Details

Time bar (total: 3.8s)

analyze210.0ms (5.6%)

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%56.2%18.8%7
25%48.4%26.6%8
25%35.1%39.9%9
28.1%18.3%53.6%10
31.6%12.3%56.1%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.5s (40.3%)

Results
1.5s8256×body128valid
1.0msbody128invalid
Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify59.0ms (1.6%)

Algorithm
egg-herbie
Rules
725×fma-def_binary64
669×unsub-neg_binary64
596×cancel-sign-sub-inv_binary64
340×+-commutative_binary64
277×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02042
16340
217036
354236
4186732
5328132
6488132
7495832

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

Compiled 172 to 108 computations (37.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.8b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series95.0ms (2.5%)

Counts
4 → 96
Calls

4 calls:

39.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
34.0ms
(pow.f64 (hypot.f64 a b) 4)
12.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
10.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

rewrite10.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
10×add-exp-log_binary64
10×pow1_binary64
add-cbrt-cube_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
Counts
4 → 63
Calls

4 calls:

5.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
1.0ms
(pow.f64 (hypot.f64 a b) 4)
0.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))

simplify125.0ms (3.3%)

Algorithm
egg-herbie
Rules
821×fma-def_binary64
417×fma-neg_binary64
408×associate-+l+_binary64
315×cancel-sign-sub-inv_binary64
250×exp-prod_binary64
Counts
159 → 140
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01493218
13642814
210652628
333672622
447542618
549902618

prune178.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1364140
Fresh101
Picked011
Done000
Total1375142
Error
0.0b
Counts
142 → 5
Alt Table
StatusErrorProgram
11.9b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))) -1)
11.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 b 4))) -1)
0.2b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) -1)
14.1b
(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 4176 to 2300 computations (44.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2))
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.8b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series38.0ms (1%)

Counts
2 → 48
Calls

2 calls:

22.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2))
16.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-exp-log_binary64
pow1_binary64
Counts
2 → 30
Calls

2 calls:

4.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2))

simplify111.0ms (3%)

Algorithm
egg-herbie
Rules
599×fma-def_binary64
590×unswap-sqr_binary64
490×cancel-sign-sub-inv_binary64
404×associate-+l+_binary64
319×exp-prod_binary64
Counts
78 → 79
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0921914
12361771
26621521
326871517
445551517
547031517
651171517

prune175.0ms (4.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1450145
Fresh033
Picked011
Done011
Total1455150
Error
0.0b
Counts
150 → 5
Alt Table
StatusErrorProgram
11.9b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))) -1)
11.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 b 4))) -1)
0.2b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) -1)
14.1b
(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 4740 to 2352 computations (50.4% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series21.0ms (0.6%)

Counts
2 → 48
Calls

2 calls:

11.0ms
(*.f64 a (*.f64 a (*.f64 b b)))
10.0ms
(*.f64 a (*.f64 b b))

rewrite12.0ms (0.3%)

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)))
4.0ms
(*.f64 a (*.f64 b b))

simplify80.0ms (2.1%)

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

prune142.0ms (3.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1170117
Fresh022
Picked011
Done022
Total1175122
Error
0.0b
Counts
122 → 5
Alt Table
StatusErrorProgram
11.9b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))) -1)
11.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 b 4))) -1)
0.2b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) -1)
14.1b
(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 4243 to 2006 computations (52.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series62.0ms (1.6%)

Counts
4 → 96
Calls

4 calls:

26.0ms
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))) -1)
20.0ms
(*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12))))
10.0ms
(+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))
5.0ms
(fma.f64 b b (*.f64 a -12))

rewrite22.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
add-log-exp_binary64
Counts
4 → 71
Calls

4 calls:

9.0ms
(*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12))))
6.0ms
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))) -1)
3.0ms
(+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))
0.0ms
(fma.f64 b b (*.f64 a -12))

simplify141.0ms (3.7%)

Algorithm
egg-herbie
Rules
347×exp-prod_binary64
296×*-commutative_binary64
274×sub-neg_binary64
263×unsub-neg_binary64
235×associate-+l+_binary64
Counts
167 → 145
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01343743
13683156
212973026
330693026
447473026
549203026

prune168.0ms (4.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1450145
Fresh011
Picked011
Done033
Total1455150
Error
0.0b
Counts
150 → 5
Alt Table
StatusErrorProgram
11.9b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 2 (*.f64 a a) 4) (fma.f64 b b (*.f64 a -12)))) -1)
11.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 2 (*.f64 a (*.f64 a (*.f64 b b))) (pow.f64 b 4))) -1)
0.2b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)) -1)
14.1b
(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 3915 to 2342 computations (40.2% saved)

regimes412.0ms (11%)

Accuracy

Total 0.0b remaining (79.1%)

Threshold costs 0.0b (79.1%)

Counts
80 → 1
Compiler

Compiled 9181 to 6273 computations (31.7% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
11425
21425

end104.0ms (2.8%)

Compiler

Compiled 158 to 101 computations (36.1% saved)

Profiling

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