Details

analyze1.4s (33.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (26.6%)

Results

833.0ms	8254×	body	128	valid
1.0ms	2×	body	1024	valid

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify273.0ms (6.4%)

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)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series17.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

16.0ms

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

rewrite14.0ms (0.3%)

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:

10.0ms

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

simplify90.0ms (2.1%)

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

prune80.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	3	110

Error

Counts

110 → 3

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
	30.2b	(-.f64 (+.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (pow.f64 (/.f64 x (-.f64 2 y)) 3)) (fma.f64 (/.f64 y (pow.f64 (-.f64 2 y) 4)) (pow.f64 x 3) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y)))))))
▶	0.0b	(/.f64 (/.f64 (-.f64 x y) 1) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 2717 to 1420 computations (47.7% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series17.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

17.0ms

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

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

226×	`*-un-lft-identity_binary64`
219×	`times-frac_binary64`
166×	`add-sqr-sqrt_binary64`
84×	`add-cube-cbrt_binary64`
61×	`distribute-lft-out--_binary64`

Counts

1 → 160

Calls

1 calls:

12.0ms

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

simplify140.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-def_binary64`
632×	`times-frac_binary64`
244×	`cancel-sign-sub-inv_binary64`
229×	`distribute-rgt-in_binary64`
229×	`sub-neg_binary64`

Counts

184 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	5136
1	649	5045
2	2194	4930
3	5011	4930

prune116.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	185	3	188

Error

Counts

188 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
	30.2b	(-.f64 (+.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (pow.f64 (/.f64 x (-.f64 2 y)) 3)) (fma.f64 (/.f64 y (pow.f64 (-.f64 2 y) 4)) (pow.f64 x 3) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y)))))))
✓	0.0b	(/.f64 (/.f64 (-.f64 x y) 1) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 4849 to 2614 computations (46.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 2 (+.f64 x y)))
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

series30.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
13.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
24×	`associate-r_binary64`
24×	`add-cube-cbrt_binary64`

Counts

2 → 102

Calls

2 calls:

14.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
6.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

654×	`times-frac_binary64`
403×	`fma-neg_binary64`
325×	`sub-neg_binary64`
288×	`cancel-sign-sub-inv_binary64`
188×	`+-commutative_binary64`

Counts

150 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	3603
1	851	3445
2	3068	3427
3	4942	3427
4	5145	3427

prune149.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	192	3	195

Error

Counts

195 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
✓	0.0b	(/.f64 (/.f64 (-.f64 x y) 1) (-.f64 2 (+.f64 x y)))
▶	0.1b	(*.f64 (-.f64 x y) (expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))))

Compiler

Compiled 4660 to 2699 computations (42.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (-.f64 2 (+.f64 x y)))
✓	0.0b	(log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y)))))
✓	0.1b	(*.f64 (-.f64 x y) (expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))))

series63.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))
19.0ms	(*.f64 (-.f64 x y) (expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))))
13.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y)))))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 46

Calls

3 calls:

5.0ms	(*.f64 (-.f64 x y) (expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))))
0.0ms	(log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y)))))

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

440×	`sub-neg_binary64`
270×	`+-commutative_binary64`
261×	`associate-+r+_binary64`
228×	`associate-+l+_binary64`
223×	`fma-def_binary64`

Counts

118 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	376	4179
1	1122	3986
2	4326	3961
3	5107	3961

prune188.0ms (4.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	245	3	248

Error

Counts

248 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
✓	0.0b	(/.f64 (/.f64 (-.f64 x y) 1) (-.f64 2 (+.f64 x y)))
✓	0.1b	(*.f64 (-.f64 x y) (expm1.f64 (log1p.f64 (/.f64 1 (-.f64 2 (+.f64 x y))))))

Compiler

Compiled 7090 to 4586 computations (35.3% saved)

regimes156.0ms (3.6%)

Accuracy

Total 0.0b remaining (24%)

Threshold costs 0.0b (24%)

Counts

53 → 1

Compiler

Compiled 3133 to 2047 computations (34.7% 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

end51.0ms (1.2%)

Compiler: Compiled 63 to 43 computations (31.7% saved)

Details

analyze1.4s (33.4%)

sample1.1s (26.6%)

simplify273.0ms (6.4%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series17.0ms (0.4%)

rewrite14.0ms (0.3%)

simplify90.0ms (2.1%)

prune80.0ms (1.9%)

localize7.0ms (0.2%)

series17.0ms (0.4%)

rewrite36.0ms (0.9%)

simplify140.0ms (3.3%)

prune116.0ms (2.7%)

localize9.0ms (0.2%)

series30.0ms (0.7%)

rewrite26.0ms (0.6%)

simplify116.0ms (2.7%)

prune149.0ms (3.5%)

localize10.0ms (0.2%)

series63.0ms (1.5%)

rewrite7.0ms (0.2%)

simplify104.0ms (2.4%)

prune188.0ms (4.4%)

regimes156.0ms (3.6%)

simplify3.0ms (0.1%)

end51.0ms (1.2%)

Profiling