Details

Time bar (total: 5.1s)

analyze592.0ms (11.7%)

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
0%99.9%0.1%5
0%99.9%0.1%6
25%74.9%0.1%7
31.2%68.6%0.1%8
35.9%64%0.1%9
47.6%49.9%2.5%10
49.1%46.8%4%11
51.1%44.1%4.8%12
60.2%29.9%9.9%13
60.6%27.9%11.6%14
Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.3s (26.3%)

Symmetry

(sort x y)

Results
939.0ms8256×body128valid
206.0ms1615×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify92.0ms (1.8%)

Algorithm
egg-herbie
Rules
826×associate-*r/_binary64
769×associate-/l/_binary64
660×associate-*l/_binary64
522×associate-/l*_binary64
421×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01016
13016
27814
319514
431414
538314
642614
763114
8100914
9220414
10286814
11296714
12307914
13319314
14305814
15371214
16498814
17482414

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
10.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
18.3b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
Compiler

Compiled 78 to 45 computations (42.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 y (fma.f64 z z z)) z)
7.1b
(/.f64 y (fma.f64 z z z))
8.9b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series197.0ms (3.9%)

Counts
3 → 84
Calls

3 calls:

104.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
56.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
37.0ms
(/.f64 y (fma.f64 z z z))

rewrite36.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
153×times-frac_binary64
98×add-sqr-sqrt_binary64
89×*-un-lft-identity_binary64
89×add-cube-cbrt_binary64
43×associate-*r*_binary64
Counts
3 → 168
Calls

3 calls:

10.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
4.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
4.0ms
(/.f64 y (fma.f64 z z z))

simplify164.0ms (3.2%)

Algorithm
egg-herbie
Rules
805×fma-def_binary64
353×fma-neg_binary64
351×*-commutative_binary64
341×associate-/r/_binary64
275×sub-neg_binary64
Counts
252 → 296
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02874846
16874599
223044515
336074509
448174509
549634509

prune260.0ms (5.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New28511296
Fresh101
Picked011
Done000
Total28612298
Error
1.7b
Counts
298 → 12
Alt Table
StatusErrorProgram
5.6b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
19.9b
(*.f64 (*.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
18.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
17.1b
(*.f64 (*.f64 x (/.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 (/.f64 y (fma.f64 z z z))) (cbrt.f64 z)))
10.6b
(*.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (fma.f64 z z z) (cbrt.f64 y))) z))
5.6b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
28.0b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
37.5b
(*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
16.2b
(*.f64 x (*.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
57.1b
(*.f64 (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
10.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
10.3b
(*.f64 x (/.f64 1 (/.f64 z (/.f64 y (fma.f64 z z z)))))
Compiler

Compiled 6361 to 1474 computations (76.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
2.3b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
3.7b
(*.f64 x (/.f64 y (fma.f64 z z z)))
7.1b
(/.f64 y (fma.f64 z z z))

series175.0ms (3.4%)

Counts
2 → 72
Calls

2 calls:

102.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
72.0ms
(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
13×associate-*r*_binary64
13×times-frac_binary64
Counts
2 → 60
Calls

2 calls:

5.0ms
(*.f64 x (/.f64 y (fma.f64 z z z)))
4.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify79.0ms (1.6%)

Algorithm
egg-herbie
Rules
604×fma-neg_binary64
483×associate-*l*_binary64
433×associate-/r*_binary64
417×associate-*r*_binary64
378×associate-/r/_binary64
Counts
132 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01532289
13972096
215391990
344391990
449681990

prune134.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1723175
Fresh6410
Picked101
Done011
Total1798187
Error
1.2b
Counts
187 → 8
Alt Table
StatusErrorProgram
11.7b
(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
28.0b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
37.5b
(*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
5.6b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
16.2b
(*.f64 x (*.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
10.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
33.4b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
9.6b
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
Compiler

Compiled 3187 to 888 computations (72.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
2.3b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
3.7b
(*.f64 x (/.f64 y (fma.f64 z z z)))
7.1b
(/.f64 y (fma.f64 z z z))

series104.0ms (2.1%)

Counts
1 → 36
Calls

1 calls:

104.0ms
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))

rewrite13.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
40×add-exp-log_binary64
22×add-cbrt-cube_binary64
20×prod-exp_binary64
13×associate-*r*_binary64
10×cbrt-unprod_binary64
Counts
1 → 48
Calls

1 calls:

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

simplify66.0ms (1.3%)

Algorithm
egg-herbie
Rules
798×times-frac_binary64
611×associate-*l/_binary64
545×fma-def_binary64
504×associate-/l*_binary64
299×fma-neg_binary64
Counts
84 → 82
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01221588
13101380
210831336
344651336
449671336

prune132.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2020202
Fresh066
Picked011
Done011
Total2028210
Error
1.2b
Counts
210 → 8
Alt Table
StatusErrorProgram
11.7b
(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
28.0b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
37.5b
(*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
5.6b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
16.2b
(*.f64 x (*.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
10.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
33.4b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
9.6b
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
Compiler

Compiled 4013 to 1383 computations (65.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 z (/.f64 y (fma.f64 z z z)))
7.1b
(/.f64 y (fma.f64 z z z))
8.5b
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))

series123.0ms (2.4%)

Counts
2 → 60
Calls

2 calls:

105.0ms
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
18.0ms
(/.f64 z (/.f64 y (fma.f64 z z z)))

rewrite57.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
471×times-frac_binary64
229×*-un-lft-identity_binary64
229×add-sqr-sqrt_binary64
229×add-cube-cbrt_binary64
57×associate-/r*_binary64
Counts
2 → 270
Calls

2 calls:

9.0ms
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
4.0ms
(/.f64 z (/.f64 y (fma.f64 z z z)))

simplify237.0ms (4.7%)

Algorithm
egg-herbie
Rules
579×associate-/r/_binary64
431×associate-/l/_binary64
401×fma-def_binary64
378×associate-*l/_binary64
332×associate-*r/_binary64
Counts
330 → 488
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04879126
110858731
241368600
346398600
449898600

prune338.0ms (6.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New5354539
Fresh325
Picked011
Done022
Total5389547
Error
1.2b
Counts
547 → 9
Alt Table
StatusErrorProgram
5.6b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
33.0b
(*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (*.f64 (/.f64 y (hypot.f64 z (sqrt.f64 z))) (/.f64 x z)))
6.0b
(/.f64 (/.f64 x (/.f64 z y)) (fma.f64 z z z))
33.4b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
4.5b
(*.f64 (/.f64 y z) (/.f64 x (fma.f64 z z z)))
9.6b
(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
37.5b
(*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 y z) (hypot.f64 z (sqrt.f64 z)))))
10.2b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
15.9b
(*.f64 y (/.f64 x (*.f64 z (fma.f64 z z z))))
Compiler

Compiled 12414 to 2247 computations (81.9% saved)

regimes778.0ms (15.3%)

Accuracy

Total 2.8b remaining (66.9%)

Threshold costs 0b (0%)

Counts
126 → 2
Compiler

Compiled 14721 to 7642 computations (48.1% saved)

bsearch4.0ms (0.1%)

Compiler

Compiled 10 to 7 computations (30% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02355
13055
22955

end111.0ms (2.2%)

Remove

(sort x y)

Compiler

Compiled 300 to 165 computations (45% saved)

Profiling

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