Details

Time bar (total: 4.9s)

analyze177.0ms (3.6%)

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)

sample1.3s (25.5%)

Results
1.2s8256×body128valid
1.0msbody128invalid
Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify60.0ms (1.2%)

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
0.0b
(+.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)
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)
Compiler

Compiled 172 to 108 computations (37.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) 4)
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))
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
1.1b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series96.0ms (2%)

Counts
4 → 96
Calls

4 calls:

39.0ms
(pow.f64 (hypot.f64 a b) 4)
35.0ms
(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))
13.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
9.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

rewrite12.0ms (0.2%)

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:

7.0ms
(*.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)))

simplify120.0ms (2.4%)

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

prune181.0ms (3.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1364140
Fresh101
Picked101
Done000
Total1384142
Error
0b
Counts
142 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)
0.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.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)))) -1)
14.6b
(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (fma.f64 a -3 1) (*.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
Compiler

Compiled 4199 to 2330 computations (44.5% saved)

localize20.0ms (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))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
1.1b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
2.1b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series37.0ms (0.8%)

Counts
2 → 24
Calls

2 calls:

26.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))
11.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite10.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
16×unswap-sqr_binary64
14×unpow-prod-down_binary64
14×add-exp-log_binary64
10×sqr-pow_binary64
Counts
2 → 63
Calls

2 calls:

7.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
0.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))))

simplify72.0ms (1.5%)

Algorithm
egg-herbie
Rules
746×distribute-rgt-in_binary64
701×fma-def_binary64
420×associate-+l+_binary64
232×associate-+r+_binary64
218×*-commutative_binary64
Counts
87 → 111
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01331938
12971757
29291569
329901514
454131514

prune303.0ms (6.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1770177
Fresh033
Picked011
Done000
Total1774181
Error
0b
Counts
181 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)
0.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.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)))) -1)
14.6b
(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (fma.f64 a -3 1) (*.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
Compiler

Compiled 7153 to 4495 computations (37.2% saved)

localize18.0ms (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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.3b
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
1.1b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series69.0ms (1.4%)

Counts
2 → 48
Calls

2 calls:

36.0ms
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
32.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×unpow-prod-down_binary64
pow-unpow_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 39
Calls

2 calls:

3.0ms
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))

simplify92.0ms (1.9%)

Algorithm
egg-herbie
Rules
637×fma-neg_binary64
598×fma-def_binary64
490×cancel-sign-sub-inv_binary64
402×associate-+l+_binary64
273×distribute-lft-out_binary64
Counts
87 → 87
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01122078
12731827
27261634
328231611
446421585
549061585

prune204.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1530153
Fresh022
Picked011
Done011
Total1534157
Error
0b
Counts
157 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)
0.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.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)))) -1)
14.6b
(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (fma.f64 a -3 1) (*.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
Compiler

Compiled 4903 to 2862 computations (41.6% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.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)))
0.4b
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
1.1b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
17.9b
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

series135.0ms (2.7%)

Counts
3 → 72
Calls

3 calls:

53.0ms
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
47.0ms
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))
35.0ms
(*.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)))

rewrite28.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod_binary64
47×add-sqr-sqrt_binary64
29×pow1_binary64
27×unpow-prod-down_binary64
20×associate-*r*_binary64
Counts
3 → 127
Calls

3 calls:

11.0ms
(*.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)))
7.0ms
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
1.0ms
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

simplify184.0ms (3.7%)

Algorithm
egg-herbie
Rules
475×fma-neg_binary64
388×fma-def_binary64
356×cancel-sign-sub-inv_binary64
346×*-commutative_binary64
305×sqr-pow_binary64
Counts
199 → 198
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02024349
14524264
212863883
325093825
437313345
548063345
649873345
749063345

prune439.0ms (8.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3110311
Fresh011
Picked011
Done022
Total3114315
Error
0b
Counts
315 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)
0.5b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.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)))) -1)
14.6b
(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (fma.f64 a -3 1) (*.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
Compiler

Compiled 14340 to 8167 computations (43% saved)

regimes1.2s (24.8%)

Accuracy

Total 0.0b remaining (37.4%)

Threshold costs 0.0b (37.4%)

Counts
173 → 1
Compiler

Compiled 24800 to 16743 computations (32.5% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02350
13150
23050

end138.0ms (2.8%)

Compiler

Compiled 207 to 141 computations (31.9% saved)

Profiling

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