Details

Time bar (total: 6.6s)

analyze586.0ms (8.9%)

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)

sample1.4s (20.9%)

Symmetry

(sort x y)

Results
991.0ms8256×body128valid
186.0ms1600×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify96.0ms (1.5%)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
4.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
9.4b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
14.9b
(/.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)
7.0b
(/.f64 y (fma.f64 z z z))
8.8b
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series201.0ms (3.1%)

Counts
3 → 84
Calls

3 calls:

116.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
50.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
35.0ms
(/.f64 y (fma.f64 z z z))

rewrite35.0ms (0.5%)

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:

11.0ms
(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
6.0ms
(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms
(/.f64 y (fma.f64 z z z))

simplify170.0ms (2.6%)

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

prune302.0ms (4.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New28412296
Fresh011
Picked101
Done000
Total28513298
Error
2.0b
Counts
298 → 13
Alt Table
StatusErrorProgram
15.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
12.9b
(*.f64 (*.f64 x (/.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) z))
34.7b
(*.f64 (*.f64 x (/.f64 y (sqrt.f64 z))) (/.f64 (/.f64 1 (fma.f64 z z z)) (sqrt.f64 z)))
31.0b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
4.8b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
14.4b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
4.8b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
24.4b
(*.f64 x (/.f64 (/.f64 y z) z))
14.1b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
9.4b
(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
15.3b
(*.f64 x (*.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
34.1b
(*.f64 (/.f64 x (*.f64 (sqrt.f64 z) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
14.9b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
Compiler

Compiled 6400 to 1513 computations (76.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
1.1b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.0b
(*.f64 x (/.f64 y (fma.f64 z z z)))
7.0b
(/.f64 y (fma.f64 z z z))

series176.0ms (2.7%)

Counts
2 → 72
Calls

2 calls:

104.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
71.0ms
(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite13.0ms (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)))
5.0ms
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify84.0ms (1.3%)

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

prune160.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1732175
Fresh4812
Picked011
Done000
Total17711188
Error
1.3b
Counts
188 → 11
Alt Table
StatusErrorProgram
15.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
31.0b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
4.8b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
24.4b
(*.f64 x (/.f64 (/.f64 y z) z))
32.2b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
14.1b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
9.4b
(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
4.8b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
15.3b
(*.f64 x (*.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
10.3b
(/.f64 (/.f64 (*.f64 y x) (fma.f64 z z z)) z)
14.9b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
Compiler

Compiled 3277 to 944 computations (71.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
1.2b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
5.0b
(*.f64 x (/.f64 y (fma.f64 z z z)))
7.0b
(/.f64 y (fma.f64 z z z))

series102.0ms (1.6%)

Counts
1 → 36
Calls

1 calls:

102.0ms
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))

rewrite14.0ms (0.2%)

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:

9.0ms
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))

simplify70.0ms (1.1%)

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

prune233.0ms (3.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2011202
Fresh189
Picked011
Done011
Total20211213
Error
1.3b
Counts
213 → 11
Alt Table
StatusErrorProgram
15.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
31.0b
(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
4.8b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
24.4b
(*.f64 x (/.f64 (/.f64 y z) z))
32.2b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
14.1b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
9.4b
(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
4.8b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
10.3b
(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))
15.3b
(*.f64 x (*.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
14.9b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
Compiler

Compiled 4103 to 1439 computations (64.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z)
0.7b
(/.f64 1 (/.f64 (fma.f64 z z z) y))
6.9b
(/.f64 (fma.f64 z z z) y)
8.8b
(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))

series262.0ms (4%)

Counts
4 → 108
Calls

4 calls:

160.0ms
(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
53.0ms
(/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z)
37.0ms
(/.f64 1 (/.f64 (fma.f64 z z z) y))
11.0ms
(/.f64 (fma.f64 z z z) y)

rewrite123.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
821×times-frac_binary64
411×add-sqr-sqrt_binary64
392×*-un-lft-identity_binary64
390×add-cube-cbrt_binary64
136×associate-*r*_binary64
Counts
4 → 478
Calls

4 calls:

30.0ms
(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
12.0ms
(/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z)
4.0ms
(/.f64 1 (/.f64 (fma.f64 z z z) y))
2.0ms
(/.f64 (fma.f64 z z z) y)

simplify458.0ms (7%)

Algorithm
egg-herbie
Rules
445×fma-neg_binary64
305×sub-neg_binary64
250×fma-def_binary64
241×associate-/l*_binary64
229×associate-*r/_binary64
Counts
586 → 780
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
036712886
188911543
2293111229
3406411225
4478711225
5499711225
6497811225

prune736.0ms (11.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New7773780
Fresh358
Picked101
Done022
Total78110791
Error
1.0b
Counts
791 → 10
Alt Table
StatusErrorProgram
4.8b
(*.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
32.2b
(/.f64 (*.f64 x (*.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
14.1b
(*.f64 (*.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
15.3b
(*.f64 (*.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
4.8b
(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.7b
(*.f64 (/.f64 x (fma.f64 z z z)) (/.f64 y z))
10.3b
(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))
9.4b
(*.f64 x (/.f64 1 (*.f64 z (/.f64 (fma.f64 z z z) y))))
14.9b
(/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))
9.1b
(*.f64 x (/.f64 (/.f64 1 (*.f64 (+.f64 z 1) (/.f64 z y))) z))
Compiler

Compiled 19654 to 6465 computations (67.1% saved)

regimes1.1s (16.3%)

Accuracy

Total 4.0b remaining (83.6%)

Threshold costs 0b (0%)

Counts
188 → 1
Compiler

Compiled 22032 to 11839 computations (46.3% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01438
11638
21638

end255.0ms (3.9%)

Compiler

Compiled 266 to 144 computations (45.9% saved)

Profiling

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