Details

analyze140.0ms (4.7%)

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)

sample931.0ms (31.2%)

Results

802.0ms	8256×	body	128	valid
67.0ms	335×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify77.0ms (2.6%)

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

2.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.7b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

Compiler

Compiled 50 to 38 computations (24% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) (-.f64 3 x))
✓	2.6b	(/.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (.f64 y 3))

series14.0ms (0.5%)

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))

rewrite24.0ms (0.8%)

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

simplify84.0ms (2.8%)

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

prune125.0ms (4.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	149	5	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
	2.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1/3 y))
	2.9b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1 (*.f64 y 3)))
▶	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	2.6b	(/.f64 (/.f64 (*.f64 (-.f64 1 x) (-.f64 3 x)) y) 3)
	0.4b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))

Compiler

Compiled 3313 to 2250 computations (32.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series20.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

12.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
7.0ms	(/.f64 (-.f64 1 x) y)
1.0ms	(/.f64 (-.f64 3 x) 3)

rewrite35.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
22×	`associate-l_binary64`

Counts

3 → 151

Calls

3 calls:

16.0ms	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
5.0ms	(/.f64 (-.f64 1 x) y)
4.0ms	(/.f64 (-.f64 3 x) 3)

simplify133.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-in_binary64`
490×	`times-frac_binary64`
284×	`fma-def_binary64`
153×	`associate-*r/_binary64`
150×	`associate-*l/_binary64`

Counts

203 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3302
1	602	3033
2	1953	2971
3	4746	2959
4	4996	2959
5	4946	2959

prune138.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	211	4	215

Error

Counts

215 → 4

Alt Table

Status	Error	Program
	2.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1/3 y))
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
	2.4b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3))) y)
▶	0.4b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))

Compiler

Compiled 3977 to 2866 computations (27.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
✓	0.4b	(/.f64 (*.f64 y 3) (-.f64 3 x))

series23.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
11.0ms	(/.f64 (*.f64 y 3) (-.f64 3 x))

rewrite26.0ms (0.9%)

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:

9.0ms	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))
5.0ms	(/.f64 (*.f64 y 3) (-.f64 3 x))

simplify124.0ms (4.2%)

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

prune352.0ms (11.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	219	4	223

Error

Counts

223 → 4

Alt Table

Status	Error	Program
	2.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1/3 y))
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
▶	2.4b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3))) y)
✓	0.4b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))

Compiler

Compiled 4514 to 3303 computations (26.8% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3)))
✓	0.1b	(fma.f64 x 1/3 -4/3)
✓	0.3b	(*.f64 x (fma.f64 x 1/3 -4/3))
✓	2.2b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3))) y)

series22.0ms (0.7%)

Counts

4 → 60

Calls

4 calls:

16.0ms	(/.f64 (+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3))) y)
3.0ms	(*.f64 x (fma.f64 x 1/3 -4/3))
2.0ms	(+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3)))
1.0ms	(fma.f64 x 1/3 -4/3)

rewrite48.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 81

Calls

4 calls:

39.0ms	(/.f64 (+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3))) y)
3.0ms	(*.f64 x (fma.f64 x 1/3 -4/3))
2.0ms	(+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3)))
0.0ms	(fma.f64 x 1/3 -4/3)

simplify124.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-neg_binary64`
309×	`associate-l_binary64`
306×	`div-sub_binary64`
280×	`cancel-sign-sub-inv_binary64`
257×	`fma-def_binary64`

Counts

141 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	2206
1	294	1856
2	763	1643
3	2747	1638
4	4373	1638
5	4978	1638
6	4927	1638

prune173.0ms (5.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	147	4	151

Error

Counts

151 → 4

Alt Table

Status	Error	Program
	2.7b	(.f64 (.f64 (-.f64 1 x) (-.f64 3 x)) (/.f64 1/3 y))
✓	0.1b	(*.f64 (/.f64 (-.f64 1 x) y) (/.f64 (-.f64 3 x) 3))
✓	2.4b	(/.f64 (+.f64 1 (*.f64 x (fma.f64 x 1/3 -4/3))) y)
✓	0.4b	(/.f64 (-.f64 1 x) (/.f64 (*.f64 y 3) (-.f64 3 x)))

Compiler

Compiled 2457 to 1758 computations (28.4% saved)

regimes274.0ms (9.2%)

Accuracy

Total 0.1b remaining (82.9%)

Threshold costs 0.1b (82.9%)

Counts

53 → 1

Compiler

Compiled 4014 to 3021 computations (24.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	16	16
2	21	16
3	23	16
4	24	16
5	23	16

end64.0ms (2.1%)

Compiler: Compiled 77 to 59 computations (23.4% saved)

Details

analyze140.0ms (4.7%)

sample931.0ms (31.2%)

simplify77.0ms (2.6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series14.0ms (0.5%)

rewrite24.0ms (0.8%)

simplify84.0ms (2.8%)

prune125.0ms (4.2%)

localize7.0ms (0.2%)

series20.0ms (0.7%)

rewrite35.0ms (1.2%)

simplify133.0ms (4.5%)

prune138.0ms (4.6%)

localize6.0ms (0.2%)

series23.0ms (0.8%)

rewrite26.0ms (0.9%)

simplify124.0ms (4.2%)

prune352.0ms (11.8%)

localize6.0ms (0.2%)

series22.0ms (0.7%)

rewrite48.0ms (1.6%)

simplify124.0ms (4.2%)

prune173.0ms (5.8%)

regimes274.0ms (9.2%)

simplify3.0ms (0.1%)

end64.0ms (2.1%)

Profiling