Details

analyze3.0ms (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)

sample854.0ms (26.9%)

Infinites

0% of outputs are infinite.

Symmetry

(sort x y z)

Results

796.0ms

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

36.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.8b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	0.1b	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓	36.8b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series123.0ms (3.9%)

Counts

3 → 96

Calls

3 calls:

93.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
24.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
6.0ms	(fma.f64 x x (*.f64 y y))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
2.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify105.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

162 → 203

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	395	4965
1	1008	4633
2	4052	4633
3	5004	4633

prune154.0ms (4.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	201	3	204

Error

0.2b

Counts

204 → 3

Alt Table

Status	Error	Program
	36.8b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
▶	29.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	31.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 6310 to 3656 computations (42.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series36.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
15.0ms	(hypot.f64 y z)

rewrite5.0ms (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:

4.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
0.0ms	(hypot.f64 y z)

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-neg_binary64`
680×	`times-frac_binary64`
411×	`associate-/l*_binary64`
353×	`associate-l_binary64`
322×	`fma-def_binary64`

Counts

83 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1671
1	386	1602
2	1289	1582
3	4782	1582
4	5382	1582

prune64.0ms (2%)

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	0	0	0
Total	94	8	102

Error

0.1b

Counts

102 → 8

Alt Table

Status	Error	Program
	30.1b	(.f64 (.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 (hypot.f64 y z)) (cbrt.f64 (hypot.f64 y z)))) (cbrt.f64 (hypot.f64 y z)))
	29.7b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (cbrt.f64 1/3)) (hypot.f64 y z)))
▶	29.5b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z)))
	36.8b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	29.7b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 y z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 y z))))
	29.7b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 y z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 y z))))
✓	29.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	31.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 1910 to 1344 computations (29.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 y z)
✓	0.1b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z)))

series42.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z))
20.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z)))

rewrite18.0ms (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:

10.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z)))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z))

simplify107.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

793×	`times-frac_binary64`
578×	`fma-def_binary64`
278×	`fma-neg_binary64`
270×	`cancel-sign-sub-inv_binary64`
196×	`associate-r_binary64`

Counts

104 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2514
1	490	2292
2	1768	2170
3	4626	2170
4	4982	2170
5	4958	2170

prune121.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	174	7	181

Error

0.1b

Counts

181 → 7

Alt Table

Status	Error	Program
▶	29.7b	(.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 y z))))
	30.1b	(.f64 (.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 (hypot.f64 y z)) (cbrt.f64 (hypot.f64 y z)))) (cbrt.f64 (hypot.f64 y z)))
✓	29.5b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z)))
	36.8b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	29.7b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 y z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 y z))))
✓	29.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	31.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 3727 to 2839 computations (23.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 y z)
	0.1b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z))
✓	0.3b	(.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 y z))))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z)))

series74.0ms (2.3%)

Counts

2 → 48

Calls

2 calls:

54.0ms

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

19.0ms

(*.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 y z))))

rewrite29.0ms (0.9%)

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:

13.0ms

(*.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 y z))))

10.0ms

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

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

787×	`times-frac_binary64`
540×	`fma-def_binary64`
292×	`cancel-sign-sub-inv_binary64`
258×	`fma-neg_binary64`
248×	`associate-r_binary64`

Counts

111 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	3441
1	549	2716
2	1981	2662
3	5025	2662

prune175.0ms (5.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	255	6	261

Error

0.1b

Counts

261 → 6

Alt Table

Status	Error	Program
✓	29.5b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 y z)))
	36.8b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	29.7b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 y z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 y z))))
✓	29.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	29.8b	(.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 y z)))
	31.2b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 6735 to 5513 computations (18.1% saved)

regimes563.0ms (17.7%)

Accuracy

Total 0.6b remaining (63.3%)

Threshold costs 0.6b (63.3%)

Counts

50 → 1

Compiler

Compiled 8371 to 6177 computations (26.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
2	8	9

end495.0ms (15.6%)

Compiler: Compiled 122 to 95 computations (22.1% saved)

Details

analyze3.0ms (0.1%)

sample854.0ms (26.9%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series123.0ms (3.9%)

rewrite9.0ms (0.3%)

simplify105.0ms (3.3%)

prune154.0ms (4.9%)

localize7.0ms (0.2%)

series36.0ms (1.1%)

rewrite5.0ms (0.2%)

simplify74.0ms (2.3%)

prune64.0ms (2%)

localize6.0ms (0.2%)

series42.0ms (1.3%)

rewrite18.0ms (0.6%)

simplify107.0ms (3.4%)

prune121.0ms (3.8%)

localize10.0ms (0.3%)

series74.0ms (2.3%)

rewrite29.0ms (0.9%)

simplify77.0ms (2.4%)

prune175.0ms (5.5%)

regimes563.0ms (17.7%)

simplify2.0ms (0.1%)

end495.0ms (15.6%)

Profiling