Details

analyze19.0ms (0.5%)

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)

sample992.0ms (27.2%)

Symmetry

(sort x y z)

Results

953.0ms

8256×

body

128

valid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify6.0ms (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

35.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.1b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓	32.8b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series80.0ms (2.2%)

Counts

2 → 72

Calls

2 calls:

59.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
21.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 56

Calls

2 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))

simplify104.0ms (2.8%)

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

128 → 180

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	385	4690
1	1002	4370
2	4043	4370
3	4995	4370

prune130.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	176	4	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	4	181

Error

0.2b

Counts

181 → 4

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	35.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	32.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	28.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 5980 to 3534 computations (40.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series15.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

15.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 25

Calls

1 calls:

3.0ms

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

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

635×	`distribute-rgt-neg-in_binary64`
498×	`times-frac_binary64`
397×	`distribute-neg-frac_binary64`
345×	`associate-r_binary64`
302×	`associate-/l*_binary64`

Counts

49 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1097
1	269	1061
2	905	1057
3	3923	1057
4	5279	1057

prune44.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	53	8	61

Error

0.0b

Counts

61 → 8

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	35.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.2b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (cbrt.f64 1/3)) (hypot.f64 x z)))
	32.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
▶	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	28.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.2b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
	1.9b	(.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))))

Compiler

Compiled 1257 to 920 computations (26.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)))

series30.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
14.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

rewrite14.0ms (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:

7.0ms	(.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))

simplify86.0ms (2.3%)

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

prune104.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	132	7	139

Error

0.0b

Counts

139 → 7

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	35.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	32.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
✓	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	28.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.9b	(.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))))
▶	1.0b	(.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 2907 to 2247 computations (22.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.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)))
✓	0.3b	(.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 x z))))

series52.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

36.0ms

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

16.0ms

(*.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))))

rewrite29.0ms (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:

15.0ms

(*.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))))

8.0ms

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

simplify241.0ms (6.6%)

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

prune188.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	212	7	219

Error

0.0b

Counts

219 → 7

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	35.2b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.3b	(.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)))
	32.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
✓	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	28.9b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
✓	1.0b	(.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 5673 to 4679 computations (17.5% saved)

regimes891.0ms (24.4%)

Accuracy

Total 0.8b remaining (98.5%)

Threshold costs 0.8b (98.5%)

Counts

67 → 1

Compiler

Compiled 11563 to 9071 computations (21.6% 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

end516.0ms (14.1%)

Compiler: Compiled 159 to 129 computations (18.9% saved)

Details

analyze19.0ms (0.5%)

sample992.0ms (27.2%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series80.0ms (2.2%)

rewrite7.0ms (0.2%)

simplify104.0ms (2.8%)

prune130.0ms (3.6%)

localize4.0ms (0.1%)

series15.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify61.0ms (1.7%)

prune44.0ms (1.2%)

localize6.0ms (0.2%)

series30.0ms (0.8%)

rewrite14.0ms (0.4%)

simplify86.0ms (2.3%)

prune104.0ms (2.9%)

localize8.0ms (0.2%)

series52.0ms (1.4%)

rewrite29.0ms (0.8%)

simplify241.0ms (6.6%)

prune188.0ms (5.2%)

regimes891.0ms (24.4%)

simplify2.0ms (0.1%)

end516.0ms (14.1%)

Profiling