Details

analyze161.0ms (4.4%)

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
37.5%	62.4%	0.1%	6
50%	46.8%	3.2%	7
56.2%	37.5%	6.3%	8
62.4%	25.8%	11.8%	9
65.6%	20.3%	14.1%	10
68.7%	13.5%	17.9%	11
70.2%	10.5%	19.2%	12
71.8%	6.9%	21.3%	13
72.6%	5.4%	22%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample963.0ms (26.5%)

Results

863.0ms	8256×	body	128	valid
32.0ms	323×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify79.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

877×	`div-sub_binary64`
637×	`sub-neg_binary64`
618×	`unsub-neg_binary64`
440×	`neg-sub0_binary64`
439×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	16
2	71	16
3	192	16
4	634	16
5	1914	16
6	3304	16
7	4241	16
8	4674	16
9	4931	16

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

5.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 50 to 38 computations (24% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) (-.f64 3 x))
✓	5.2b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

series15.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

12.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
2.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 90

Calls

2 calls:

12.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
8.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

simplify96.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
614×	`associate-/r*_binary64`
196×	`associate-l_binary64`
194×	`associate-/l/_binary64`
174×	`associate-r_binary64`

Counts

126 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	2319
1	508	2006
2	2204	1772
3	4855	1760
4	4865	1760

prune142.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	7	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	147	8	155

Error

0.0b

Counts

155 → 8

Alt Table

Status	Error	Program
✓	5.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
	5.2b	(/.f64 (/.f64 (*.f64 (-.f64 1 x) (-.f64 3 x)) y) 3)
	0.2b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
▶	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	5.1b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	5.2b	(/.f64 1 (/.f64 3 (/.f64 (*.f64 (-.f64 3 x) (-.f64 1 x)) y)))
	5.1b	(-.f64 (+.f64 (/.f64 1 y) (.f64 1/3 (/.f64 (pow.f64 x 2) y))) (.f64 4/3 (/.f64 x y)))

Compiler

Compiled 3396 to 2306 computations (32.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 x) y)
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))

series21.0ms (0.6%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
6.0ms	(/.f64 (-.f64 1 x) y)

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
55×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
22×	`associate-l_binary64`

Counts

2 → 111

Calls

2 calls:

17.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
5.0ms	(/.f64 (-.f64 1 x) y)

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Rules

523×	`distribute-rgt-in_binary64`
502×	`distribute-lft-in_binary64`
476×	`times-frac_binary64`
235×	`fma-def_binary64`
146×	`associate-*l/_binary64`

Counts

151 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2665
1	522	2432
2	1767	2402
3	5327	2402

prune126.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	157	7	164

Error

Counts

164 → 7

Alt Table

Status	Error	Program
	5.1b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
	0.2b	(/.f64 (*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x)) 3)
✓	5.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
▶	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	5.2b	(/.f64 1 (/.f64 3 (/.f64 (*.f64 (-.f64 3 x) (-.f64 1 x)) y)))
	5.1b	(-.f64 (+.f64 (/.f64 1 y) (.f64 1/3 (/.f64 (pow.f64 x 2) y))) (.f64 4/3 (/.f64 x y)))
	0.2b	(.f64 (.f64 (-.f64 1 x) (/.f64 1 y)) (/.f64 (-.f64 3 x) 3))

Compiler

Compiled 3168 to 2246 computations (29.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 y (/.f64 (-.f64 3 x) 3))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

series26.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
12.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

rewrite129.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1203×	`times-frac_binary64`
789×	`*-un-lft-identity_binary64`
789×	`add-sqr-sqrt_binary64`
450×	`add-cube-cbrt_binary64`
201×	`difference-of-squares_binary64`

Counts

2 → 558

Calls

2 calls:

22.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
6.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))

simplify392.0ms (10.8%)

Algorithm

1×	egg-herbie

Rules

544×	`associate-/l/_binary64`
531×	`associate-/r*_binary64`
489×	`associate-/r/_binary64`
393×	`associate-/l*_binary64`
265×	`div-sub_binary64`

Counts

606 → 697

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	717	20450
1	1959	20177
2	5139	20177

prune532.0ms (14.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	695	2	697
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	698	6	704

Error

Counts

704 → 6

Alt Table

Status	Error	Program
	5.1b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
▶	0.2b	(/.f64 (*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x)) 3)
	0.2b	(/.f64 (-.f64 1 x) (*.f64 3 (/.f64 y (-.f64 3 x))))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
	5.1b	(-.f64 (fma.f64 1/3 (/.f64 (.f64 x x) y) (/.f64 1 y)) (.f64 4/3 (/.f64 x y)))
✓	5.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 18522 to 13227 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 1 x) y)
✓	0.2b	(/.f64 (*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x)) 3)
✓	0.3b	(*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x))

series23.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(/.f64 (*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x)) 3)
9.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
22×	`associate-l_binary64`
22×	`times-frac_binary64`

Counts

2 → 105

Calls

2 calls:

10.0ms	(/.f64 (*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x)) 3)
10.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x))

simplify102.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

695×	`times-frac_binary64`
526×	`fma-def_binary64`
397×	`fma-neg_binary64`
165×	`div-sub_binary64`
149×	`cancel-sign-sub-inv_binary64`

Counts

153 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	3015
1	566	2705
2	1966	2461
3	4347	2441
4	4872	2441

prune168.0ms (4.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	235	6	241

Error

Counts

241 → 6

Alt Table

Status	Error	Program
	5.1b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 1/3 x -4/3))) y)
✓	0.2b	(/.f64 (*.f64 (/.f64 (-.f64 1 x) y) (-.f64 3 x)) 3)
	0.2b	(/.f64 (-.f64 1 x) (*.f64 3 (/.f64 y (-.f64 3 x))))
	5.1b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 (/.f64 (*.f64 x x) y) 1/3 (/.f64 1 y)))
✓	5.5b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

Compiler

Compiled 4693 to 3150 computations (32.9% saved)

regimes388.0ms (10.7%)

Accuracy

Total 0.1b remaining (93.6%)

Threshold costs 0.1b (93.6%)

Counts

77 → 1

Compiler

Compiled 5529 to 4199 computations (24.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	18	19
2	26	19
3	30	19
4	32	19
5	31	19

end81.0ms (2.2%)

Compiler: Compiled 111 to 82 computations (26.1% saved)

Details

analyze161.0ms (4.4%)

sample963.0ms (26.5%)

simplify79.0ms (2.2%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series15.0ms (0.4%)

rewrite26.0ms (0.7%)

simplify96.0ms (2.6%)

prune142.0ms (3.9%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite33.0ms (0.9%)

simplify74.0ms (2%)

prune126.0ms (3.5%)

localize7.0ms (0.2%)

series26.0ms (0.7%)

rewrite129.0ms (3.6%)

simplify392.0ms (10.8%)

prune532.0ms (14.6%)

localize8.0ms (0.2%)

series23.0ms (0.6%)

rewrite28.0ms (0.8%)

simplify102.0ms (2.8%)

prune168.0ms (4.6%)

regimes388.0ms (10.7%)

simplify3.0ms (0.1%)

end81.0ms (2.2%)

Profiling