Details

analyze20.0ms (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)

sample1.1s (27%)

Symmetry

(sort x y z)

Results

1.1s

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

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

37.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.1b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

Compiler

Compiled 63 to 38 computations (39.7% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	0.1b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
✓	34.5b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

series139.0ms (3.3%)

Counts

3 → 96

Calls

3 calls:

103.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
29.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
7.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite21.0ms (0.5%)

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 → 72

Calls

3 calls:

8.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
5.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify134.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-neg_binary64`
332×	`fma-def_binary64`
284×	`times-frac_binary64`
276×	`associate-r_binary64`
196×	`associate-/l*_binary64`

Counts

168 → 214

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	420	5195
1	1141	4747
2	4857	4747
3	5222	4747

prune167.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	211	4	215

Error

0.2b

Counts

215 → 4

Alt Table

Status	Error	Program
	24.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
	36.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	37.1b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 3))
▶	0.7b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))

Compiler

Compiled 6894 to 3774 computations (45.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series23.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

22.0ms

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

rewrite5.0ms (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:

4.0ms

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

simplify61.0ms (1.5%)

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

prune54.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	52	9	61

Error

0.0b

Counts

61 → 9

Alt Table

Status	Error	Program
	24.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
	1.0b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))))
▶	0.6b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x)))
	37.1b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 3))
	1.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))) (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))))
	0.9b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 z x))) (sqrt.f64 (hypot.f64 z x)))
	36.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.0b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (cbrt.f64 1/3)) (hypot.f64 z x)))
	1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 z x))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 z x))))

Compiler

Compiled 1297 to 948 computations (26.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series44.0ms (1%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x))
20.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x)))

rewrite17.0ms (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:

9.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x)))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x))

simplify100.0ms (2.4%)

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

prune109.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	132	8	140

Error

0.0b

Counts

140 → 8

Alt Table

Status	Error	Program
	24.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
	1.0b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))))
✓	0.6b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x)))
	37.1b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 3))
▶	0.7b	(.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 z x))))
	1.7b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))) (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))))
	36.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 z x))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 z x))))

Compiler

Compiled 2959 to 2289 computations (22.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x))
✓	0.3b	(.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 z x))))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x)))
✓	1.0b	(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

series138.0ms (3.3%)

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 z x)))

62.0ms

(*.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 z x))))

0.0ms

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

rewrite40.0ms (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:

17.0ms

(*.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 z x))))

13.0ms

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

5.0ms

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

simplify144.0ms (3.4%)

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 → 181

Iterations

Useful iterations: 3 (0.0ms)

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

prune273.0ms (6.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	241	2	243
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	245	6	251

Error

0.0b

Counts

251 → 6

Alt Table

Status	Error	Program
	24.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z y))
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (sqrt.f64 (sqrt.f64 1/3))) (hypot.f64 z x)))
	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (cbrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 z x))))
	36.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	37.1b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 3))
	1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 z x))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 z x))))

Compiler

Compiled 7787 to 6698 computations (14% saved)

regimes999.0ms (23.9%)

Accuracy

Total 0.8b remaining (97.7%)

Threshold costs 0.8b (97.7%)

Counts

88 → 1

Compiler

Compiled 17141 to 13045 computations (23.9% 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

end512.0ms (12.3%)

Compiler: Compiled 152 to 124 computations (18.4% saved)

Details

analyze20.0ms (0.5%)

sample1.1s (27%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize12.0ms (0.3%)

series139.0ms (3.3%)

rewrite21.0ms (0.5%)

simplify134.0ms (3.2%)

prune167.0ms (4%)

localize5.0ms (0.1%)

series23.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify61.0ms (1.5%)

prune54.0ms (1.3%)

localize6.0ms (0.1%)

series44.0ms (1%)

rewrite17.0ms (0.4%)

simplify100.0ms (2.4%)

prune109.0ms (2.6%)

localize12.0ms (0.3%)

series138.0ms (3.3%)

rewrite40.0ms (1%)

simplify144.0ms (3.4%)

prune273.0ms (6.5%)

regimes999.0ms (23.9%)

simplify2.0ms (0.1%)

end512.0ms (12.3%)

Profiling