Details

Time bar (total: 2.3s)

analyze172.0ms (7.6%)

Algorithm
search
Search
TrueOtherFalseIter
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
49.9%49.9%0.1%5
74.9%25%0.1%6
74.9%25%0.1%7
74.9%25%0.1%8
81.1%18.7%0.1%9
81.1%18.7%0.1%10
81.1%15.6%3.3%11
84.3%10.9%4.8%12
84.3%10.9%4.8%13
84.3%8.6%7.2%14
Compiler

Compiled 13 to 10 computations (23.1% saved)

sample962.0ms (42.4%)

Symmetry

(sort x y)

Results
831.0ms8256×body128valid
50.0ms545×body128invalid
Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify23.0ms (1%)

Algorithm
egg-herbie
Rules
209×fma-def_binary64
157×fma-neg_binary64
56×cancel-sign-sub-inv_binary64
42×distribute-rgt-neg-in_binary64
36×associate-/l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01013
11513
22613
33913
46611
510911
619811
730711
842911
952211
1057811
1159311
1259611
1351311

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.0b
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
Compiler

Compiled 42 to 29 computations (31% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

series7.0ms (0.3%)

Counts
1 → 36
Calls

1 calls:

7.0ms
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

rewrite45.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
830×log1p-expm1-u_binary64
830×expm1-log1p-u_binary64
127×prod-diff_binary64
94×add-sqr-sqrt_binary64
88×add-log-exp_binary64
Counts
1 → 24
Calls

1 calls:

44.0ms
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
119011
2217311
3528611
000
100

simplify39.0ms (1.7%)

Algorithm
egg-herbie
Rules
269×fma-def_binary64
143×fma-neg_binary64
49×distribute-rgt-neg-in_binary64
47×cancel-sign-sub-inv_binary64
27×unsub-neg_binary64
Counts
60 → 29
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
012402
123348
238348
355348
492348
5138348
6228348
7346348
8413348
9472348
10488348
11492348
12433348

prune16.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New28129
Fresh000
Picked011
Done000
Total28230
Error
0.0b
Counts
30 → 2
Alt Table
StatusErrorProgram
28.8b
(/.f64 (-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4)) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
0.0b
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
Compiler

Compiled 422 to 270 computations (36% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2))
0.3b
(pow.f64 (*.f64 x y) 2)
2.3b
(-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4))
27.3b
(/.f64 (-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4)) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))

series75.0ms (3.3%)

Counts
4 → 132
Calls

4 calls:

36.0ms
(/.f64 (-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4)) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
25.0ms
(-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4))
7.0ms
(-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2))
6.0ms
(pow.f64 (*.f64 x y) 2)

rewrite92.0ms (4%)

Algorithm
batch-egg-rewrite
Rules
310×log1p-udef_binary64
180×log1p-expm1-u_binary64
180×expm1-log1p-u_binary64
179×add-sqr-sqrt_binary64
174×add-cbrt-cube_binary64
Counts
4 → 149
Calls

4 calls:

88.0ms
(-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2))
88.0ms
(pow.f64 (*.f64 x y) 2)
88.0ms
(-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4))
88.0ms
(/.f64 (-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4)) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01673
137946
2464746
3498346
000
100

simplify140.0ms (6.1%)

Algorithm
egg-herbie
Rules
878×fma-neg_binary64
549×associate-*l*_binary64
521×distribute-rgt-neg-in_binary64
456×distribute-lft-neg-in_binary64
440×neg-mul-1_binary64
Counts
281 → 166
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0281731
1741623
21651569
35091569
418901569
535241569
645031569
749561569
849041569

prune119.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1651166
Fresh000
Picked011
Done011
Total1653168
Error
0.0b
Counts
168 → 3
Alt Table
StatusErrorProgram
28.8b
(/.f64 (-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4)) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
0.0b
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
55.6b
(/.f64 (*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2))) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
Compiler

Compiled 4912 to 3084 computations (37.2% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2)))
0.0b
(-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2))
16.6b
(/.f64 (*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2))) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
17.9b
(*.f64 (pow.f64 y 2) (pow.f64 x 2))

series51.0ms (2.2%)

Counts
3 → 36
Calls

3 calls:

25.0ms
(/.f64 (*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2))) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
16.0ms
(*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2)))
9.0ms
(*.f64 (pow.f64 y 2) (pow.f64 x 2))

rewrite78.0ms (3.4%)

Algorithm
batch-egg-rewrite
Rules
295×expm1-udef_binary64
295×log1p-udef_binary64
170×add-sqr-sqrt_binary64
166×log1p-expm1-u_binary64
166×expm1-log1p-u_binary64
Counts
3 → 80
Calls

3 calls:

76.0ms
(*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2)))
76.0ms
(/.f64 (*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2))) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
76.0ms
(*.f64 (pow.f64 y 2) (pow.f64 x 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01642
135740
2434940
3506540
000
100

simplify83.0ms (3.6%)

Algorithm
egg-herbie
Rules
618×fma-neg_binary64
514×times-frac_binary64
512×unswap-sqr_binary64
314×associate-/l*_binary64
266×associate-*r*_binary64
Counts
116 → 95
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0551191
11701155
25971137
333841137
448361101
549991101
649791101

prune84.0ms (3.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1410141
Fresh000
Picked011
Done022
Total1413144
Error
0.0b
Counts
144 → 3
Alt Table
StatusErrorProgram
28.8b
(/.f64 (-.f64 (*.f64 (*.f64 z -1/8) (*.f64 z -1/8)) (/.f64 (pow.f64 (*.f64 x y) 2) 4)) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
0.0b
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
55.6b
(/.f64 (*.f64 -1/4 (*.f64 (pow.f64 y 2) (pow.f64 x 2))) (-.f64 (*.f64 z -1/8) (/.f64 (*.f64 x y) 2)))
Compiler

Compiled 3513 to 2237 computations (36.3% saved)

regimes190.0ms (8.4%)

Accuracy

Total 0.0b remaining (3.4%)

Threshold costs 0.0b (3.4%)

Counts
23 → 1
Compiler

Compiled 3641 to 2611 computations (28.3% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11011
21011

end63.0ms (2.8%)

Remove

(sort x y)

Compiler

Compiled 105 to 77 computations (26.7% saved)

Profiling

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