Details

analyze37.0ms (1.2%)

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
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample866.0ms (28%)

Infinites

0% of outputs are infinite.

Results

525.0ms	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify287.0ms (9.3%)

Algorithm

1×	egg-herbie

Rules

1222×	`fma-neg_binary64`
983×	`fma-def_binary64`
688×	`div-sub_binary64`
423×	`sub-neg_binary64`
412×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	35	13
3	74	13
4	151	13
5	245	13
6	641	13
7	1125	13
8	2158	13
9	2729	13
10	3037	13
11	2995	13
12	3049	13
13	3063	13
14	3569	13
15	3559	13
16	3559	13
17	3559	13
18	3559	13
19	3559	13
20	3655	13
21	3703	13
22	3785	13
23	3593	13

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series19.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

19.0ms

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

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
19×	`distribute-lft-out--_binary64`
14×	`add-cube-cbrt_binary64`

Counts

1 → 60

Calls

1 calls:

8.0ms

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

simplify83.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-def_binary64`
518×	`times-frac_binary64`
339×	`fma-neg_binary64`
291×	`distribute-rgt-in_binary64`
228×	`cancel-sign-sub-inv_binary64`

Counts

84 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2433
1	635	2369
2	2115	2256
3	4853	2256
4	5045	2256

prune84.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	107	3	110

Error

Counts

110 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
▶	0.3b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
	28.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 x (-.f64 2 y)) (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 2 y) 3)))) (+.f64 (/.f64 (.f64 y (pow.f64 x 3)) (pow.f64 (-.f64 2 y) 4)) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))))))

Compiler

Compiled 2720 to 1427 computations (47.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	2.8b	(log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))

series140.0ms (4.5%)

Counts

2 → 48

Calls

2 calls:

122.0ms	(log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
18.0ms	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

simplify86.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-/r*_binary64`
621×	`times-frac_binary64`
513×	`fma-def_binary64`
386×	`associate-/l*_binary64`
192×	`+-commutative_binary64`

Counts

70 → 105

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	578	5361
1	1944	5178
2	5391	5178

prune238.0ms (7.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	214	3	217

Error

Counts

217 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
▶	28.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 x (-.f64 2 y)) (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 2 y) 3)))) (+.f64 (/.f64 (.f64 y (pow.f64 x 3)) (pow.f64 (-.f64 2 y) 4)) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))))))

Compiler

Compiled 9780 to 6559 computations (32.9% saved)

localize25.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.3b	(*.f64 y (pow.f64 x 2))
✓	8.9b	(/.f64 (*.f64 y (pow.f64 x 3)) (pow.f64 (-.f64 2 y) 4))
✓	9.0b	(/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))
✓	10.1b	(/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2))

series160.0ms (5.2%)

Counts

4 → 44

Calls

4 calls:

51.0ms	(/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))
49.0ms	(/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2))
48.0ms	(/.f64 (*.f64 y (pow.f64 x 3)) (pow.f64 (-.f64 2 y) 4))
12.0ms	(*.f64 y (pow.f64 x 2))

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-exp-log_binary64`
43×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
35×	`associate-/r*_binary64`
35×	`times-frac_binary64`

Counts

4 → 176

Calls

4 calls:

7.0ms	(/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))
7.0ms	(/.f64 (*.f64 y (pow.f64 x 3)) (pow.f64 (-.f64 2 y) 4))
6.0ms	(/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2))
4.0ms	(*.f64 y (pow.f64 x 2))

simplify136.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
370×	`associate-/l*_binary64`
368×	`log-prod_binary64`
293×	`associate-/r*_binary64`
277×	`log-div_binary64`

Counts

220 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	4319
1	854	3833
2	4023	3780
3	4451	3780
4	5034	3780

prune453.0ms (14.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	256	3	259

Error

Counts

259 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))
✓	28.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 x (-.f64 2 y)) (/.f64 (pow.f64 x 3) (pow.f64 (-.f64 2 y) 3)))) (+.f64 (/.f64 (.f64 y (pow.f64 x 3)) (pow.f64 (-.f64 2 y) 4)) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))))))

Compiler

Compiled 18600 to 13380 computations (28.1% saved)

regimes337.0ms (10.9%)

Accuracy

Total 0.0b remaining (21.8%)

Threshold costs 0.0b (21.8%)

Counts

106 → 1

Compiler

Compiled 8158 to 5368 computations (34.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	13	13
2	24	13
3	32	13
4	36	13
5	37	13
6	37	13

end75.0ms (2.4%)

Compiler: Compiled 113 to 80 computations (29.2% saved)

Details

analyze37.0ms (1.2%)

sample866.0ms (28%)

simplify287.0ms (9.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.6%)

rewrite12.0ms (0.4%)

simplify83.0ms (2.7%)

prune84.0ms (2.7%)

localize8.0ms (0.3%)

series140.0ms (4.5%)

rewrite1.0ms (0%)

simplify86.0ms (2.8%)

prune238.0ms (7.7%)

localize25.0ms (0.8%)

series160.0ms (5.2%)

rewrite37.0ms (1.2%)

simplify136.0ms (4.4%)

prune453.0ms (14.6%)

regimes337.0ms (10.9%)

simplify3.0ms (0.1%)

end75.0ms (2.4%)

Profiling