Details

analyze42.0ms (0.9%)

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
25%	74.9%	0.1%	3
37.5%	62.4%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample676.0ms (15.3%)

Infinites

100% of outputs are infinite.

Results

549.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

959×	`fma-neg_binary64`
595×	`times-frac_binary64`
494×	`neg-mul-1_binary64`
491×	`neg-sub0_binary64`
301×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	52	10
3	113	10
4	203	10
5	436	10
6	758	10
7	2592	10
8	4299	10
9	5002	10

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 36 to 26 computations (27.8% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
13×	`fma-def_binary64`
11×	`times-frac_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

1 → 29

Calls

1 calls:

11.0ms

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

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Rules

889×	`div-sub_binary64`
786×	`sub-neg_binary64`
324×	`distribute-rgt-in_binary64`
310×	`associate-*l/_binary64`
292×	`distribute-lft-in_binary64`

Counts

53 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	466
1	128	436
2	336	435
3	1291	435
4	3780	435
5	4265	435
6	4960	435
7	5783	435

prune23.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	2	45

Error

0.0b

Counts

45 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

Compiler

Compiled 651 to 483 computations (25.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))
✓	0.5b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

series95.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

45.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

33.0ms

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

17.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

rewrite259.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`cbrt-div_binary64`
90×	`frac-times_binary64`
57×	`flip-+_binary64`
57×	`flip3-+_binary64`
57×	`frac-add_binary64`

Counts

3 → 186

Calls

3 calls:

111.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

38.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

37.0ms

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

simplify197.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

483×	`cancel-sign-sub-inv_binary64`
324×	`associate-l_binary64`
265×	`associate-r_binary64`
248×	`*-commutative_binary64`
196×	`fma-neg_binary64`

Counts

258 → 343

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	438	10726
1	1080	9883
2	3363	9393
3	5045	9393

prune585.0ms (13.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	613	2	615
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	614	3	617

Error

0.0b

Counts

617 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))) (cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 y)) (/.f64 -1/2 x))))
▶	1.2b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

Compiler

Compiled 25103 to 19085 computations (24% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x)))
	0.5b	(cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))
✓	0.5b	(.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x))))
✓	1.0b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

series73.0ms (1.7%)

Counts

3 → 48

Calls

3 calls:

44.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x))))

29.0ms

(cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x)))

0.0ms

(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
14×	`associate-l_binary64`

Counts

3 → 90

Calls

3 calls:

15.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x))))

4.0ms

(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

1.0ms

(cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x)))

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
407×	`fma-neg_binary64`
383×	`cancel-sign-sub-inv_binary64`
235×	`distribute-rgt-neg-in_binary64`
216×	`distribute-lft-neg-in_binary64`

Counts

138 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	4497
1	882	3735
2	2681	3472
3	4627	3459
4	4938	3459

prune422.0ms (9.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	342	3	345

Error

0.0b

Counts

345 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))) (cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 y)) (/.f64 -1/2 x))))
✓	1.2b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

Compiler

Compiled 15493 to 12469 computations (19.5% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series941.0ms (21.3%)

Counts

2 → 36

Calls

2 calls:

906.0ms	(cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 y)) (/.f64 -1/2 x)))
35.0ms	(cbrt.f64 y)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 26

Calls

2 calls:

1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 y)) (/.f64 -1/2 x)))

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

487×	`fma-neg_binary64`
452×	`associate-/r*_binary64`
447×	`associate-/l*_binary64`
385×	`associate-r_binary64`
339×	`associate-l_binary64`

Counts

62 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1476
1	284	1000
2	883	965
3	4368	901
4	4942	901
5	4907	901

prune357.0ms (8.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	364	0	364
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	364	3	367

Error

0.0b

Counts

367 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x)))) (cbrt.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 y)) (/.f64 -1/2 x))))
✓	1.2b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))) (cbrt.f64 (fma.f64 (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1) (/.f64 (cbrt.f64 1/2) y) (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))))

Compiler

Compiled 17654 to 12316 computations (30.2% saved)

regimes247.0ms (5.6%)

Accuracy

Total 0.0b remaining (22.2%)

Threshold costs 0.0b (22.2%)

Counts

63 → 1

Compiler

Compiled 5548 to 4441 computations (20% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
2	9	10

end69.0ms (1.5%)

Compiler: Compiled 101 to 79 computations (21.8% saved)

Details

analyze42.0ms (0.9%)

sample676.0ms (15.3%)

simplify55.0ms (1.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite12.0ms (0.3%)

simplify88.0ms (2%)

prune23.0ms (0.5%)

localize8.0ms (0.2%)

series95.0ms (2.2%)

rewrite259.0ms (5.9%)

simplify197.0ms (4.5%)

prune585.0ms (13.2%)

localize15.0ms (0.3%)

series73.0ms (1.7%)

rewrite25.0ms (0.6%)

simplify123.0ms (2.8%)

prune422.0ms (9.5%)

localize16.0ms (0.4%)

series941.0ms (21.3%)

rewrite2.0ms (0%)

simplify80.0ms (1.8%)

prune357.0ms (8.1%)

regimes247.0ms (5.6%)

simplify2.0ms (0%)

end69.0ms (1.5%)

Profiling