Details

analyze16.0ms (0.6%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample1.1s (42.3%)

Results

943.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify103.0ms (4%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (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

29.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 44 computations (45% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.2b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	29.2b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series23.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
7.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

rewrite30.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

24.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
3.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify92.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-l_binary64`
433×	`fma-def_binary64`
328×	`times-frac_binary64`
299×	`associate-/l*_binary64`
248×	`associate-/r*_binary64`

Counts

98 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	2360
1	338	2193
2	1191	2164
3	4702	2164
4	4914	2164

prune74.0ms (2.9%)

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

0.3b

Counts

110 → 3

Alt Table

Status	Error	Program
	35.4b	1
▶	28.1b	-1
	29.8b	(-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 y y) 4))) (/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (*.f64 y y) 4))))

Compiler

Compiled 3265 to 1710 computations (47.6% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 3

Alt Table

Status	Error	Program
	35.4b	1
✓	28.1b	-1
▶	29.8b	(-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 y y) 4))) (/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (*.f64 y y) 4))))

Compiler

Compiled 67 to 39 computations (41.8% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 y y) 4))) (/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (*.f64 y y) 4))))
✓	0.0b	(.f64 (.f64 y y) 4)
✓	21.9b	(/.f64 (.f64 x x) (fma.f64 x x (.f64 (*.f64 y y) 4)))
✓	23.4b	(/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (.f64 y y) 4)))

series59.0ms (2.3%)

Counts

4 → 84

Calls

4 calls:

23.0ms	(-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 y y) 4))) (/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (*.f64 y y) 4))))
18.0ms	(/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (.f64 y y) 4)))
16.0ms	(/.f64 (.f64 x x) (fma.f64 x x (.f64 (*.f64 y y) 4)))
2.0ms	(.f64 (.f64 y y) 4)

rewrite41.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`times-frac_binary64`
49×	`prod-diff_binary64`
46×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`

Counts

4 → 151

Calls

4 calls:

8.0ms	(-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 y y) 4))) (/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (*.f64 y y) 4))))
8.0ms	(.f64 (.f64 y y) 4)
5.0ms	(/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (.f64 y y) 4)))
3.0ms	(/.f64 (.f64 x x) (fma.f64 x x (.f64 (*.f64 y y) 4)))

simplify194.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

437×	`cancel-sign-sub-inv_binary64`
351×	`fma-neg_binary64`
288×	`neg-mul-1_binary64`
287×	`distribute-rgt-neg-in_binary64`
247×	`distribute-lft-neg-in_binary64`

Counts

235 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	10747
1	740	8088
2	2675	6628
3	4308	6628
4	4905	6628

prune310.0ms (12.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	335	0	335
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	335	3	338

Error

0.3b

Counts

338 → 3

Alt Table

Status	Error	Program
▶	35.4b	1
✓	28.1b	-1
✓	29.8b	(-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 y y) 4))) (/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (*.f64 y y) 4))))

Compiler

Compiled 15285 to 7377 computations (51.7% saved)

localize0.0ms (0%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

0.3b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	35.4b	1
✓	28.1b	-1
✓	29.8b	(-.f64 (/.f64 (.f64 x x) (fma.f64 x x (.f64 (.f64 y y) 4))) (/.f64 (.f64 (.f64 y y) 4) (fma.f64 x x (.f64 (*.f64 y y) 4))))

Compiler

Compiled 35 to 21 computations (40% saved)

regimes377.0ms (14.7%)

Accuracy

Total 12.7b remaining (97.2%)

Threshold costs 0b (0%)

Counts

31 → 5

Compiler

Compiled 4129 to 2548 computations (38.3% saved)

bsearch68.0ms (2.6%)

Steps

Iters	Range		Point
10	1.4201779954658556e+95	6.029135533610017e+108	7.048940344096351e+96
9	3.618681489573081e-167	4.5683290359466876e-160	4.1575865434538223e-162
8	-1.7974487199906995e-96	-1.57612231211111e-100	-2.029692625314952e-98
3	-1.0574550404107041e+70	-7.323696027716415e+69	-1.0371372005582628e+70

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	93
1	37	93
2	42	93
3	50	93
4	58	93
5	63	93
6	66	93
7	67	93
8	65	93

end60.0ms (2.4%)

Compiler: Compiled 169 to 99 computations (41.4% saved)

Details

analyze16.0ms (0.6%)

sample1.1s (42.3%)

simplify103.0ms (4%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series23.0ms (0.9%)

rewrite30.0ms (1.2%)

simplify92.0ms (3.6%)

prune74.0ms (2.9%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize9.0ms (0.4%)

series59.0ms (2.3%)

rewrite41.0ms (1.6%)

simplify194.0ms (7.6%)

prune310.0ms (12.1%)

localize0.0ms (0%)

prune2.0ms (0.1%)

regimes377.0ms (14.7%)

bsearch68.0ms (2.6%)

simplify7.0ms (0.3%)

end60.0ms (2.4%)

Profiling