Details

analyze17.0ms (0.4%)

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)

sample55.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort x y z)

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify9.0ms (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

38.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	38.4b	(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 z z (fma.f64 x x (*.f64 y y)))
✓	0.1b	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓	35.6b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series138.0ms (3.1%)

Counts

3 → 108

Calls

3 calls:

95.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
27.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
15.0ms	(fma.f64 z z (fma.f64 x x (*.f64 y y)))

rewrite8.0ms (0.2%)

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 z z (fma.f64 x x (*.f64 y y)))

simplify121.0ms (2.7%)

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

174 → 211

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	390	5238
1	1006	4889
2	4099	4889
3	5071	4889

prune151.0ms (3.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	208	3	211
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	209	3	212

Error

0.2b

Counts

212 → 3

Alt Table

Status	Error	Program
▶	0.7b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	38.5b	(/.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 x))

Compiler

Compiled 6400 to 3669 computations (42.7% 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))

series21.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

21.0ms

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

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 x z))

simplify63.0ms (1.4%)

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

prune41.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	54	6	60

Error

0.1b

Counts

60 → 6

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	38.5b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
	0.9b	(.f64 (.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
	1.5b	(.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)))
✓	0.7b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	29.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 1166 to 841 computations (27.9% saved)

localize8.0ms (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))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

series41.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

rewrite16.0ms (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 x z)))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))

simplify91.0ms (2.1%)

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

prune108.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	130	7	137

Error

0.0b

Counts

137 → 7

Alt Table

Status	Error	Program
	0.8b	(.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))))
▶	0.7b	(.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 x z))))
	0.8b	(.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))))
	1.5b	(.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)))
✓	0.7b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	38.5b	(/.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 x))

Compiler

Compiled 2928 to 2272 computations (22.4% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series125.0ms (2.8%)

Counts

3 → 48

Calls

3 calls:

67.0ms

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

57.0ms

(*.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))

rewrite39.0ms (0.9%)

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:

19.0ms

(*.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))))

8.0ms

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

6.0ms

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

simplify133.0ms (3%)

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

prune259.0ms (5.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	246	6	252

Error

0.0b

Counts

252 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))))
	29.6b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	0.8b	(.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))))
✓	0.7b	(.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 x z))))
	0.8b	(.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))))
✓	0.7b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

Compiler

Compiled 7833 to 6750 computations (13.8% saved)

regimes1.0s (23.6%)

Accuracy

Total 0.5b remaining (63.5%)

Threshold costs 0.5b (63.5%)

Counts

87 → 1

Compiler

Compiled 16287 to 13279 computations (18.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	17	18
2	15	18

end14.0ms (0.3%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

sample1.9s (42.8%)

Algorithm

1×

intervals

Results

810.0ms

8000×

body

128

valid

Compiler

Compiled 141 to 121 computations (14.2% saved)

Details

analyze17.0ms (0.4%)

sample55.0ms (1.2%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series138.0ms (3.1%)

rewrite8.0ms (0.2%)

simplify121.0ms (2.7%)

prune151.0ms (3.4%)

localize4.0ms (0.1%)

series21.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify63.0ms (1.4%)

prune41.0ms (0.9%)

localize8.0ms (0.2%)

series41.0ms (0.9%)

rewrite16.0ms (0.4%)

simplify91.0ms (2.1%)

prune108.0ms (2.4%)

localize16.0ms (0.4%)

series125.0ms (2.8%)

rewrite39.0ms (0.9%)

simplify133.0ms (3%)

prune259.0ms (5.8%)

regimes1.0s (23.6%)

simplify2.0ms (0.1%)

end14.0ms (0.3%)

sample1.9s (42.8%)

Profiling