Details

analyze19.0ms (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)

sample1.2s (27.6%)

Symmetry

(sort x y z)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 53 to 35 computations (34% 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`

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

38.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	38.8b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize14.0ms (0.3%)

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)
✓	36.1b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series167.0ms (3.8%)

Counts

4 → 132

Calls

4 calls:

113.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
28.0ms	(/.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)))
13.0ms	(fma.f64 x x (*.f64 y y))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`

Counts

4 → 76

Calls

4 calls:

3.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
3.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
1.0ms	(fma.f64 z z (fma.f64 x x (*.f64 y y)))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify151.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

358×	`sub-neg_binary64`
354×	`fma-neg_binary64`
279×	`fma-def_binary64`
227×	`times-frac_binary64`
207×	`associate-r_binary64`

Counts

208 → 228

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	400	5513
1	1012	5152
2	4107	5152
3	5078	5152

prune195.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	225	4	229

Error

0.2b

Counts

229 → 4

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	33.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
✓	38.8b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
	38.9b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))

Compiler

Compiled 6702 to 3782 computations (43.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series42.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
19.0ms	(hypot.f64 x z)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`

Counts

2 → 35

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
1.0ms	(hypot.f64 x z)

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

904×	`fma-neg_binary64`
600×	`times-frac_binary64`
384×	`associate-/l*_binary64`
380×	`associate-r_binary64`
345×	`associate-l_binary64`

Counts

83 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1647
1	381	1602
2	1245	1582
3	5000	1582
4	5673	1582

prune80.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	2	2
Picked	0	1	1
Done	1	0	1
Total	95	8	103

Error

0.0b

Counts

103 → 8

Alt Table

Status	Error	Program
	33.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	1.3b	(.f64 (sqrt.f64 1/3) (.f64 (*.f64 (cbrt.f64 (hypot.f64 x z)) (cbrt.f64 (hypot.f64 x z))) (cbrt.f64 (hypot.f64 x z))))
	38.9b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.3b	(.f64 (.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 (hypot.f64 x z)) (cbrt.f64 (hypot.f64 x z)))) (cbrt.f64 (hypot.f64 x z)))
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	0.7b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
▶	0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	0.7b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))

Compiler

Compiled 1910 to 1326 computations (30.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x z)
✓	0.0b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

series53.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
22.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
15×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

11.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
4.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))

simplify112.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
710×	`times-frac_binary64`
483×	`associate-/l*_binary64`
470×	`fma-def_binary64`
235×	`cancel-sign-sub-inv_binary64`

Counts

104 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2514
1	463	2398
2	1657	2278
3	4785	2274
4	5301	2274

prune153.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	173	8	181

Error

0.0b

Counts

181 → 8

Alt Table

Status	Error	Program
▶	0.6b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
	0.7b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	33.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	0.7b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	38.9b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (cbrt.f64 (hypot.f64 x z)) (cbrt.f64 (hypot.f64 x z)))) (cbrt.f64 (hypot.f64 x z))))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

Compiler

Compiled 3810 to 2905 computations (23.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x z)
	0.0b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))

series83.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

55.0ms

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

28.0ms

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

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`sqrt-prod_binary64`
24×	`associate-l_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`

Counts

2 → 63

Calls

2 calls:

12.0ms

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

12.0ms

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

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
669×	`fma-neg_binary64`
449×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
239×	`associate-r_binary64`

Counts

111 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	3441
1	522	2910
2	1867	2694
3	4763	2690
4	5167	2690

prune233.0ms (5.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	256	6	262

Error

0.0b

Counts

262 → 6

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	33.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	0.7b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	0.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3)))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓	0.6b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))

Compiler

Compiled 6783 to 5564 computations (18% saved)

regimes954.0ms (21.7%)

Accuracy

Total 0.5b remaining (61%)

Threshold costs 0.5b (61%)

Counts

73 → 1

Compiler

Compiled 12174 to 9326 computations (23.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	11	18
2	11	18

end608.0ms (13.8%)

Compiler: Compiled 143 to 119 computations (16.8% saved)

Details

analyze19.0ms (0.4%)

sample1.2s (27.6%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

series167.0ms (3.8%)

rewrite13.0ms (0.3%)

simplify151.0ms (3.4%)

prune195.0ms (4.4%)

localize4.0ms (0.1%)

series42.0ms (0.9%)

rewrite7.0ms (0.2%)

simplify91.0ms (2.1%)

prune80.0ms (1.8%)

localize6.0ms (0.1%)

series53.0ms (1.2%)

rewrite19.0ms (0.4%)

simplify112.0ms (2.5%)

prune153.0ms (3.5%)

localize8.0ms (0.2%)

series83.0ms (1.9%)

rewrite34.0ms (0.8%)

simplify123.0ms (2.8%)

prune233.0ms (5.3%)

regimes954.0ms (21.7%)

simplify2.0ms (0.1%)

end608.0ms (13.8%)

Profiling