Details

Time bar (total: 2.9s)

analyze171.0ms (5.9%)

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%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)

sample78.0ms (2.7%)

Algorithm
intervals
Results
22.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify59.0ms (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 (0.2%)

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)

localize14.0ms (0.5%)

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))
0.0b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
1.2b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series104.0ms (3.6%)

Counts
4 → 96
Calls

4 calls:

43.0ms
(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))
36.0ms
(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)))
10.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

rewrite24.0ms (0.8%)

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:

16.0ms
(pow.f64 (hypot.f64 a b) 4)
5.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
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))

simplify188.0ms (6.4%)

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

prune182.0ms (6.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1382140
Fresh101
Picked011
Done000
Total1393142
Error
0.0b
Counts
142 → 3
Alt Table
StatusErrorProgram
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)
2.2b
(+.f64 (expm1.f64 (log1p.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)
0.0b
(+.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 4070 to 2238 computations (45% saved)

localize15.0ms (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))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2))
0.0b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.4b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
1.2b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series41.0ms (1.4%)

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))) (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2))
15.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

rewrite5.0ms (0.2%)

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))

simplify114.0ms (3.9%)

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

prune179.0ms (6.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1450145
Fresh011
Picked011
Done011
Total1453148
Error
0.0b
Counts
148 → 3
Alt Table
StatusErrorProgram
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)
2.2b
(+.f64 (expm1.f64 (log1p.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)
0.0b
(+.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 4666 to 2304 computations (50.6% saved)

localize18.0ms (0.6%)

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
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
1.2b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
2.2b
(expm1.f64 (log1p.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))))

series40.0ms (1.4%)

Counts
1 → 24
Calls

1 calls:

40.0ms
(expm1.f64 (log1p.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))))

rewrite1.0ms (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
1 → 11
Calls

1 calls:

0.0ms
(expm1.f64 (log1p.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))))

simplify73.0ms (2.5%)

Algorithm
egg-herbie
Rules
838×fma-neg_binary64
561×fma-def_binary64
488×cancel-sign-sub-inv_binary64
410×associate--l+_binary64
406×associate-+l+_binary64
Counts
35 → 42
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0651204
11821113
2548950
32233927
44588901
55105901

prune183.0ms (6.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1500150
Fresh000
Picked011
Done022
Total1503153
Error
0.0b
Counts
153 → 3
Alt Table
StatusErrorProgram
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)
2.2b
(+.f64 (expm1.f64 (log1p.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)
0.0b
(+.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 4495 to 2661 computations (40.8% saved)

regimes425.0ms (14.6%)

Accuracy

Total 0.0b remaining (73.4%)

Threshold costs 0.0b (73.4%)

Counts
78 → 1
Compiler

Compiled 9132 to 6314 computations (30.9% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01225
11325
21325

end1.0ms (0%)

Compiler

Compiled 20 to 12 computations (40% saved)

sample994.0ms (34.1%)

Algorithm
intervals
Results
681.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 137 to 87 computations (36.5% saved)

Profiling

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