Details

Time bar (total: 5.7s)

analyze241.0ms (4.2%)

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)

sample1.2s (20.8%)

Results
986.0ms8256×body128valid
154.0ms1489×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)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series14.0ms (0.2%)

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)

simplify89.0ms (1.6%)

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

prune12.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New12315
Fresh000
Picked011
Done000
Total12416
Error
0.1b
Counts
16 → 4
Alt Table
StatusErrorProgram
41.0b
(*.f64 1/2 (cbrt.f64 (*.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x))))
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
32.5b
(*.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))))
Compiler

Compiled 298 to 126 computations (57.7% saved)

localize8.0ms (0.1%)

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))

series446.0ms (7.8%)

Counts
3 → 75
Calls

3 calls:

278.0ms
(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
151.0ms
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
17.0ms
(*.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)))

rewrite19.0ms (0.3%)

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:

7.0ms
(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
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)))
1.0ms
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

simplify130.0ms (2.3%)

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

prune223.0ms (3.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New3399348
Fresh022
Picked101
Done011
Total34012352
Error
0.0b
Counts
352 → 12
Alt Table
StatusErrorProgram
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
33.0b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
2.2b
(*.f64 1/2 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.6b
(*.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 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
1.4b
(*.f64 1/2 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3))
1.7b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
32.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
41.0b
(*.f64 1/2 (cbrt.f64 (*.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x))))
1.6b
(*.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))))
33.1b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (sqrt.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))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
32.9b
(*.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))))))
32.1b
(*.f64 1/2 (*.f64 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
Compiler

Compiled 13705 to 5414 computations (60.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 y (sqrt.f64 z) x)
0.6b
(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
0.7b
(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)

series1.7s (29.1%)

Counts
1 → 25
Calls

1 calls:

1.7s
(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)

rewrite3.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
cube-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
cbrt-prod_binary64
unpow-prod-down_binary64
Counts
1 → 32
Calls

1 calls:

2.0ms
(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)

simplify115.0ms (2%)

Algorithm
egg-herbie
Rules
494×distribute-rgt-in_binary64
452×associate-*l*_binary64
363×associate-*r*_binary64
351×fma-def_binary64
349×log-prod_binary64
Counts
57 → 51
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0881069
1193980
2537929
32377692
44661692
54951692
64996692
74888692

prune78.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1192121
Fresh1910
Picked101
Done011
Total12112133
Error
0.0b
Counts
133 → 12
Alt Table
StatusErrorProgram
11.8b
(*.f64 1/2 (fma.f64 (sqrt.f64 z) (/.f64 (*.f64 x y) x) x))
33.1b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (sqrt.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))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
33.0b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
1.7b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
32.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
41.0b
(*.f64 1/2 (cbrt.f64 (*.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x)) (fma.f64 y (sqrt.f64 z) x))))
1.6b
(*.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))))
35.8b
(*.f64 1/2 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y)))
32.9b
(*.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))))))
32.1b
(*.f64 1/2 (*.f64 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.6b
(*.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 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))))
Compiler

Compiled 3552 to 1932 computations (45.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series303.0ms (5.3%)

Counts
2 → 50
Calls

2 calls:

219.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
84.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite4.0ms (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:

2.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
1.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

simplify85.0ms (1.5%)

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

prune397.0ms (6.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New5561557
Fresh1910
Picked101
Done011
Total55811569
Error
0.0b
Counts
569 → 11
Alt Table
StatusErrorProgram
41.0b
(*.f64 1/2 (cbrt.f64 (*.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x)) (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 (*.f64 1 (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))))))
11.8b
(*.f64 1/2 (fma.f64 (sqrt.f64 z) (/.f64 (*.f64 x y) x) x))
33.1b
(*.f64 1/2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (sqrt.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))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
0.1b
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
33.0b
(*.f64 1/2 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 3)) (sqrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
1.6b
(*.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))))
35.8b
(*.f64 1/2 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y)))
32.9b
(*.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))))))
32.1b
(*.f64 1/2 (*.f64 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
32.5b
(*.f64 1/2 (*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))))
Compiler

Compiled 32909 to 11338 computations (65.5% saved)

regimes516.0ms (9%)

Accuracy

Total 0.1b remaining (58.4%)

Threshold costs 0.1b (58.4%)

Counts
65 → 1
Compiler

Compiled 13352 to 6107 computations (54.3% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
1910
2910

end130.0ms (2.3%)

Compiler

Compiled 307 to 140 computations (54.4% saved)

Profiling

Loading profile data...