Details

Time bar (total: 3.2s)

analyze166.0ms (5.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
25%74.9%0.1%3
25%62.4%12.6%4
37.5%43.7%18.8%5
37.5%34.3%28.2%6
43.7%23.4%32.9%7
43.7%18%38.3%8
46.8%12.1%41.1%9
46.8%9.2%44%10
48.4%6.1%45.5%11
48.4%4.6%47%12
49.2%3.1%47.7%13
49.2%2.3%48.5%14
Compiler

Compiled 7 to 5 computations (28.6% saved)

sample1.4s (44%)

Symmetry

(sort x y)

Results
1.3s8256×body128valid
39.0ms289×body128invalid
Compiler

Compiled 20 to 14 computations (30% saved)

simplify14.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
266

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶0.0b
(sqrt.f64 (+.f64 x y))
Compiler

Compiled 18 to 12 computations (33.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x y))

series36.0ms (1.1%)

Counts
1 → 8
Calls

1 calls:

36.0ms
(sqrt.f64 (+.f64 x y))

rewrite127.0ms (4%)

Algorithm
2×batch-egg-rewrite
Rules
553×log1p-expm1-u_binary64
553×expm1-log1p-u_binary64
464×prod-diff_binary64
352×fma-udef_binary64
223×fma-def_binary64
Counts
1 → 25
Calls

1 calls:

126.0ms
(sqrt.f64 (+.f64 x y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11086
213816
348636
448526
549706
000
100

simplify74.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
873×fma-neg_binary64
845×fma-def_binary64
562×associate-*l*_binary64
465×distribute-rgt-neg-in_binary64
431×distribute-lft-neg-in_binary64
Counts
33 → 39
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
051212
1135212
2345204
3984198
42981196
54841196
65010196

prune42.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New37239
Fresh000
Picked011
Done000
Total37340
Error
0b
Counts
40 → 3
Alt Table
StatusErrorProgram
21.2b
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
✓0.0b
(sqrt.f64 (+.f64 x y))
▶0.9b
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
Compiler

Compiled 529 to 316 computations (40.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (cbrt.f64 (+.f64 x y)))
✓0.4b
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
✓0.5b
(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
✓0.6b
(cbrt.f64 (+.f64 x y))

series189.0ms (6%)

Counts
4 → 80
Calls

4 calls:

65.0ms
(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
45.0ms
(sqrt.f64 (cbrt.f64 (+.f64 x y)))
39.0ms
(cbrt.f64 (+.f64 x y))
39.0ms
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))

rewrite103.0ms (3.3%)

Algorithm
2×batch-egg-rewrite
Rules
779×log1p-expm1-u_binary64
779×expm1-log1p-u_binary64
455×prod-diff_binary64
94×egg-rr
85×add-sqr-sqrt_binary64
Counts
4 → 94
Calls

4 calls:

99.0ms
(sqrt.f64 (cbrt.f64 (+.f64 x y)))
99.0ms
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
99.0ms
(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
99.0ms
(cbrt.f64 (+.f64 x y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01029
118526
2200426
3555626
000
100

simplify177.0ms (5.6%)

Algorithm
1×egg-herbie
Rules
724×associate-/l*_binary64
370×cancel-sign-sub-inv_binary64
237×associate-*r*_binary64
234×unswap-sqr_binary64
230×associate-/r/_binary64
Counts
174 → 202
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02733170
18313126
227252708
354522708

prune288.0ms (9.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2650265
Fresh011
Picked011
Done011
Total2653268
Error
0b
Counts
268 → 3
Alt Table
StatusErrorProgram
▶21.2b
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
✓0.0b
(sqrt.f64 (+.f64 x y))
✓0.9b
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
Compiler

Compiled 6881 to 4178 computations (39.3% saved)

localize12.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 x y) 3/2)
✓20.3b
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))

series69.0ms (2.2%)

Counts
2 → 32
Calls

2 calls:

37.0ms
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
32.0ms
(pow.f64 (+.f64 x y) 3/2)

rewrite61.0ms (1.9%)

Algorithm
2×batch-egg-rewrite
Rules
698×log1p-expm1-u_binary64
698×expm1-log1p-u_binary64
455×prod-diff_binary64
73×add-sqr-sqrt_binary64
71×add-cube-cbrt_binary64
Counts
2 → 46
Calls

2 calls:

59.0ms
(pow.f64 (+.f64 x y) 3/2)
59.0ms
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0716
115313
2174913
3499813
000
100

simplify135.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
565×fma-neg_binary64
382×associate-*r*_binary64
371×times-frac_binary64
348×fma-def_binary64
325×associate-*l*_binary64
Counts
78 → 92
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01111106
13141092
2979926
34246845
44967845
54967845

prune82.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New92092
Fresh000
Picked011
Done022
Total92395
Error
0b
Counts
95 → 3
Alt Table
StatusErrorProgram
✓21.2b
(cbrt.f64 (pow.f64 (+.f64 x y) 3/2))
✓0.0b
(sqrt.f64 (+.f64 x y))
✓0.9b
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
Compiler

Compiled 1523 to 1000 computations (34.3% saved)

regimes69.0ms (2.2%)

Accuracy

Total 0.0b remaining (51.6%)

Threshold costs 0.0b (51.6%)

Counts
6 → 1
Compiler

Compiled 282 to 182 computations (35.5% saved)

simplify5.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
266

end95.0ms (3%)

Remove

(sort x y)

Compiler

Compiled 53 to 35 computations (34% saved)

Profiling

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