Details

analyze5.0ms (0.1%)

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
99.9%	0%	0.1%	4

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.3s (19.6%)

Symmetry

(sort x y z)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify8.0ms (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%)

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

36.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.1b	(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 (0.1%)

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))

series239.0ms (3.6%)

Counts

4 → 132

Calls

4 calls:

139.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
54.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
30.0ms	(fma.f64 z z (fma.f64 x x (*.f64 y y)))
14.0ms	(fma.f64 x x (*.f64 y y))

rewrite22.0ms (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:

6.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
5.0ms	(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)))
1.0ms	(fma.f64 x x (*.f64 y y))

simplify249.0ms (3.7%)

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

prune334.0ms (5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	224	4	228
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	4	229

Error

0.3b

Counts

229 → 4

Alt Table

Status	Error	Program
	36.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	36.3b	(sqrt.f64 (/.f64 (fma.f64 x x (*.f64 z z)) 3))
▶	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	29.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 6711 to 3789 computations (43.5% saved)

localize10.0ms (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))

series68.0ms (1%)

Counts

2 → 48

Calls

2 calls:

44.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
23.0ms	(hypot.f64 x z)

rewrite15.0ms (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:

8.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
5.0ms	(hypot.f64 x z)

simplify133.0ms (2%)

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

prune300.0ms (4.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Error

0.1b

Counts

103 → 7

Alt Table

Status	Error	Program
	36.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.8b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
✓	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	1.1b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
▶	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	29.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))

Compiler

Compiled 1878 to 1320 computations (29.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x z)
✓	0.1b	(*.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)))

series106.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

69.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
37.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

rewrite41.0ms (0.6%)

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:

16.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
9.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))

simplify167.0ms (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

prune214.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	171	9	180

Error

0.0b

Counts

180 → 9

Alt Table

Status	Error	Program
	36.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.8b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
✓	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
▶	0.8b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
	1.0b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (hypot.f64 x z))))
	0.9b	(.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))))
✓	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	29.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))

Compiler

Compiled 3864 to 2969 computations (23.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
✓	1.0b	(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

series147.0ms (2.2%)

Counts

3 → 48

Calls

3 calls:

75.0ms

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

71.0ms

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

0.0ms

(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

rewrite64.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-l_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`pow1_binary64`
20×	`sqrt-prod_binary64`
19×	`cbrt-prod_binary64`

Counts

3 → 100

Calls

3 calls:

28.0ms

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

18.0ms

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

7.0ms

(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

simplify267.0ms (4%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-neg_binary64`
583×	`cancel-sign-sub-inv_binary64`
372×	`associate-r_binary64`
356×	`times-frac_binary64`
295×	`associate-l_binary64`

Counts

148 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	4743
1	634	4297
2	2293	4289
3	4476	4282
4	4992	4282

prune547.0ms (8.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	246	8	254

Error

0.0b

Counts

254 → 8

Alt Table

Status	Error	Program
✓	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
✓	0.8b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
	36.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.2b	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) 3) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	0.9b	(.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))))
✓	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	29.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))

Compiler

Compiled 7853 to 6759 computations (13.9% saved)

regimes1.4s (20.3%)

Accuracy

Total 0.7b remaining (83.5%)

Threshold costs 0.7b (83.5%)

Counts

68 → 1

Compiler

Compiled 11355 to 8989 computations (20.8% saved)

simplify4.0ms (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

end1.0s (15.3%)

Compiler: Compiled 182 to 151 computations (17% saved)

Details

analyze5.0ms (0.1%)

sample1.3s (19.6%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series239.0ms (3.6%)

rewrite22.0ms (0.3%)

simplify249.0ms (3.7%)

prune334.0ms (5%)

localize10.0ms (0.1%)

series68.0ms (1%)

rewrite15.0ms (0.2%)

simplify133.0ms (2%)

prune300.0ms (4.5%)

localize12.0ms (0.2%)

series106.0ms (1.6%)

rewrite41.0ms (0.6%)

simplify167.0ms (2.5%)

prune214.0ms (3.2%)

localize14.0ms (0.2%)

series147.0ms (2.2%)

rewrite64.0ms (1%)

simplify267.0ms (4%)

prune547.0ms (8.2%)

regimes1.4s (20.3%)

simplify4.0ms (0.1%)

end1.0s (15.3%)

Profiling