Details

Time bar (total: 5.9s)

analyze247.0ms (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
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)

sample28.0ms (0.5%)

Algorithm
intervals
Results
19.0ms256×body128valid
Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify67.0ms (1.1%)

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
0.0b
(+.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)

localize14.0ms (0.2%)

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)))
0.8b
(*.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:

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)))

series167.0ms (2.8%)

Counts
4 → 96
Calls

4 calls:

69.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))
40.0ms
(+.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)
19.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))

simplify97.0ms (1.7%)

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 → 315
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01743413
14643143
215563045
350743045

prune203.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New3123315
Fresh101
Picked011
Done000
Total3134317
Error
0b
Counts
317 → 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))
8.2b
(+.f64 -1 (fma.f64 (*.f64 a a) 4 (*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))))
10.1b
(/.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)))
14.4b
(cbrt.f64 (pow.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)) 3))
Compiler

Compiled 5136 to 3012 computations (41.4% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 a (+.f64 4 (*.f64 2 a)))
0.0b
(fma.f64 (*.f64 a a) 4 (*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a))))))
1.4b
(*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
12×associate-*r/_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
10×pow1_binary64
add-sqr-sqrt_binary64
Counts
3 → 63
Calls

3 calls:

11.0ms
(*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))
4.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))
0.0ms
(fma.f64 (*.f64 a a) 4 (*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a))))))

series86.0ms (1.5%)

Counts
3 → 60
Calls

3 calls:

38.0ms
(*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))
35.0ms
(fma.f64 (*.f64 a a) 4 (*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a))))))
12.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))

simplify131.0ms (2.2%)

Algorithm
egg-herbie
Rules
404×associate-+l+_binary64
330×associate-+r+_binary64
284×associate-*l*_binary64
253×associate-*r*_binary64
238×exp-sum_binary64
Counts
123 → 234
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01703219
15332280
221742272
341942272
449522272
549422272

prune214.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2340234
Fresh022
Picked011
Done011
Total2344238
Error
0b
Counts
238 → 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))
8.2b
(+.f64 -1 (fma.f64 (*.f64 a a) 4 (*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))))
10.1b
(/.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)))
14.4b
(cbrt.f64 (pow.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)) 3))
Compiler

Compiled 4729 to 2876 computations (39.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.8b
(*.f64 (+.f64 3 a) (*.f64 b b))
0.8b
(*.f64 (+.f64 3 a) (*.f64 b b))
2.8b
(-.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)))
9.4b
(/.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)))

rewrite40.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
77×add-sqr-sqrt_binary64
48×difference-of-squares_binary64
42×times-frac_binary64
39×*-un-lft-identity_binary64
23×add-cube-cbrt_binary64
Counts
3 → 131
Calls

3 calls:

9.0ms
(/.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)))
9.0ms
(*.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)))

series616.0ms (10.5%)

Counts
3 → 72
Calls

3 calls:

542.0ms
(/.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)))
53.0ms
(-.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)))
20.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))

simplify540.0ms (9.2%)

Algorithm
egg-herbie
Rules
580×times-frac_binary64
314×+-commutative_binary64
275×fma-def_binary64
272×associate-+r+_binary64
203×*-commutative_binary64
Counts
203 → 389
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
096623877
1309122838
2492522573
3491722573
4493022573

prune889.0ms (15.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New4820482
Fresh011
Picked011
Done022
Total4824486
Error
0b
Counts
486 → 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))
8.2b
(+.f64 -1 (fma.f64 (*.f64 a a) 4 (*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))))
10.1b
(/.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)))
14.4b
(cbrt.f64 (pow.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)) 3))
Compiler

Compiled 38296 to 24917 computations (34.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
0.1b
(pow.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)) 3)
0.8b
(*.f64 (+.f64 3 a) (*.f64 b b))
13.4b
(cbrt.f64 (pow.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)) 3))

rewrite28.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity_binary64
41×add-sqr-sqrt_binary64
36×prod-diff_binary64
34×add-cube-cbrt_binary64
21×cube-prod_binary64
Counts
3 → 126
Calls

3 calls:

6.0ms
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
6.0ms
(pow.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)) 3)
5.0ms
(cbrt.f64 (pow.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)) 3))

series145.0ms (2.5%)

Counts
3 → 72
Calls

3 calls:

79.0ms
(pow.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)) 3)
43.0ms
(cbrt.f64 (pow.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)) 3))
23.0ms
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))

simplify164.0ms (2.8%)

Algorithm
egg-herbie
Rules
812×fma-def_binary64
488×associate-+l+_binary64
426×associate-*r*_binary64
326×associate-*l*_binary64
183×+-commutative_binary64
Counts
198 → 371
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05268417
115507675
254667675

prune445.0ms (7.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New5570557
Fresh000
Picked011
Done033
Total5574561
Error
0b
Counts
561 → 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))
8.2b
(+.f64 -1 (fma.f64 (*.f64 a a) 4 (*.f64 (*.f64 b b) (+.f64 (+.f64 (*.f64 b b) 12) (*.f64 a (+.f64 4 (*.f64 2 a)))))))
10.1b
(/.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)))
14.4b
(cbrt.f64 (pow.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)) 3))
Compiler

Compiled 11903 to 7741 computations (35% saved)

regimes693.0ms (11.8%)

Accuracy

Total 0.0b remaining (50.3%)

Threshold costs 0.0b (50.3%)

Compiler

Compiled 14440 to 10234 computations (29.1% saved)

simplify4.0ms (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
01633
12133
22533
32733
42833
52833

end1.0ms (0%)

Compiler

Compiled 25 to 17 computations (32% saved)

sample986.0ms (16.7%)

Algorithm
intervals
Results
649.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 205 to 135 computations (34.1% saved)

Profiling

Loading profile data...