Details

analyze20.0ms (0.6%)

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)

sample1.0s (27.3%)

Symmetry

(sort x y z)

Results

962.0ms

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

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)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓	34.2b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series130.0ms (3.6%)

Counts

2 → 72

Calls

2 calls:

102.0ms	(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)

rewrite8.0ms (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:

3.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
2.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

simplify107.0ms (2.9%)

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

prune134.0ms (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
	36.9b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	27.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	34.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
▶	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

Compiler

Compiled 5980 to 3534 computations (40.9% 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))

series33.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
12.0ms	(hypot.f64 x z)

rewrite5.0ms (0.1%)

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 x z))
0.0ms	(hypot.f64 x z)

simplify77.0ms (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

prune67.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Error

0.0b

Counts

103 → 8

Alt Table

Status	Error	Program
	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))))
	36.9b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.7b	(.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))))
	27.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
	34.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.0b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	1.7b	(.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)))
▶	0.8b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

Compiler

Compiled 1927 to 1347 computations (30.1% saved)

localize8.0ms (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)))

series42.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

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

rewrite15.0ms (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)))
6.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))

simplify94.0ms (2.6%)

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

prune128.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	172	9	181

Error

Counts

181 → 9

Alt Table

Status	Error	Program
	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))))
	36.9b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.7b	(.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))))
	27.3b	(*.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)))
▶	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))))
	34.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	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))))
	1.0b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))

Compiler

Compiled 3857 to 2952 computations (23.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 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 (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))))

series74.0ms (2%)

Counts

2 → 48

Calls

2 calls:

52.0ms

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

22.0ms

(*.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))))

rewrite26.0ms (0.7%)

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))))

9.0ms

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

simplify104.0ms (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

prune217.0ms (5.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	254	9	263

Error

Counts

263 → 9

Alt Table

Status	Error	Program
	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))))
	36.9b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	1.7b	(.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))))
	27.3b	(*.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)))
✓	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))))
	34.1b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	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))))
	1.0b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))

Compiler

Compiled 6843 to 5605 computations (18.1% saved)

regimes774.0ms (21.1%)

Accuracy

Total 0.7b remaining (97.7%)

Threshold costs 0.7b (97.7%)

Counts

70 → 1

Compiler

Compiled 11186 to 8767 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

end572.0ms (15.6%)

Compiler: Compiled 203 to 160 computations (21.2% saved)

Details

analyze20.0ms (0.6%)

sample1.0s (27.3%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series130.0ms (3.6%)

rewrite8.0ms (0.2%)

simplify107.0ms (2.9%)

prune134.0ms (3.6%)

localize4.0ms (0.1%)

series33.0ms (0.9%)

rewrite5.0ms (0.1%)

simplify77.0ms (2.1%)

prune67.0ms (1.8%)

localize8.0ms (0.2%)

series42.0ms (1.1%)

rewrite15.0ms (0.4%)

simplify94.0ms (2.6%)

prune128.0ms (3.5%)

localize9.0ms (0.2%)

series74.0ms (2%)

rewrite26.0ms (0.7%)

simplify104.0ms (2.8%)

prune217.0ms (5.9%)

regimes774.0ms (21.1%)

simplify2.0ms (0.1%)

end572.0ms (15.6%)

Profiling