Details

Time bar (total: 5.5s)

analyze235.0ms (4.3%)

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
25%74.9%0.1%6
34.3%40.6%25.1%7
35.9%39%25.1%8
42.1%32.8%25.1%9
42.9%19.5%37.6%10
43.3%19.1%37.6%11
45%17.5%37.6%12
45.1%10.3%44.6%13
45.2%10.2%44.6%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.1s (20.9%)

Results
942.0ms8256×body128valid
164.0ms1502×body128invalid
Compiler

Compiled 41 to 32 computations (22% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
10×fma-def_binary64
associate-*r*_binary64
associate-*l*_binary64
distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01212
12310
23510
34110
43910

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
Compiler

Compiled 40 to 27 computations (32.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 y (sqrt.f64 z) x)

series14.0ms (0.3%)

Counts
1 → 25
Calls

1 calls:

14.0ms
(fma.f64 y (sqrt.f64 z) x)

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 y (sqrt.f64 z) x)

simplify93.0ms (1.7%)

Algorithm
egg-herbie
Rules
642×distribute-rgt-in_binary64
492×distribute-lft-in_binary64
436×distribute-rgt-out_binary64
421×associate-*l*_binary64
413×*-commutative_binary64
Counts
35 → 15
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
018262
120247
243247
3104247
4281247
5915247
61563247
72177247
82401247
93023247
103557247
114430247
124903247

prune11.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New12315
Fresh000
Picked011
Done000
Total12416
Error
0.0b
Counts
16 → 4
Alt Table
StatusErrorProgram
30.8b
(*.f64 1/2 (*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.4b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
42.4b
(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
Compiler

Compiled 278 to 126 computations (54.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 y (sqrt.f64 z) x)
0.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
0.5b
(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
0.6b
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series349.0ms (6.4%)

Counts
3 → 75
Calls

3 calls:

257.0ms
(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
76.0ms
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
15.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite20.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

6.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
4.0ms
(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
1.0ms
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

simplify112.0ms (2.1%)

Algorithm
egg-herbie
Rules
374×cancel-sign-sub-inv_binary64
265×associate-*r*_binary64
242×associate-/r/_binary64
235×associate-*l*_binary64
225×unswap-sqr_binary64
Counts
168 → 193
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03044425
18424181
228183870
349743870

prune335.0ms (6.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3444348
Fresh022
Picked101
Done011
Total3457352
Error
0.0b
Counts
352 → 7
Alt Table
StatusErrorProgram
2.3b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
31.2b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
1.8b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
30.8b
(*.f64 1/2 (*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
42.4b
(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
1.5b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
Compiler

Compiled 13421 to 5316 computations (60.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
0.6b
(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
0.6b
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series312.0ms (5.7%)

Counts
2 → 50
Calls

2 calls:

229.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
82.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 27
Calls

2 calls:

3.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
2.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))

simplify89.0ms (1.6%)

Algorithm
egg-herbie
Rules
766×associate-/l*_binary64
352×cancel-sign-sub-inv_binary64
242×associate-/r/_binary64
215×associate-*r*_binary64
189×unswap-sqr_binary64
Counts
77 → 104
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02783302
17843208
226323071
353893071

prune376.0ms (6.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New4653468
Fresh055
Picked011
Done011
Total46510475
Error
0.0b
Counts
475 → 10
Alt Table
StatusErrorProgram
56.2b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (+.f64 (log.f64 z) (*.f64 2 (log.f64 y)))))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.7b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
2.3b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
31.2b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
1.8b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
30.8b
(*.f64 1/2 (*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
42.4b
(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
3.4b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
1.5b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
Compiler

Compiled 28625 to 10381 computations (63.7% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4)))
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
0.6b
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
0.8b
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4)

series467.0ms (8.5%)

Counts
2 → 50
Calls

2 calls:

243.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4)
223.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4)))

rewrite9.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod_binary64
unpow-prod-down_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 37
Calls

2 calls:

4.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4)))
3.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4)

simplify129.0ms (2.4%)

Algorithm
egg-herbie
Rules
334×cancel-sign-sub-inv_binary64
257×associate-/r/_binary64
253×unswap-sqr_binary64
233×associate-*r*_binary64
187×associate-*l*_binary64
Counts
87 → 123
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03153905
18563786
228633670
348673573
449283573

prune452.0ms (8.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New5011502
Fresh167
Picked011
Done022
Total50210512
Error
0.0b
Counts
512 → 10
Alt Table
StatusErrorProgram
2.9b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 1/3) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.5b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
2.3b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.7b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 4))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
31.2b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
1.8b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
30.8b
(*.f64 1/2 (*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
42.4b
(*.f64 1/2 (cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3)))
3.4b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
Compiler

Compiled 36198 to 13414 computations (62.9% saved)

regimes1.1s (19.9%)

Accuracy

Total 0.1b remaining (43.4%)

Threshold costs 0.1b (43.4%)

Counts
127 → 1
Compiler

Compiled 28610 to 13099 computations (54.2% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
1910
2910

end162.0ms (3%)

Compiler

Compiled 361 to 157 computations (56.5% saved)

Profiling

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