Details

analyze142.0ms (6.5%)

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
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)

sample886.0ms (40.2%)

Results

768.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify68.0ms (3.1%)

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

prune4.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
	13.6b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 58 to 40 computations (31% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite11.0ms (0.5%)

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:

9.0ms

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

simplify97.0ms (4.4%)

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

prune27.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	2	46

Error

0.0b

Counts

46 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
▶	13.6b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

Compiler

Compiled 617 to 453 computations (26.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.2b	(/.f64 (-.f64 x y) (.f64 (.f64 x 2) y))

series9.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`associate-/l*_binary64`

Counts

1 → 32

Calls

1 calls:

9.0ms

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

simplify58.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
658×	`times-frac_binary64`
546×	`associate-/r*_binary64`
522×	`associate-l_binary64`
490×	`div-sub_binary64`

Counts

56 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	826
1	241	704
2	891	655
3	4160	655
4	6127	655

prune23.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	49	3	52

Error

Counts

52 → 3

Alt Table

Status	Error	Program
	49.4b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 (.f64 y (.f64 x 2)) (fma.f64 x x (.f64 y (+.f64 x y)))))
▶	8.1b	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y)))
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 827 to 430 computations (48% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) y)
✓	0.0b	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y)))
✓	7.6b	(/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y))

series26.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y))
8.0ms	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y)))
5.0ms	(/.f64 (-.f64 x y) y)

rewrite59.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

272×	`times-frac_binary64`
140×	`*-un-lft-identity_binary64`
140×	`add-sqr-sqrt_binary64`
96×	`add-cube-cbrt_binary64`
61×	`add-exp-log_binary64`

Counts

3 → 234

Calls

3 calls:

16.0ms	(/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y))
9.0ms	(/.f64 1 (/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y)))
5.0ms	(/.f64 (-.f64 x y) y)

simplify229.0ms (10.4%)

Algorithm

1×	egg-herbie

Rules

803×	`associate-/r*_binary64`
326×	`fma-def_binary64`
235×	`distribute-rgt-in_binary64`
206×	`distribute-lft-in_binary64`
187×	`associate-/r/_binary64`

Counts

306 → 338

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	5820
1	621	5328
2	2232	4961
3	4660	4958
4	4974	4958
5	4993	4958
6	4960	4958

prune149.0ms (6.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	337	1	338
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	339	2	341

Error

Counts

341 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
▶	8.1b	(/.f64 1 (/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2)))

Compiler

Compiled 6627 to 2926 computations (55.8% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	0.0b	(/.f64 1 (/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	7.6b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series26.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
9.0ms	(/.f64 1 (/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2)))
6.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

rewrite18.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

3 → 117

Calls

3 calls:

4.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
4.0ms	(/.f64 1 (/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2)))
0.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

simplify131.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

542×	`fma-neg_binary64`
392×	`cancel-sign-sub-inv_binary64`
358×	`times-frac_binary64`
271×	`div-sub_binary64`
254×	`associate-/l*_binary64`

Counts

189 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	3448
1	320	3158
2	949	3083
3	3213	3078
4	4791	3078
5	5333	3078

prune105.0ms (4.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	170	2	172

Error

Counts

172 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))
✓	8.1b	(/.f64 1 (/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2)))

Compiler

Compiled 3333 to 2090 computations (37.3% saved)

regimes53.0ms (2.4%)

Accuracy

Total 0.0b remaining (56.2%)

Threshold costs 0.0b (56.2%)

Counts

18 → 1

Compiler

Compiled 652 to 451 computations (30.8% saved)

simplify2.0ms (0.1%)

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

end42.0ms (1.9%)

Compiler: Compiled 39 to 30 computations (23.1% saved)

Details

analyze142.0ms (6.5%)

sample886.0ms (40.2%)

simplify68.0ms (3.1%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series9.0ms (0.4%)

rewrite11.0ms (0.5%)

simplify97.0ms (4.4%)

prune27.0ms (1.2%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite11.0ms (0.5%)

simplify58.0ms (2.6%)

prune23.0ms (1.1%)

localize6.0ms (0.3%)

series26.0ms (1.2%)

rewrite59.0ms (2.7%)

simplify229.0ms (10.4%)

prune149.0ms (6.8%)

localize6.0ms (0.3%)

series26.0ms (1.2%)

rewrite18.0ms (0.8%)

simplify131.0ms (5.9%)

prune105.0ms (4.7%)

regimes53.0ms (2.4%)

simplify2.0ms (0.1%)

end42.0ms (1.9%)

Profiling