Details

analyze164.0ms (1.8%)

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)

sample1.0s (11.2%)

Results

924.0ms	8256×	body	128	valid
40.0ms	331×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify83.0ms (0.9%)

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

prune4.0ms (0%)

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

4.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.0b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 50 to 38 computations (24% saved)

localize10.0ms (0.1%)

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))

series16.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

12.0ms	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))
3.0ms	(*.f64 (-.f64 1 x) (-.f64 3 x))

rewrite25.0ms (0.3%)

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:

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

simplify92.0ms (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

prune143.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	6	155

Error

0.0b

Counts

155 → 6

Alt Table

Status	Error	Program
	0.2b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	3.9b	(/.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)))
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
	4.0b	(/.f64 (fma.f64 x (+.f64 x -4) 3) (*.f64 y 3))
	4.1b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1 (*.f64 y 3)))

Compiler

Compiled 3335 to 2266 computations (32.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series28.0ms (0.3%)

Counts

3 → 60

Calls

3 calls:

14.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
12.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
2.0ms	(/.f64 (-.f64 3 x) 3)

rewrite140.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

1218×	`times-frac_binary64`
808×	`*-un-lft-identity_binary64`
808×	`add-sqr-sqrt_binary64`
461×	`add-cube-cbrt_binary64`
205×	`difference-of-squares_binary64`

Counts

3 → 598

Calls

3 calls:

19.0ms	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
8.0ms	(/.f64 y (/.f64 (-.f64 3 x) 3))
4.0ms	(/.f64 (-.f64 3 x) 3)

simplify375.0ms (4%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/l/_binary64`
532×	`associate-/r*_binary64`
489×	`associate-/r/_binary64`
395×	`associate-/l*_binary64`
278×	`div-sub_binary64`

Counts

658 → 750

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	740	21081
1	2010	20780
2	5237	20780

prune683.0ms (7.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	747	3	750
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	750	6	756

Error

Counts

756 → 6

Alt Table

Status	Error	Program
	3.9b	(.f64 (/.f64 1 y) (.f64 (-.f64 1 x) (/.f64 (-.f64 3 x) 3)))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) y) (*.f64 (cbrt.f64 (-.f64 1 x)) (/.f64 (-.f64 3 x) 3)))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
▶	0.1b	(/.f64 1 (/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x)))
	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
	4.0b	(/.f64 (fma.f64 x (+.f64 x -4) 3) (*.f64 y 3))

Compiler

Compiled 19460 to 13954 computations (28.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series50.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x))
12.0ms	(/.f64 1 (/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x)))

rewrite616.0ms (6.6%)

Algorithm

1×	rewrite-expression-head

Rules

6156×	`times-frac_binary64`
3644×	`*-un-lft-identity_binary64`
3644×	`add-sqr-sqrt_binary64`
2153×	`add-cube-cbrt_binary64`
901×	`difference-of-squares_binary64`

Counts

2 → 2007

Calls

2 calls:

61.0ms	(/.f64 1 (/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x)))
21.0ms	(/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x))

simplify1.6s (17.1%)

Algorithm

1×	egg-herbie

Rules

606×	`associate-/l*_binary64`
511×	`associate-/r/_binary64`
445×	`times-frac_binary64`
368×	`associate-/l/_binary64`
220×	`distribute-lft-in_binary64`

Counts

2055 → 2083

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1132	82013
1	2678	78310
2	5082	78310

prune2.3s (24.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	2273	1	2274
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	2274	6	2280

Error

Counts

2280 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x)))
	3.9b	(/.f64 (-.f64 (fma.f64 1/3 (.f64 x x) 1) (.f64 x 4/3)) y)
	3.9b	(.f64 (/.f64 1 y) (.f64 (-.f64 1 x) (/.f64 (-.f64 3 x) 3)))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) y) (*.f64 (cbrt.f64 (-.f64 1 x)) (/.f64 (-.f64 3 x) 3)))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
▶	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))

Compiler

Compiled 73104 to 54480 computations (25.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
✓	0.2b	(/.f64 (*.f64 y 3) (-.f64 3 x))

series25.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(/.f64 (*.f64 y 3) (-.f64 3 x))
12.0ms	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))

rewrite120.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`times-frac_binary64`
84×	`*-un-lft-identity_binary64`
84×	`add-sqr-sqrt_binary64`
33×	`difference-of-squares_binary64`
30×	`add-cube-cbrt_binary64`

Counts

2 → 134

Calls

2 calls:

105.0ms	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
4.0ms	(/.f64 (*.f64 y 3) (-.f64 3 x))

simplify241.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
439×	`distribute-rgt-in_binary64`
182×	`associate-/r/_binary64`
182×	`fma-neg_binary64`
155×	`associate-/l*_binary64`

Counts

182 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	263	4259
1	702	3987
2	2701	3912
3	4634	3900
4	4948	3900

prune234.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	219	6	225

Error

Counts

225 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f64 (/.f64 (-.f64 1 x) y) (/.f64 3 (-.f64 3 x)))
✓	0.1b	(/.f64 1 (/.f64 (/.f64 y (/.f64 (-.f64 3 x) 3)) (-.f64 1 x)))
	3.9b	(.f64 (/.f64 1 y) (.f64 (-.f64 1 x) (/.f64 (-.f64 3 x) 3)))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) y) (*.f64 (cbrt.f64 (-.f64 1 x)) (/.f64 (-.f64 3 x) 3)))
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
✓	0.2b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))

Compiler

Compiled 4531 to 3318 computations (26.8% saved)

regimes1.2s (13%)

Accuracy

Total 0.1b remaining (88.8%)

Threshold costs 0.1b (88.8%)

Counts

214 → 1

Compiler

Compiled 19631 to 15435 computations (21.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	20	16
3	22	16
4	23	16
5	22	16

end88.0ms (0.9%)

Compiler: Compiled 119 to 93 computations (21.8% saved)

Details

analyze164.0ms (1.8%)

sample1.0s (11.2%)

simplify83.0ms (0.9%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series16.0ms (0.2%)

rewrite25.0ms (0.3%)

simplify92.0ms (1%)

prune143.0ms (1.5%)

localize7.0ms (0.1%)

series28.0ms (0.3%)

rewrite140.0ms (1.5%)

simplify375.0ms (4%)

prune683.0ms (7.3%)

localize10.0ms (0.1%)

series50.0ms (0.5%)

rewrite616.0ms (6.6%)

simplify1.6s (17.1%)

prune2.3s (24.9%)

localize7.0ms (0.1%)

series25.0ms (0.3%)

rewrite120.0ms (1.3%)

simplify241.0ms (2.6%)

prune234.0ms (2.5%)

regimes1.2s (13%)

simplify3.0ms (0%)

end88.0ms (0.9%)

Profiling