Details

analyze20.0ms (0.4%)

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)

sample1.1s (22.9%)

Symmetry

(sort x y z)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	17	17
2	27	17
3	31	17
4	31	17

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

37.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.8b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	0.0b	(fma.f64 z z (fma.f64 x x (*.f64 y y)))
✓	0.1b	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓	35.0b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series122.0ms (2.5%)

Counts

4 → 132

Calls

4 calls:

67.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
36.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
13.0ms	(fma.f64 z z (fma.f64 x x (*.f64 y y)))
6.0ms	(fma.f64 x x (*.f64 y y))

rewrite65.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u_binary64`
864×	`expm1-log1p-u_binary64`
135×	`prod-diff_binary64`
108×	`egg-rr`
100×	`add-sqr-sqrt_binary64`

Counts

4 → 108

Calls

4 calls:

62.0ms	(fma.f64 x x (*.f64 y y))
62.0ms	(fma.f64 z z (fma.f64 x x (*.f64 y y)))
62.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
62.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	52
1	206	42
2	2285	42
3	5517	42
0	0	0
1	0	0

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

796×	`cancel-sign-sub-inv_binary64`
354×	`fma-neg_binary64`
351×	`sub-neg_binary64`
281×	`fma-def_binary64`
226×	`times-frac_binary64`

Counts

240 → 205

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	304	4008
1	892	3575
2	3812	3575
3	5588	3575

prune191.0ms (3.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	204	2	206

Error

0.0b

Counts

206 → 2

Alt Table

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

Compiler

Compiled 5452 to 3747 computations (31.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)
✓	0.0b	(hypot.f64 z (hypot.f64 x y))
✓	0.3b	(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))

series137.0ms (2.8%)

Counts

3 → 96

Calls

3 calls:

78.0ms	(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))
49.0ms	(hypot.f64 z (hypot.f64 x y))
10.0ms	(hypot.f64 x y)

rewrite63.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 74

Calls

3 calls:

62.0ms	(hypot.f64 x y)
62.0ms	(hypot.f64 z (hypot.f64 x y))
62.0ms	(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	185	23
2	2104	23
3	5229	23
0	0	0
1	0	0

simplify119.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-neg_binary64`
429×	`fma-def_binary64`
272×	`times-frac_binary64`
264×	`associate--l+_binary64`
262×	`associate-/r*_binary64`

Counts

170 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	5230
1	1366	4872
2	4973	4870
3	5619	4870

prune229.0ms (4.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	235	3	238

Error

Counts

238 → 3

Alt Table

Status	Error	Program
	0.5b	(*.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3))))
▶	0.4b	(fabs.f64 (*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3)))
✓	0.4b	(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))

Compiler

Compiled 8053 to 5599 computations (30.5% saved)

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series88.0ms (1.8%)

Counts

1 → 36

Calls

1 calls:

88.0ms

(*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3))

rewrite42.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

717×	`log1p-expm1-u_binary64`
717×	`expm1-log1p-u_binary64`
155×	`expm1-udef_binary64`
155×	`log1p-udef_binary64`
102×	`prod-diff_binary64`

Counts

1 → 16

Calls

1 calls:

41.0ms

(*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	179	12
2	1895	12
3	5083	12
0	0	0
1	0	0

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

819×	`cancel-sign-sub-inv_binary64`
361×	`sub-neg_binary64`
351×	`fma-neg_binary64`
273×	`fma-def_binary64`
226×	`times-frac_binary64`

Counts

52 → 85

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	299	2697
1	874	2555
2	3780	2555
3	5587	2555

prune226.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	218	3	221

Error

Counts

221 → 3

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3))))
✓	0.4b	(fabs.f64 (*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3)))
✓	0.4b	(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))

Compiler

Compiled 7936 to 5641 computations (28.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 z (hypot.f64 x y))
✓	0.1b	(/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3)))
✓	0.4b	(*.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3))))
✓	1.0b	(/.f64 1 (cbrt.f64 3))

series554.0ms (11.2%)

Counts

3 → 72

Calls

3 calls:

404.0ms	(*.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3))))
150.0ms	(/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3)))
0.0ms	(/.f64 1 (cbrt.f64 3))

rewrite72.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

613×	`log-prod_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
216×	`log-pow_binary64`
150×	`prod-diff_binary64`

Counts

3 → 118

Calls

3 calls:

70.0ms	(/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3)))
70.0ms	(*.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3))))
70.0ms	(/.f64 1 (cbrt.f64 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	282	31
2	3171	31
3	5729	31
0	0	0
1	0	0

simplify140.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
332×	`times-frac_binary64`
268×	`associate-/l*_binary64`
250×	`associate-*r/_binary64`
249×	`associate-/r*_binary64`

Counts

190 → 262

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	582	7677
1	1736	6665
2	5048	6665

prune487.0ms (9.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	351	3	354

Error

Counts

354 → 3

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z (hypot.f64 x y)) (cbrt.f64 (sqrt.f64 3))))
✓	0.4b	(fabs.f64 (*.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 1/3)))
✓	0.4b	(/.f64 (hypot.f64 z (hypot.f64 x y)) (sqrt.f64 3))

Compiler

Compiled 15828 to 12242 computations (22.7% saved)

regimes948.0ms (19.2%)

Accuracy

Total 0.4b remaining (99.5%)

Threshold costs 0.4b (99.5%)

Counts

77 → 1

Compiler

Compiled 10641 to 8427 computations (20.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	9	12

end75.0ms (1.5%)

Remove: (sort x y z)
Compiler: Compiled 84 to 63 computations (25% saved)

Details

analyze20.0ms (0.4%)

sample1.1s (22.9%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series122.0ms (2.5%)

rewrite65.0ms (1.3%)

simplify95.0ms (1.9%)

prune191.0ms (3.9%)

localize7.0ms (0.1%)

series137.0ms (2.8%)

rewrite63.0ms (1.3%)

simplify119.0ms (2.4%)

prune229.0ms (4.6%)

localize16.0ms (0.3%)

series88.0ms (1.8%)

rewrite42.0ms (0.8%)

simplify82.0ms (1.7%)

prune226.0ms (4.6%)

localize13.0ms (0.3%)

series554.0ms (11.2%)

rewrite72.0ms (1.5%)

simplify140.0ms (2.8%)

prune487.0ms (9.8%)

regimes948.0ms (19.2%)

simplify5.0ms (0.1%)

end75.0ms (1.5%)

Profiling