Details

Time bar (total: 6.1s)

analyze160.0ms (2.6%)

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)

sample1.3s (21.4%)

Results
1.2s8256×body128valid
1.0msbody128invalid
Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify61.0ms (1%)

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
0.2b
(-.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)
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))
Compiler

Compiled 166 to 104 computations (37.3% saved)

localize15.0ms (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)))
0.8b
(*.f64 (*.f64 b b) (+.f64 a 3))

series87.0ms (1.4%)

Counts
4 → 96
Calls

4 calls:

35.0ms
(+.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))
32.0ms
(pow.f64 (hypot.f64 a b) 4)
10.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
9.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))

rewrite16.0ms (0.3%)

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:

7.0ms
(*.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)))

simplify81.0ms (1.3%)

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

prune221.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1593162
Fresh101
Picked011
Done000
Total1604164
Error
0.0b
Counts
164 → 4
Alt Table
StatusErrorProgram
15.4b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
13.3b
(/.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)))
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 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
Compiler

Compiled 5025 to 2940 computations (41.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (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)))
0.4b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.8b
(*.f64 (*.f64 b b) (+.f64 a 3))

series41.0ms (0.7%)

Counts
2 → 48
Calls

2 calls:

29.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
12.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
fma-def_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
unpow-prod-down_binary64
add-cube-cbrt_binary64
Counts
2 → 43
Calls

2 calls:

6.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
3.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

simplify86.0ms (1.4%)

Algorithm
egg-herbie
Rules
833×fma-neg_binary64
753×fma-def_binary64
561×associate-+l+_binary64
335×associate--l+_binary64
227×distribute-rgt-in_binary64
Counts
91 → 96
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01112281
13192122
29741866
347011852
454091852

prune271.0ms (4.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1681169
Fresh022
Picked011
Done011
Total1685173
Error
0.0b
Counts
173 → 5
Alt Table
StatusErrorProgram
15.4b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
13.3b
(/.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)))
0.1b
(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
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 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
Compiler

Compiled 5859 to 3075 computations (47.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 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)))
0.2b
(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))
0.8b
(*.f64 (*.f64 b b) (+.f64 a 3))

series43.0ms (0.7%)

Counts
2 → 48
Calls

2 calls:

25.0ms
(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
18.0ms
(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-log-exp_binary64
fma-def_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 29
Calls

2 calls:

2.0ms
(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.0ms
(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))

simplify91.0ms (1.5%)

Algorithm
egg-herbie
Rules
881×fma-neg_binary64
789×fma-def_binary64
604×associate-+l+_binary64
347×associate--l+_binary64
298×distribute-rgt-in_binary64
Counts
77 → 78
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0972550
12892385
29252234
349362220
457062220

prune245.0ms (4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1510151
Fresh022
Picked011
Done022
Total1515156
Error
0.0b
Counts
156 → 5
Alt Table
StatusErrorProgram
15.4b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
13.3b
(/.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)))
0.1b
(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
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 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
Compiler

Compiled 6224 to 3368 computations (45.9% saved)

localize17.0ms (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))
0.8b
(*.f64 (+.f64 3 a) (*.f64 b b))
4.2b
(-.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)))
12.4b
(/.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)))

series612.0ms (10%)

Counts
4 → 96
Calls

4 calls:

501.0ms
(/.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)))
59.0ms
(-.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)))
39.0ms
(*.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))
14.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite51.0ms (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:

11.0ms
(/.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))
4.0ms
(-.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))

simplify328.0ms (5.4%)

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 (19.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New4381439
Fresh011
Picked101
Done033
Total4395444
Error
0b
Counts
444 → 5
Alt Table
StatusErrorProgram
15.4b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
0.1b
(+.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
13.3b
(/.f64 1 (/.f64 (-.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)) (-.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)))))
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 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
Compiler

Compiled 48417 to 31118 computations (35.7% saved)

regimes1.0s (16.4%)

Accuracy

Total 0.0b remaining (83.2%)

Threshold costs 0.0b (83.2%)

Counts
142 → 1
Compiler

Compiled 32436 to 21347 computations (34.2% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01630
12230
22530
32730
42830
52730

end125.0ms (2%)

Compiler

Compiled 223 to 146 computations (34.5% saved)

Profiling

Loading profile data...