Details

Time bar (total: 4.2s)

analyze197.0ms (4.6%)

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 (31%)

Results
1.2s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify58.0ms (1.4%)

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)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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))
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.0b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.6b
(*.f64 (*.f64 b b) (+.f64 a 3))

series95.0ms (2.2%)

Counts
4 → 96
Calls

4 calls:

36.0ms
(+.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))
35.0ms
(pow.f64 (hypot.f64 a b) 4)
13.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))

rewrite16.0ms (0.4%)

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))
2.0ms
(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 (1.9%)

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

prune197.0ms (4.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1584162
Fresh101
Picked101
Done000
Total1604164
Error
0b
Counts
164 → 4
Alt Table
StatusErrorProgram
0.2b
(fma.f64 (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
9.6b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
0.4b
(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))
Compiler

Compiled 5040 to 2955 computations (41.4% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))
0.0b
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.6b
(*.f64 (+.f64 3 a) (*.f64 b b))

series60.0ms (1.4%)

Counts
3 → 72
Calls

3 calls:

39.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))
12.0ms
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
8.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite28.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt_binary64
37×*-un-lft-identity_binary64
36×prod-diff_binary64
31×add-cube-cbrt_binary64
16×unpow-prod-down_binary64
Counts
3 → 116
Calls

3 calls:

9.0ms
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
6.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))
4.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))

simplify138.0ms (3.3%)

Algorithm
egg-herbie
Rules
706×fma-neg_binary64
672×distribute-rgt-in_binary64
514×cancel-sign-sub-inv_binary64
255×unswap-sqr_binary64
176×distribute-rgt-out_binary64
Counts
188 → 179
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02424373
15323968
220223657
349993647
452583647

prune290.0ms (6.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2130213
Fresh033
Picked011
Done000
Total2134217
Error
0b
Counts
217 → 4
Alt Table
StatusErrorProgram
0.2b
(fma.f64 (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
9.6b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (*.f64 4 (pow.f64 a 3)) 1))
0.4b
(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))
Compiler

Compiled 7510 to 4491 computations (40.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) (/.f64 4 2))
0.0b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.2b
(fma.f64 (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.6b
(*.f64 (*.f64 b b) (+.f64 a 3))

series100.0ms (2.4%)

Counts
2 → 48
Calls

2 calls:

51.0ms
(pow.f64 (hypot.f64 a b) (/.f64 4 2))
48.0ms
(fma.f64 (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×pow-unpow_binary64
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
Counts
2 → 40
Calls

2 calls:

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

simplify96.0ms (2.3%)

Algorithm
egg-herbie
Rules
629×fma-neg_binary64
626×fma-def_binary64
513×associate-+l+_binary64
434×unswap-sqr_binary64
321×associate--l+_binary64
Counts
88 → 96
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01181804
13111614
29141463
335651448
449901448
549841448

prune306.0ms (7.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2211222
Fresh112
Picked011
Done011
Total2224226
Error
0b
Counts
226 → 4
Alt Table
StatusErrorProgram
0.2b
(fma.f64 (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.4b
(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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 (*.f64 b b) (+.f64 (fma.f64 b b 12) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) (-.f64 (fma.f64 a a 4) (*.f64 4 a)) -1))
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))
Compiler

Compiled 8123 to 4880 computations (39.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (fma.f64 a a 4) (*.f64 4 a))
0.0b
(*.f64 a (+.f64 4 (*.f64 2 a)))
0.1b
(fma.f64 (*.f64 a a) (-.f64 (fma.f64 a a 4) (*.f64 4 a)) -1)
0.9b
(*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))

series28.0ms (0.7%)

Counts
4 → 60
Calls

4 calls:

20.0ms
(*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))
3.0ms
(fma.f64 (*.f64 a a) (-.f64 (fma.f64 a a 4) (*.f64 4 a)) -1)
3.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))
2.0ms
(-.f64 (fma.f64 a a 4) (*.f64 4 a))

rewrite19.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
*-un-lft-identity_binary64
Counts
4 → 80
Calls

4 calls:

6.0ms
(*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))
4.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))
3.0ms
(-.f64 (fma.f64 a a 4) (*.f64 4 a))
0.0ms
(fma.f64 (*.f64 a a) (-.f64 (fma.f64 a a 4) (*.f64 4 a)) -1)

simplify114.0ms (2.7%)

Algorithm
egg-herbie
Rules
532×fma-neg_binary64
239×associate-*l*_binary64
238×exp-prod_binary64
228×associate-+l+_binary64
222×unswap-sqr_binary64
Counts
140 → 172
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01832740
14882045
218252005
334752003
449672003
550192003

prune226.0ms (5.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1711172
Fresh101
Picked101
Done022
Total1733176
Error
0b
Counts
176 → 3
Alt Table
StatusErrorProgram
0.2b
(fma.f64 (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (pow.f64 (hypot.f64 a b) (/.f64 4 2)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
7.9b
(+.f64 (cbrt.f64 (pow.f64 (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))) 3)) (fma.f64 (*.f64 a a) (-.f64 (fma.f64 a a 4) (*.f64 4 a)) -1))
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))
Compiler

Compiled 6283 to 3810 computations (39.4% saved)

regimes697.0ms (16.5%)

Accuracy

Total 0.0b remaining (53.2%)

Threshold costs 0.0b (53.2%)

Counts
132 → 1
Compiler

Compiled 18060 to 12248 computations (32.2% saved)

simplify3.0ms (0.1%)

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
01941
12641
23041
33241
43341
53341

end101.0ms (2.4%)

Compiler

Compiled 152 to 108 computations (28.9% saved)

Profiling

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