`
558×	`fma-def_binary64`
543×	`associate-l_binary64`
247×	`*-commutative_binary64`
226×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1307
1	407	1099
2	1290	1071

Stop Event

1×	node limit

Counts

74 → 98

prune134.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	201	3	204

Error

Counts

204 → 3

Alt Table

Status	Error	Program
▶	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3))
✓	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 5810 to 3583 computations (38.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))))
✓	0.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3))
✓	0.6b	(cbrt.f64 (hypot.f64 x (hypot.f64 y z)))
✓	0.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3)

series501.0ms (12.3%)

Counts

4 → 120

Calls

36 calls:

25.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3)	z	-inf
24.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3)	y	-inf
23.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3)	y	inf
23.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3)	z	inf
23.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3)	x	-inf

rewrite62.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

795×	`log1p-expm1-u_binary64`
795×	`expm1-log1p-u_binary64`
102×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
95×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	229	35
2	2403	35

Stop Event

1×	node limit

Counts

4 → 95

simplify116.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

327×	`*-commutative_binary64`
244×	`cancel-sign-sub-inv_binary64`
228×	`times-frac_binary64`
215×	`+-commutative_binary64`
204×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	885	8237
1	2993	7650

Stop Event

1×	node limit

Counts

215 → 326

prune509.0ms (12.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	563	0	563
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	563	3	566

Error

Counts

566 → 3

Alt Table

Status	Error	Program
✓	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z)))) 3))
✓	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 26748 to 16065 computations (39.9% saved)

regimes284.0ms (7%)

Accuracy

Total 0.0b remaining (33.3%)

Threshold costs 0.0b (33.3%)

Counts

30 → 1

Compiler

Compiled 3916 to 2603 computations (33.5% 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

end72.0ms (1.8%)

Stop Event

1×

done

Remove

(sort x y z)

Compiler

Compiled 73 to 45 computations (38.4% saved)

Details

analyze646.0ms (15.8%)

sample1.0s (25%)

preprocess31.0ms (0.8%)

simplify8.0ms (0.2%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

series56.0ms (1.4%)

rewrite43.0ms (1.1%)

simplify57.0ms (1.4%)

prune92.0ms (2.3%)

localize3.0ms (0.1%)

series45.0ms (1.1%)

rewrite33.0ms (0.8%)

simplify50.0ms (1.2%)

prune76.0ms (1.9%)

localize6.0ms (0.1%)

series135.0ms (3.3%)

rewrite41.0ms (1%)

simplify37.0ms (0.9%)

prune134.0ms (3.3%)

localize13.0ms (0.3%)

series501.0ms (12.3%)

rewrite62.0ms (1.5%)

simplify116.0ms (2.8%)

prune509.0ms (12.5%)

regimes284.0ms (7%)

simplify2.0ms (0.1%)

end72.0ms (1.8%)

Profiling