Details

analyze19.0ms (0.7%)

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.0s (35.7%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 36 to 24 computations (33.3% 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	24	76
1	35	68
2	40	68
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y z)

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify13.0ms (0.4%)

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	12	19
1	17	17
2	28	17
3	34	17

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

39.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.6b	(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3)
✓	36.7b	(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3))

series90.0ms (3.1%)

Counts

2 → 72

Calls

18 calls:

10.0ms	(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3))	x	-inf
9.0ms	(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3))	y	inf
8.0ms	(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3))	z	inf
7.0ms	(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3))	z	-inf
7.0ms	(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) 3))	y	-inf

rewrite50.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u_binary64`
864×	`expm1-log1p-u_binary64`
135×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
94×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	207	25
2	2426	25

Stop Event

1×	node limit

Counts

2 → 61

simplify74.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

361×	`sub-neg_binary64`
351×	`fma-neg_binary64`
287×	`fma-def_binary64`
226×	`times-frac_binary64`
205×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	307	3318
1	1135	3089
2	4292	3089

Stop Event

1×	node limit

Counts

133 → 146

prune122.0ms (4.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	4	147

Error

Counts

147 → 4

Alt Table

Status	Error	Program
	0.9b	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))
	32.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x y))
	28.5b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
▶	0.4b	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))

Compiler

Compiled 4649 to 3317 computations (28.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 y (hypot.f64 x z))
✓	0.4b	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))

series135.0ms (4.6%)

Counts

2 → 72

Calls

18 calls:

11.0ms	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))	y	0
10.0ms	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))	z	-inf
10.0ms	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))	y	-inf
10.0ms	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))	x	inf
10.0ms	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))	z	inf

rewrite45.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`log1p-expm1-u_binary64`
809×	`expm1-log1p-u_binary64`
126×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	186	19
2	2225	19

Stop Event

1×	node limit

Counts

2 → 52

simplify79.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

411×	`fma-def_binary64`
272×	`times-frac_binary64`
262×	`associate-/r*_binary64`
254×	`associate--l+_binary64`
240×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	417	4742
1	1484	4402

Stop Event

1×	node limit

Counts

124 → 190

prune163.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	190	4	194

Error

Counts

194 → 4

Alt Table

Status	Error	Program
▶	0.9b	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))
	32.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x y))
	28.5b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
✓	0.4b	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))

Compiler

Compiled 7250 to 5109 computations (29.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 y (hypot.f64 x z))
✓	0.4b	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))
✓	1.0b	(/.f64 1 (sqrt.f64 3))

series81.0ms (2.8%)

Counts

2 → 36

Calls

9 calls:

12.0ms	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))	y	-inf
10.0ms	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))	z	inf
10.0ms	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))	x	-inf
9.0ms	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))	y	inf
9.0ms	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))	y	0

rewrite46.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

874×	`log1p-expm1-u_binary64`
874×	`expm1-log1p-u_binary64`
114×	`prod-diff_binary64`
107×	`add-sqr-sqrt_binary64`
100×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	222	15
2	2528	15

Stop Event

1×	node limit

Counts

2 → 50

simplify67.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

725×	`cancel-sign-sub-inv_binary64`
326×	`fma-neg_binary64`
312×	`sub-neg_binary64`
220×	`fma-def_binary64`
201×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	264	2765
1	960	2581
2	3900	2581

Stop Event

1×	node limit

Counts

86 → 119

prune172.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	207	4	211

Error

Counts

211 → 4

Alt Table

Status	Error	Program
✓	0.9b	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))
	32.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x y))
▶	28.5b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
✓	0.4b	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))

Compiler

Compiled 7535 to 5384 computations (28.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 z y)
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))

series27.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

4.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	y	-inf
2.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	z	-inf
2.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	y	inf
2.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	z	inf
2.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))	z	0

rewrite36.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log1p-expm1-u_binary64`
552×	`expm1-log1p-u_binary64`
292×	`log-prod_binary64`
169×	`pow2_binary64`
119×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	140	13
2	1550	13

Stop Event

1×	node limit

Counts

2 → 42

simplify38.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

404×	`times-frac_binary64`
323×	`associate-/l*_binary64`
268×	`fma-def_binary64`
267×	`associate-r_binary64`
264×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1264
1	382	1228
2	1150	1208

Stop Event

1×	node limit

Counts

90 → 109

prune53.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
✓	0.9b	(*.f64 (hypot.f64 y (hypot.f64 x z)) (/.f64 1 (sqrt.f64 3)))
	32.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x y))
✓	28.5b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
✓	0.4b	(/.f64 (hypot.f64 y (hypot.f64 x z)) (sqrt.f64 3))

Compiler

Compiled 1878 to 1345 computations (28.4% saved)

regimes418.0ms (14.4%)

Accuracy

Total 0.4b remaining (98.1%)

Threshold costs 0.4b (98.1%)

Counts

36 → 1

Compiler

Compiled 4859 to 3760 computations (22.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12

Stop Event

1×

saturated

end84.0ms (2.9%)

Stop Event

1×

fuel

Remove

(sort x y z)

Compiler

Compiled 86 to 64 computations (25.6% saved)

Details

analyze19.0ms (0.7%)

sample1.0s (35.7%)

preprocess29.0ms (1%)

simplify13.0ms (0.4%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

series90.0ms (3.1%)

rewrite50.0ms (1.7%)

simplify74.0ms (2.5%)

prune122.0ms (4.2%)

localize5.0ms (0.2%)

series135.0ms (4.6%)

rewrite45.0ms (1.5%)

simplify79.0ms (2.7%)

prune163.0ms (5.6%)

localize6.0ms (0.2%)

series81.0ms (2.8%)

rewrite46.0ms (1.6%)

simplify67.0ms (2.3%)

prune172.0ms (5.9%)

localize5.0ms (0.2%)

series27.0ms (0.9%)

rewrite36.0ms (1.2%)

simplify38.0ms (1.3%)

prune53.0ms (1.8%)

regimes418.0ms (14.4%)

simplify2.0ms (0.1%)

end84.0ms (2.9%)

Profiling