Details

analyze36.0ms (0.5%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample695.0ms (9.9%)

Results

627.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify159.0ms (2.3%)

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

prune5.0ms (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

3.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 50 to 38 computations (24% saved)

localize18.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) (-.f64 3 x))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

series30.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

26.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
4.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

rewrite62.0ms (0.9%)

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:

29.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
18.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

simplify150.0ms (2.1%)

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

prune137.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	150	5	155

Error

0.0b

Counts

155 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	2.9b	(fma.f64 (/.f64 x y) -4/3 (fma.f64 1/3 (*.f64 (/.f64 x y) x) (/.f64 1 y)))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
	3.2b	(/.f64 (/.f64 (*.f64 (-.f64 1 x) (-.f64 3 x)) y) 3)
▶	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

Compiler

Compiled 3304 to 2236 computations (32.3% saved)

localize12.0ms (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)))

series47.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
20.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))

rewrite277.0ms (4%)

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:

42.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
15.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))

simplify693.0ms (9.9%)

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

prune883.0ms (12.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	694	3	697
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	697	5	702

Error

Counts

702 → 5

Alt Table

Status	Error	Program
	13.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 3 x)) (.f64 (cbrt.f64 3) (cbrt.f64 3))))) (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 y (/.f64 (sqrt.f64 (-.f64 3 x)) (cbrt.f64 3)))))
▶	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
	0.1b	(/.f64 1 (/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x)))
	0.2b	(/.f64 (-.f64 1 x) (*.f64 3 (/.f64 y (-.f64 3 x))))

Compiler

Compiled 18547 to 13257 computations (28.5% saved)

localize9.0ms (0.1%)

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 (0.3%)

Counts

2 → 40

Calls

2 calls:

14.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
7.0ms	(/.f64 (-.f64 1 x) y)

rewrite47.0ms (0.7%)

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:

28.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
11.0ms	(/.f64 (-.f64 1 x) y)

simplify94.0ms (1.3%)

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

prune262.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	156	5	161

Error

Counts

161 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
	13.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 3 x)) (.f64 (cbrt.f64 3) (cbrt.f64 3))))) (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 y (/.f64 (sqrt.f64 (-.f64 3 x)) (cbrt.f64 3)))))
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
	0.2b	(/.f64 (-.f64 1 x) (*.f64 3 (/.f64 y (-.f64 3 x))))

Compiler

Compiled 3127 to 2220 computations (29% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series50.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
16.0ms	(/.f64 (/.f64 (-.f64 3 x) 3) y)

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

222×	`times-frac_binary64`
160×	`add-sqr-sqrt_binary64`
151×	`*-un-lft-identity_binary64`
106×	`add-cube-cbrt_binary64`
61×	`associate-r_binary64`

Counts

2 → 189

Calls

2 calls:

21.0ms	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
12.0ms	(/.f64 (/.f64 (-.f64 3 x) 3) y)

simplify157.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
458×	`div-sub_binary64`
278×	`fma-def_binary64`
190×	`associate-/l/_binary64`
173×	`associate-/l*_binary64`

Counts

237 → 271

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	315	4919
1	779	4646
2	2709	4472
3	4651	4460
4	5492	4460

prune270.0ms (3.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	271	5	276

Error

Counts

276 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 1 x) (/.f64 (/.f64 (-.f64 3 x) 3) y))
	13.6b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 1 (/.f64 (sqrt.f64 (-.f64 3 x)) (.f64 (cbrt.f64 3) (cbrt.f64 3))))) (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 y (/.f64 (sqrt.f64 (-.f64 3 x)) (cbrt.f64 3)))))
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
✓	3.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
	0.2b	(/.f64 (-.f64 1 x) (*.f64 3 (/.f64 y (-.f64 3 x))))

Compiler

Compiled 5831 to 4206 computations (27.9% saved)

regimes2.7s (37.9%)

Accuracy

Total 0.1b remaining (87.5%)

Threshold costs 0.1b (87.5%)

Counts

287 → 1

Compiler

Compiled 32661 to 25351 computations (22.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	22	16
3	24	16
4	25	16
5	24	16

end160.0ms (2.3%)

Compiler: Compiled 112 to 89 computations (20.5% saved)

Details

analyze36.0ms (0.5%)

sample695.0ms (9.9%)

simplify159.0ms (2.3%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

series30.0ms (0.4%)

rewrite62.0ms (0.9%)

simplify150.0ms (2.1%)

prune137.0ms (2%)

localize12.0ms (0.2%)

series47.0ms (0.7%)

rewrite277.0ms (4%)

simplify693.0ms (9.9%)

prune883.0ms (12.6%)

localize9.0ms (0.1%)

series21.0ms (0.3%)

rewrite47.0ms (0.7%)

simplify94.0ms (1.3%)

prune262.0ms (3.7%)

localize17.0ms (0.2%)

series50.0ms (0.7%)

rewrite55.0ms (0.8%)

simplify157.0ms (2.2%)

prune270.0ms (3.9%)

regimes2.7s (37.9%)

simplify6.0ms (0.1%)

end160.0ms (2.3%)

Profiling