Details

Time bar (total: 3.8s)

analyze241.0ms (6.3%)

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)

sample31.0ms (0.8%)

Algorithm
intervals
Results
21.0ms256×body128valid
Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify60.0ms (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)

localize13.0ms (0.3%)

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)))
0.9b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series92.0ms (2.4%)

Counts
4 → 96
Calls

4 calls:

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))
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)))
11.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

rewrite11.0ms (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:

6.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
1.0ms
(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)))
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))

simplify119.0ms (3.1%)

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

prune176.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1373140
Fresh101
Picked101
Done000
Total1393142
Error
0b
Counts
142 → 3
Alt Table
StatusErrorProgram
0.1b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.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))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
0.4b
(+.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)
Compiler

Compiled 4189 to 2308 computations (44.9% saved)

localize19.0ms (0.5%)

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)))
0.9b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
2.5b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series42.0ms (1.1%)

Counts
2 → 24
Calls

2 calls:

28.0ms
(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))))
13.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite9.0ms (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:

6.0ms
(*.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))))

simplify70.0ms (1.8%)

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

prune258.0ms (6.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1770177
Fresh022
Picked011
Done000
Total1773180
Error
0b
Counts
180 → 3
Alt Table
StatusErrorProgram
0.1b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.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))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
0.4b
(+.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)
Compiler

Compiled 7111 to 4459 computations (37.3% saved)

localize19.0ms (0.5%)

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))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)))
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.2b
(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))
0.9b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series44.0ms (1.1%)

Counts
2 → 48
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))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)))
18.0ms
(fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 20
Calls

2 calls:

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

simplify72.0ms (1.9%)

Algorithm
egg-herbie
Rules
953×distribute-rgt-in_binary64
632×fma-def_binary64
495×cancel-sign-sub-inv_binary64
408×associate-+l+_binary64
318×fma-neg_binary64
Counts
68 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0772062
12041870
25971701
326031658
460281658

prune158.0ms (4.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1301131
Fresh101
Picked101
Done011
Total1322134
Error
0b
Counts
134 → 2
Alt Table
StatusErrorProgram
0.1b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 b (*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b))) (pow.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))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
Compiler

Compiled 4973 to 2558 computations (48.6% saved)

localize18.0ms (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
(fma.f64 b (*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b))) (pow.f64 a 4))
0.2b
(*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b)))
0.9b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series35.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

20.0ms
(fma.f64 b (*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b))) (pow.f64 a 4))
15.0ms
(*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b)))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 32
Calls

2 calls:

3.0ms
(*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b)))
0.0ms
(fma.f64 b (*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b))) (pow.f64 a 4))

simplify126.0ms (3.3%)

Algorithm
egg-herbie
Rules
743×fma-def_binary64
659×unswap-sqr_binary64
540×exp-prod_binary64
402×associate-+r+_binary64
375×*-commutative_binary64
Counts
80 → 64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0661461
11261290
23621290
312731290
425911290
549851290
649901290
752611290

prune155.0ms (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1300130
Fresh000
Picked011
Done011
Total1302132
Error
0b
Counts
132 → 2
Alt Table
StatusErrorProgram
0.1b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (fma.f64 b (*.f64 b (fma.f64 2 (*.f64 a a) (*.f64 b b))) (pow.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))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))) -1)
Compiler

Compiled 5039 to 2486 computations (50.7% saved)

regimes1.0s (26.8%)

Accuracy

Total 0.0b remaining (11.5%)

Threshold costs 0.0b (11.5%)

Counts
181 → 1
Compiler

Compiled 25894 to 17063 computations (34.1% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02247
13047
22947

end1.0ms (0%)

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample1.0s (26.6%)

Algorithm
intervals
Results
697.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 143 to 94 computations (34.3% saved)

Profiling

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