Details

Time bar (total: 2.8s)

analyze200.0ms (7.1%)

Algorithm
1×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)

sample1.1s (37.8%)

Symmetry

(sort x y)

Results
927.0ms8255×body128valid
56.0ms551×body128invalid
0.0ms1×body512valid
Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify27.0ms (1%)

Algorithm
1×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 2 expressions with local error:

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

series12.0ms (0.4%)

Counts
2 → 60
Calls

2 calls:

8.0ms
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
5.0ms
(/.f64 (*.f64 x y) 2)

rewrite50.0ms (1.8%)

Algorithm
2×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
2 → 52
Calls

2 calls:

49.0ms
(/.f64 (*.f64 x y) 2)
49.0ms
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
119018
2217318
3528618
000
100

simplify51.0ms (1.8%)

Algorithm
1×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
112 → 57
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
012570
123516
238516
355516
492516
5138516
6228516
7346516
8413516
9472516
10488516
11492516
12433516

prune35.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New55257
Fresh000
Picked011
Done000
Total55358
Error
0.0b
Counts
58 → 3
Alt Table
StatusErrorProgram
▶0.5b
(fma.f64 z -1/8 (*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2)))
✓0.0b
(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
0.5b
(fma.f64 z -1/8 (*.f64 (cbrt.f64 (/.f64 (*.f64 x y) 2)) (pow.f64 (cbrt.f64 (/.f64 (*.f64 x y) 2)) 2)))
Compiler

Compiled 759 to 473 computations (37.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 z -1/8 (*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2)))
✓0.3b
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2))
✓0.5b
(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
✓9.3b
(cbrt.f64 (*.f64 x y))

series947.0ms (33.5%)

Counts
4 → 108
Calls

4 calls:

517.0ms
(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
371.0ms
(cbrt.f64 (*.f64 x y))
32.0ms
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2))
26.0ms
(fma.f64 z -1/8 (*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2)))

rewrite98.0ms (3.5%)

Algorithm
2×batch-egg-rewrite
Rules
560×log-prod_binary64
213×expm1-udef_binary64
213×log1p-udef_binary64
188×log-pow_binary64
186×prod-diff_binary64
Counts
4 → 99
Calls

4 calls:

96.0ms
(fma.f64 z -1/8 (*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2)))
96.0ms
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2))
96.0ms
(pow.f64 (cbrt.f64 (*.f64 x y)) 2)
96.0ms
(cbrt.f64 (*.f64 x y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01333
126231
2271731
3499431
4487131
000
100

simplify87.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
662×fma-def_binary64
597×div-sub_binary64
371×exp-sum_binary64
294×associate-*l*_binary64
266×associate-*r*_binary64
Counts
207 → 119
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0521418
11221364
22051236
3568980
41960964
53849964
65277964

prune84.0ms (3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1531154
Fresh101
Picked101
Done101
Total1561157
Error
0b
Counts
157 → 1
Alt Table
StatusErrorProgram
▶0b
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
Compiler

Compiled 2815 to 1519 computations (46% saved)

localize5.0ms (0.2%)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done000
Total011
Error
0b
Counts
1 → 1
Alt Table
StatusErrorProgram
✓0b
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes100.0ms (3.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts
9 → 1
Compiler

Compiled 1063 to 782 computations (26.4% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11111
21111

end39.0ms (1.4%)

Remove

(sort x y)

Compiler

Compiled 55 to 40 computations (27.3% saved)

Profiling

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