Details

Time bar (total: 6.1s)

analyze174.0ms (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)

sample102.0ms (1.7%)

Algorithm
intervals
Results
22.0ms256×body128valid
Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify59.0ms (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)

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))
0.0b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
1.0b
(*.f64 (*.f64 b b) (+.f64 a 3))

series105.0ms (1.7%)

Counts
4 → 96
Calls

4 calls:

50.0ms
(+.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))
34.0ms
(pow.f64 (hypot.f64 a b) 4)
11.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
10.0ms
(*.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)))

simplify86.0ms (1.4%)

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 (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1593162
Fresh101
Picked101
Done000
Total1613164
Error
0b
Counts
164 → 3
Alt Table
StatusErrorProgram
13.4b
(fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.1b
(/.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)))
Compiler

Compiled 4986 to 2915 computations (41.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series94.0ms (1.5%)

Counts
4 → 96
Calls

4 calls:

38.0ms
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
36.0ms
(fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4))
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))

rewrite26.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
37×*-un-lft-identity_binary64
36×prod-diff_binary64
31×add-cube-cbrt_binary64
13×cube-prod_binary64
Counts
4 → 123
Calls

4 calls:

6.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))
6.0ms
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
3.0ms
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
0.0ms
(fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4))

simplify163.0ms (2.7%)

Algorithm
egg-herbie
Rules
750×fma-neg_binary64
642×distribute-rgt-in_binary64
535×cancel-sign-sub-inv_binary64
249×unswap-sqr_binary64
173×distribute-rgt-out_binary64
Counts
219 → 209
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02555599
15465141
220154716
349044699
451964699

prune288.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2081209
Fresh112
Picked011
Done000
Total2093212
Error
0b
Counts
212 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.1b
(/.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)))
13.4b
(+.f64 (fma.f64 4 (*.f64 a a) (*.f64 (pow.f64 a 3) (-.f64 a 4))) -1)
Compiler

Compiled 7565 to 4560 computations (39.7% saved)

localize20.0ms (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))
1.0b
(*.f64 (+.f64 3 a) (*.f64 b b))
3.2b
(-.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)))
12.2b
(/.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)))

series671.0ms (11.1%)

Counts
3 → 72
Calls

3 calls:

570.0ms
(/.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)))
55.0ms
(-.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)))
45.0ms
(*.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))

rewrite45.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt_binary64
48×difference-of-squares_binary64
42×times-frac_binary64
40×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64
Counts
3 → 136
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)))
6.0ms
(-.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))

simplify443.0ms (7.3%)

Algorithm
egg-herbie
Rules
559×times-frac_binary64
338×+-commutative_binary64
297×fma-def_binary64
293×associate-+r+_binary64
198×*-commutative_binary64
Counts
208 → 310
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
099726410
1322125576
2499825576
3494925576

prune1.1s (18.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New4360436
Fresh011
Picked011
Done011
Total4363439
Error
0b
Counts
439 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.1b
(/.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)))
13.4b
(+.f64 (fma.f64 4 (*.f64 a a) (*.f64 (pow.f64 a 3) (-.f64 a 4))) -1)
Compiler

Compiled 48160 to 30997 computations (35.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 4 (*.f64 a a) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
0.1b
(*.f64 (pow.f64 a 3) (-.f64 a 4))

series8.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

5.0ms
(fma.f64 4 (*.f64 a a) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
3.0ms
(*.f64 (pow.f64 a 3) (-.f64 a 4))

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
18×prod-diff_binary64
13×distribute-lft-in_binary64
Counts
2 → 73
Calls

2 calls:

8.0ms
(*.f64 (pow.f64 a 3) (-.f64 a 4))
0.0ms
(fma.f64 4 (*.f64 a a) (*.f64 (pow.f64 a 3) (-.f64 a 4)))

simplify89.0ms (1.5%)

Algorithm
egg-herbie
Rules
658×exp-prod_binary64
634×fma-neg_binary64
509×unswap-sqr_binary64
356×fma-def_binary64
355×*-commutative_binary64
Counts
97 → 108
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01361504
12331217
28691201
322171177
441971177
551941177

prune133.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1080108
Fresh000
Picked011
Done022
Total1083111
Error
0b
Counts
111 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.1b
(/.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)))
13.4b
(+.f64 (fma.f64 4 (*.f64 a a) (*.f64 (pow.f64 a 3) (-.f64 a 4))) -1)
Compiler

Compiled 2608 to 1851 computations (29% saved)

regimes1.2s (20.2%)

Accuracy

Total 0.0b remaining (49.6%)

Threshold costs 0.0b (49.6%)

Counts
170 → 1
Compiler

Compiled 27967 to 19428 computations (30.5% saved)

simplify3.0ms (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
01633
12133
22533
32733
42833
52833

end1.0ms (0%)

Compiler

Compiled 25 to 17 computations (32% saved)

sample954.0ms (15.7%)

Algorithm
intervals
Results
631.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 167 to 110 computations (34.1% saved)

Profiling

Loading profile data...