Details

analyze19.0ms (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)

sample1.0s (22.3%)

Symmetry

(sort x y z)

Results

969.0ms

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

40.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.3b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize9.0ms (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)
✓	37.4b	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series90.0ms (2%)

Counts

3 → 96

Calls

3 calls:

62.0ms	(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
22.0ms	(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
6.0ms	(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 x x (*.f64 y y))

simplify110.0ms (2.4%)

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

prune149.0ms (3.3%)

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
	40.4b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
▶	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))

Compiler

Compiled 6310 to 3656 computations (42.1% 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 x z))

series15.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(*.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))

simplify65.0ms (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

prune48.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	51	9	60

Error

0.0b

Counts

60 → 9

Alt Table

Status	Error	Program
	40.4b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
✓	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	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)))
	1.1b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))) (*.f64 (sqrt.f64 (cbrt.f64 1/3)) (hypot.f64 x z)))
▶	0.7b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
	1.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))
	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))))
	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))))

Compiler

Compiled 1298 to 943 computations (27.3% 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 x z))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

series32.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
15.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

rewrite16.0ms (0.3%)

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:

8.0ms	(.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))

simplify90.0ms (2%)

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	4	3	7
Picked	1	0	1
Done	0	1	1
Total	133	7	140

Error

0.0b

Counts

140 → 7

Alt Table

Status	Error	Program
▶	0.8b	(.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))))
	40.4b	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
✓	0.8b	(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
	0.9b	(.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 (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))))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	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))))

Compiler

Compiled 2940 to 2288 computations (22.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 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))

series260.0ms (5.7%)

Counts

3 → 48

Calls

3 calls:

186.0ms

(*.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))))

74.0ms

(*.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))

rewrite36.0ms (0.8%)

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:

16.0ms

(*.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))

simplify183.0ms (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 → 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

prune254.0ms (5.6%)

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

Counts

252 → 6

Alt Table

Status	Error	Program
✓	0.8b	(.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 1/3) (hypot.f64 x z))
	0.9b	(.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 (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))))
	30.3b	(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
	0.8b	(.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 x z)))

Compiler

Compiled 7831 to 6748 computations (13.8% saved)

regimes1.4s (31.7%)

Accuracy

Total 0.5b remaining (69.5%)

Threshold costs 0.5b (69.5%)

Counts

80 → 1

Compiler

Compiled 14524 to 12092 computations (16.7% 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

end556.0ms (12.3%)

Compiler: Compiled 160 to 140 computations (12.5% saved)

Details

analyze19.0ms (0.4%)

sample1.0s (22.3%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series90.0ms (2%)

rewrite8.0ms (0.2%)

simplify110.0ms (2.4%)

prune149.0ms (3.3%)

localize5.0ms (0.1%)

series15.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify65.0ms (1.4%)

prune48.0ms (1%)

localize6.0ms (0.1%)

series32.0ms (0.7%)

rewrite16.0ms (0.3%)

simplify90.0ms (2%)

prune108.0ms (2.4%)

localize13.0ms (0.3%)

series260.0ms (5.7%)

rewrite36.0ms (0.8%)

simplify183.0ms (4%)

prune254.0ms (5.6%)

regimes1.4s (31.7%)

simplify2.0ms (0.1%)

end556.0ms (12.3%)

Profiling