Details

Time bar (total: 6.6s)

analyze191.0ms (2.9%)

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
25%74.9%0.1%5
25%68.7%6.3%6
25%53.1%22%7
25%46.8%28.2%8
25%33.6%41.5%9
28.1%18%54%10
31.6%12.1%56.3%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.4s (20.4%)

Results
1.3s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify60.0ms (0.9%)

Algorithm
egg-herbie
Rules
620×fma-def_binary64
556×cancel-sign-sub-inv_binary64
552×unswap-sqr_binary64
357×unsub-neg_binary64
344×+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01939
15737
216837
349237
4160433
5289133
6430933
7521433

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)
Compiler

Compiled 166 to 104 computations (37.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.7b
(*.f64 (*.f64 b b) (+.f64 a 3))

series101.0ms (1.5%)

Counts
4 → 96
Calls

4 calls:

39.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
38.0ms
(pow.f64 (hypot.f64 a b) 4)
12.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
12.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-exp-log_binary64
10×pow1_binary64
add-cube-cbrt_binary64
Counts
4 → 78
Calls

4 calls:

6.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))
4.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
1.0ms
(pow.f64 (hypot.f64 a b) 4)
0.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))

simplify102.0ms (1.5%)

Algorithm
egg-herbie
Rules
574×associate-+l+_binary64
469×distribute-rgt-in_binary64
453×distribute-lft-in_binary64
338×associate--l+_binary64
219×cancel-sign-sub-inv_binary64
Counts
174 → 162
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01743413
14643143
215563045
350743045

prune209.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1593162
Fresh101
Picked011
Done000
Total1604164
Error
0b
Counts
164 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
6.3b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))) -1))
0.2b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.8b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
Compiler

Compiled 5039 to 2952 computations (41.4% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.3b
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
0.7b
(*.f64 (*.f64 b b) (+.f64 a 3))

series82.0ms (1.2%)

Counts
2 → 48
Calls

2 calls:

42.0ms
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
40.0ms
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-down_binary64
12×fma-def_binary64
11×*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 56
Calls

2 calls:

7.0ms
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
3.0ms
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

simplify94.0ms (1.4%)

Algorithm
egg-herbie
Rules
861×fma-neg_binary64
756×fma-def_binary64
551×associate-+l+_binary64
327×associate--l+_binary64
260×associate-*l*_binary64
Counts
104 → 109
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01322438
13562163
210381979
346401965
453551965

prune267.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1820182
Fresh022
Picked011
Done011
Total1824186
Error
0b
Counts
186 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
6.3b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))) -1))
0.2b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.8b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
Compiler

Compiled 6109 to 3748 computations (38.6% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))) -1))
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.7b
(*.f64 (*.f64 b b) (+.f64 a 3))
1.4b
(expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))))

series54.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

41.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))) -1))
13.0ms
(expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))))

rewrite7.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
fma-def_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-log-exp_binary64
Counts
2 → 33
Calls

2 calls:

4.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))) -1))
0.0ms
(expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))))

simplify87.0ms (1.3%)

Algorithm
egg-herbie
Rules
816×fma-def_binary64
802×fma-neg_binary64
566×associate-+l+_binary64
341×associate--l+_binary64
274×associate-+r+_binary64
Counts
81 → 91
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01072223
13022023
29911883
347871865
454551865

prune232.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1640164
Fresh011
Picked011
Done022
Total1644168
Error
0b
Counts
168 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
6.3b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))) -1))
0.2b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.8b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
Compiler

Compiled 5159 to 3148 computations (39% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))
0.7b
(*.f64 (+.f64 3 a) (*.f64 b b))
4.4b
(-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
12.0b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

series733.0ms (11%)

Counts
4 → 96
Calls

4 calls:

604.0ms
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
67.0ms
(-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
52.0ms
(*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))
9.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite54.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt_binary64
48×difference-of-squares_binary64
44×*-un-lft-identity_binary64
42×times-frac_binary64
28×add-cube-cbrt_binary64
Counts
4 → 160
Calls

4 calls:

10.0ms
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
6.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))
5.0ms
(-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
3.0ms
(*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))

simplify352.0ms (5.3%)

Algorithm
egg-herbie
Rules
583×times-frac_binary64
342×+-commutative_binary64
298×fma-def_binary64
294×associate-+r+_binary64
210×*-commutative_binary64
Counts
256 → 353
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0103726974
1331926095
2498626095

prune1.2s (18%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New4390439
Fresh000
Picked011
Done033
Total4394443
Error
0b
Counts
443 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
6.3b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))))) -1))
0.2b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.8b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
Compiler

Compiled 48387 to 31102 computations (35.7% saved)

regimes1.2s (18.2%)

Accuracy

Total 0.0b remaining (36.3%)

Threshold costs 0.0b (36.3%)

Counts
167 → 1
Compiler

Compiled 29767 to 20522 computations (31.1% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×+-commutative_binary64
10×*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02767
14467
25267
36467
46967
57267
67367
77067

end141.0ms (2.1%)

Compiler

Compiled 241 to 174 computations (27.8% saved)

Profiling

Loading profile data...