Details

Time bar (total: 6.6s)

analyze173.0ms (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 (20.2%)

Results
1.2s8256×body128valid
1.0msbody128invalid
Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify61.0ms (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
0.2b
(-.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)
0.1b
(+.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)

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)
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.8b
(*.f64 (*.f64 b b) (+.f64 a 3))

series92.0ms (1.4%)

Counts
4 → 96
Calls

4 calls:

37.0ms
(+.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)
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))

rewrite15.0ms (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)))

simplify85.0ms (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

prune215.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1584162
Fresh011
Picked101
Done000
Total1595164
Error
0b
Counts
164 → 5
Alt Table
StatusErrorProgram
11.4b
(+.f64 (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 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)
24.3b
(log.f64 (*.f64 (exp.f64 (pow.f64 (hypot.f64 a b) 4)) (exp.f64 (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))))
13.4b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (*.f64 4 (pow.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 5160 to 3027 computations (41.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.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)))))
0.1b
(*.f64 (*.f64 a a) (-.f64 1 a))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.8b
(*.f64 (*.f64 b b) (+.f64 3 a))

series55.0ms (0.8%)

Counts
4 → 84
Calls

4 calls:

29.0ms
(+.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)))))
15.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
8.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
3.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))

rewrite33.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity_binary64
29×add-sqr-sqrt_binary64
24×add-cube-cbrt_binary64
18×prod-diff_binary64
15×distribute-lft-in_binary64
Counts
4 → 121
Calls

4 calls:

9.0ms
(+.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)))))
7.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
6.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
4.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

simplify96.0ms (1.5%)

Algorithm
egg-herbie
Rules
511×associate-+l+_binary64
383×associate-*l*_binary64
299×associate-*r*_binary64
268×cancel-sign-sub-inv_binary64
211×unswap-sqr_binary64
Counts
205 → 209
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02413743
16003419
223883054
348823054

prune305.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2081209
Fresh134
Picked011
Done000
Total2095214
Error
0b
Counts
214 → 5
Alt Table
StatusErrorProgram
11.4b
(+.f64 (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 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)
13.1b
(-.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))))) (*.f64 4 (pow.f64 a 3))) 1)
24.3b
(log.f64 (*.f64 (exp.f64 (pow.f64 (hypot.f64 a b) 4)) (exp.f64 (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 7954 to 4116 computations (48.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.1b
(*.f64 a (*.f64 a (*.f64 b b)))
0.8b
(*.f64 a (*.f64 b b))
0.8b
(*.f64 (*.f64 b b) (+.f64 a 3))

series20.0ms (0.3%)

Counts
2 → 48
Calls

2 calls:

11.0ms
(*.f64 a (*.f64 a (*.f64 b b)))
9.0ms
(*.f64 a (*.f64 b b))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
16×pow1_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
2 → 44
Calls

2 calls:

6.0ms
(*.f64 a (*.f64 a (*.f64 b b)))
5.0ms
(*.f64 a (*.f64 b b))

simplify70.0ms (1.1%)

Algorithm
egg-herbie
Rules
593×associate-*l*_binary64
566×fma-def_binary64
511×unswap-sqr_binary64
413×*-commutative_binary64
369×associate-*r*_binary64
Counts
92 → 51
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
057979
1125850
2375826
31084808
42147797
53407797
64998797

prune174.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1240124
Fresh033
Picked011
Done011
Total1245129
Error
0b
Counts
129 → 5
Alt Table
StatusErrorProgram
11.4b
(+.f64 (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 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)
13.1b
(-.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))))) (*.f64 4 (pow.f64 a 3))) 1)
24.3b
(log.f64 (*.f64 (exp.f64 (pow.f64 (hypot.f64 a b) 4)) (exp.f64 (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 4646 to 2369 computations (49% saved)

localize18.0ms (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))
3.4b
(-.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)))
11.9b
(/.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)))

series626.0ms (9.5%)

Counts
4 → 96
Calls

4 calls:

525.0ms
(/.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)))
51.0ms
(-.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)))
41.0ms
(*.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))
8.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite48.0ms (0.7%)

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:

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 (+.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))

simplify345.0ms (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 (17.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New4381439
Fresh112
Picked101
Done022
Total4404444
Error
0b
Counts
444 → 4
Alt Table
StatusErrorProgram
11.4b
(+.f64 (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 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)
13.1b
(-.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))))) (*.f64 4 (pow.f64 a 3))) 1)
19.0b
(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (cbrt.f64 (pow.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (*.f64 b b) (+.f64 a 3))) (pow.f64 a 3)) 4 -1) 6))) (-.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 48384 to 31101 computations (35.7% saved)

regimes1.4s (22.1%)

Accuracy

Total 0.0b remaining (62.8%)

Threshold costs 0.0b (62.8%)

Counts
216 → 1
Compiler

Compiled 36758 to 25079 computations (31.8% 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
01838
12938
23338
33538
43638
53438

end119.0ms (1.8%)

Compiler

Compiled 200 to 137 computations (31.5% saved)

Profiling

Loading profile data...