Details

Time bar (total: 3.8s)

analyze20.0ms (0.5%)

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
87.4%12.5%0.1%7
93.6%6.2%0.1%8
96.7%3.1%0.1%9
98.3%1.6%0.1%10
99.1%0.8%0.1%11
99.5%0.4%0.1%12
99.7%0.2%0.1%13
99.8%0.1%0.1%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.4s (37.4%)

Symmetry

(sort x y z)

Results
1.4s8256×body128valid
Compiler

Compiled 53 to 35 computations (34% saved)

simplify9.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
9×fma-def_binary64
5×+-commutative_binary64
3×associate-+r+_binary64
3×associate-+l+_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01219
11717
22717
33117
43117

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
37.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶37.5b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
Compiler

Compiled 59 to 34 computations (42.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)
✓34.9b
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))

series125.0ms (3.3%)

Counts
2 → 72
Calls

2 calls:

97.0ms
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
27.0ms
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

rewrite9.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
19×times-frac_binary64
17×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
13×sqrt-prod_binary64
Counts
2 → 56
Calls

2 calls:

4.0ms
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3))
2.0ms
(/.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y))) 3)

simplify108.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
356×sub-neg_binary64
354×fma-neg_binary64
279×fma-def_binary64
227×times-frac_binary64
207×associate-*r*_binary64
Counts
128 → 180
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03854690
110024370
240434370
349954370

prune139.0ms (3.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1755180
Fresh000
Picked101
Done000
Total1765181
Error
0.2b
Counts
181 → 5
Alt Table
StatusErrorProgram
29.9b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
▶1.1b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
37.6b
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
31.2b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
37.2b
(fma.f64 (sqrt.f64 1/3) z (*.f64 1/2 (+.f64 (/.f64 (*.f64 (sqrt.f64 1/3) (*.f64 x x)) z) (/.f64 (*.f64 (sqrt.f64 1/3) (*.f64 y y)) z))))
Compiler

Compiled 6032 to 3572 computations (40.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(hypot.f64 x z)
✓0.4b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

series54.0ms (1.4%)

Counts
2 → 48
Calls

2 calls:

36.0ms
(hypot.f64 x z)
17.0ms
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

rewrite5.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×add-sqr-sqrt_binary64
6×associate-*l*_binary64
5×*-un-lft-identity_binary64
5×add-cube-cbrt_binary64
4×sqrt-prod_binary64
Counts
2 → 35
Calls

2 calls:

3.0ms
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))
0.0ms
(hypot.f64 x z)

simplify80.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
904×fma-neg_binary64
600×times-frac_binary64
384×associate-/l*_binary64
380×associate-*r*_binary64
345×associate-*l*_binary64
Counts
83 → 99
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01311647
13811602
212451582
350001582
456731582

prune77.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New93699
Fresh134
Picked101
Done000
Total959104
Error
0.0b
Counts
104 → 9
Alt Table
StatusErrorProgram
29.9b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
1.3b
(*.f64 (sqrt.f64 1/3) (*.f64 (sqrt.f64 (hypot.f64 x z)) (sqrt.f64 (hypot.f64 x z))))
31.2b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
1.3b
(*.f64 (*.f64 (sqrt.f64 1/3) (sqrt.f64 (hypot.f64 x z))) (sqrt.f64 (hypot.f64 x z)))
▶1.0b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
1.3b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))
37.6b
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
1.3b
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
2.0b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z)))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z))))
Compiler

Compiled 1957 to 1373 computations (29.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 x z)
✓0.1b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
✓0.3b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

series43.0ms (1.1%)

Counts
2 → 48
Calls

2 calls:

22.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))
21.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))

rewrite17.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
21×sqrt-prod_binary64
18×associate-*l*_binary64
15×add-sqr-sqrt_binary64
9×*-un-lft-identity_binary64
9×add-cube-cbrt_binary64
Counts
2 → 56
Calls

2 calls:

7.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
4.0ms
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))

simplify89.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
785×fma-neg_binary64
710×times-frac_binary64
483×associate-/l*_binary64
470×fma-def_binary64
235×cancel-sign-sub-inv_binary64
Counts
104 → 131
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01602514
14632398
216572278
347852274
453012274

prune119.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1712173
Fresh448
Picked011
Done000
Total1757182
Error
0b
Counts
182 → 7
Alt Table
StatusErrorProgram
29.9b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
✓1.0b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
1.3b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))
37.6b
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
31.2b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
▶1.1b
(*.f64 1 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z)))
1.2b
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
Compiler

Compiled 3761 to 2882 computations (23.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 x z)
0.4b
(*.f64 (sqrt.f64 1/3) (hypot.f64 x z))

prune79.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New99099
Fresh055
Picked011
Done011
Total997106
Error
0b
Counts
106 → 7
Alt Table
StatusErrorProgram
29.9b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y x))
✓1.0b
(*.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z)))
1.3b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (hypot.f64 x z))))
37.6b
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 x x (*.f64 y y)))) (sqrt.f64 3))
31.2b
(*.f64 (sqrt.f64 1/3) (hypot.f64 y z))
✓1.1b
(*.f64 1 (*.f64 (sqrt.f64 1/3) (hypot.f64 x z)))
1.2b
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (sqrt.f64 1/3)) (hypot.f64 x z))))
Compiler

Compiled 1970 to 1450 computations (26.4% saved)

regimes802.0ms (21.4%)

Accuracy

Total 0.7b remaining (96.6%)

Threshold costs 0.7b (96.6%)

Counts
75 → 1
Compiler

Compiled 11668 to 8754 computations (25% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
11118
21118

end550.0ms (14.6%)

Compiler

Compiled 155 to 125 computations (19.4% saved)

Profiling

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