Details

analyze140.0ms (5.4%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample774.0ms (29.7%)

Symmetry

(sort x y)

Results

740.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

13×	`associate-/r*_binary64`
5×	`*-commutative_binary64`
4×	`associate-/l/_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	28	13
3	39	13
4	37	13
5	37	13

prune2.0ms (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

13.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.0b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 42 to 25 computations (40.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	12.5b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(/.f64 (+.f64 x y) (*.f64 (*.f64 x 2) y))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
4×	`associate-/l*_binary64`
4×	`times-frac_binary64`

Counts

1 → 29

Calls

1 calls:

6.0ms

(/.f64 (+.f64 x y) (*.f64 (*.f64 x 2) y))

simplify49.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
664×	`times-frac_binary64`
522×	`associate-/r*_binary64`
519×	`associate-l_binary64`
500×	`distribute-rgt-in_binary64`

Counts

53 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	767
1	222	654
2	839	654
3	3818	653
4	5409	653

prune27.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Error

0.0b

Counts

46 → 5

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
	35.8b	(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (.f64 x 2)) (/.f64 (sqrt.f64 (+.f64 x y)) y))
	11.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 x 2)) (/.f64 (cbrt.f64 (+.f64 x y)) y))
	38.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))) (sqrt.f64 (/.f64 (+.f64 x y) (.f64 (*.f64 x 2) y))))
✓	13.0b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 843 to 415 computations (50.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 32

Calls

1 calls:

9.0ms

(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))

simplify89.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-out_binary64`
539×	`times-frac_binary64`
394×	`associate-/l/_binary64`
321×	`fma-neg_binary64`
298×	`distribute-rgt-in_binary64`

Counts

56 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	504
1	127	473
2	402	472
3	1379	472
4	2965	472
5	4451	472
6	4835	472
7	5030	472

prune29.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	40	5	45

Error

0.0b

Counts

45 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
	0.9b	(*.f64 (/.f64 (sqrt.f64 1/2) 1) (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y)))
▶	0.7b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x))) (cbrt.f64 (/.f64 1/2 x)) (/.f64 1/2 y))
	11.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 x 2)) (/.f64 (cbrt.f64 (+.f64 x y)) y))
✓	13.0b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 669 to 487 computations (27.2% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x))) (cbrt.f64 (/.f64 1/2 x)) (/.f64 1/2 y))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x)))
✓	0.6b	(cbrt.f64 (/.f64 1/2 x))

series312.0ms (12%)

Counts

3 → 48

Calls

3 calls:

225.0ms	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x))) (cbrt.f64 (/.f64 1/2 x)) (/.f64 1/2 y))
49.0ms	(*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x)))
38.0ms	(cbrt.f64 (/.f64 1/2 x))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`cbrt-prod_binary64`
66×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`

Counts

3 → 114

Calls

3 calls:

11.0ms	(*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x)))
2.0ms	(cbrt.f64 (/.f64 1/2 x))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x))) (cbrt.f64 (/.f64 1/2 x)) (/.f64 1/2 y))

simplify285.0ms (10.9%)

Algorithm

1×	egg-herbie

Rules

473×	`associate-/l*_binary64`
395×	`associate-l_binary64`
374×	`associate-/r*_binary64`
329×	`associate-r_binary64`
248×	`unswap-sqr_binary64`

Counts

162 → 171

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	159	2596
1	241	2559
2	674	2489
3	1795	2469
4	4496	2289
5	4650	2289
6	4803	2289
7	4998	2289
8	4910	2289

prune187.0ms (7.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	237	5	242

Error

0.0b

Counts

242 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
▶	0.9b	(*.f64 (/.f64 (sqrt.f64 1/2) 1) (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y)))
✓	0.7b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x))) (cbrt.f64 (/.f64 1/2 x)) (/.f64 1/2 y))
	11.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 x 2)) (/.f64 (cbrt.f64 (+.f64 x y)) y))
✓	13.0b	(/.f64 (+.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 5732 to 4399 computations (23.3% saved)

localize22.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y))
✓	0.4b	(/.f64 (sqrt.f64 1/2) y)
✓	0.4b	(/.f64 (sqrt.f64 1/2) x)
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 1/2) 1) (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y)))

series31.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

15.0ms	(*.f64 (/.f64 (sqrt.f64 1/2) 1) (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y)))
9.0ms	(+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y))
4.0ms	(/.f64 (sqrt.f64 1/2) x)
3.0ms	(/.f64 (sqrt.f64 1/2) y)

rewrite64.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
107×	`*-un-lft-identity_binary64`
89×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
60×	`sqrt-prod_binary64`

Counts

4 → 193

Calls

4 calls:

26.0ms	(*.f64 (/.f64 (sqrt.f64 1/2) 1) (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y)))
19.0ms	(+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y))
3.0ms	(/.f64 (sqrt.f64 1/2) x)
3.0ms	(/.f64 (sqrt.f64 1/2) y)

simplify169.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

479×	`fma-neg_binary64`
438×	`associate-/l*_binary64`
274×	`associate-*l/_binary64`
246×	`times-frac_binary64`
244×	`distribute-rgt-in_binary64`

Counts

241 → 229

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	3190
1	413	3081
2	1180	3051
3	3243	3028
4	4314	3028
5	4815	3028
6	4937	3028

prune143.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	1	1
Picked	1	0	1
Done	1	2	3
Total	230	4	234

Error

Counts

234 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/2 y))
✓	0.7b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x))) (cbrt.f64 (/.f64 1/2 x)) (/.f64 1/2 y))
	1.3b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y))) (cbrt.f64 (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y)))) (cbrt.f64 (+.f64 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) y)))))
	11.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (*.f64 x 2)) (/.f64 (cbrt.f64 (+.f64 x y)) y))

Compiler

Compiled 4940 to 4159 computations (15.8% saved)

regimes117.0ms (4.5%)

Accuracy

Total 0.0b remaining (42.6%)

Threshold costs 0.0b (42.6%)

Counts

39 → 1

Compiler

Compiled 2076 to 1602 computations (22.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

end81.0ms (3.1%)

Remove: (sort x y)
Compiler: Compiled 125 to 93 computations (25.6% saved)

Details

analyze140.0ms (5.4%)

sample774.0ms (29.7%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite7.0ms (0.3%)

simplify49.0ms (1.9%)

prune27.0ms (1%)

localize4.0ms (0.2%)

series9.0ms (0.3%)

rewrite10.0ms (0.4%)

simplify89.0ms (3.4%)

prune29.0ms (1.1%)

localize7.0ms (0.3%)

series312.0ms (12%)

rewrite21.0ms (0.8%)

simplify285.0ms (10.9%)

prune187.0ms (7.2%)

localize22.0ms (0.8%)

series31.0ms (1.2%)

rewrite64.0ms (2.5%)

simplify169.0ms (6.5%)

prune143.0ms (5.5%)

regimes117.0ms (4.5%)

simplify2.0ms (0.1%)

end81.0ms (3.1%)

Profiling