Details

Time bar (total: 3.3s)

analyze97.0ms (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%50%25.1%6
25%31.2%43.8%7
25%21.9%53.2%8
25%14%61%9
28.1%10.9%61%10
31.6%7.4%61%11
33.4%5.7%61%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 20 to 13 computations (35% saved)

sample991.0ms (30.5%)

Results
919.0ms8256×body128valid
1.0msbody128invalid
Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify47.0ms (1.4%)

Algorithm
egg-herbie
Rules
770×unswap-sqr_binary64
631×associate-*l*_binary64
623×fma-def_binary64
311×fma-neg_binary64
283×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01323
13021
26021
315921
451817
5168717
6359717
7502617

prune4.0ms (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 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)
Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series82.0ms (2.5%)

Counts
3 → 72
Calls

3 calls:

38.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
33.0ms
(pow.f64 (hypot.f64 a b) 4)
11.0ms
(hypot.f64 a b)

rewrite7.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
fma-def_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
unpow-prod-down_binary64
Counts
3 → 52
Calls

3 calls:

4.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
1.0ms
(pow.f64 (hypot.f64 a b) 4)
0.0ms
(hypot.f64 a b)

simplify93.0ms (2.9%)

Algorithm
egg-herbie
Rules
785×fma-neg_binary64
421×fma-def_binary64
280×associate-*r*_binary64
276×associate-*l*_binary64
184×times-frac_binary64
Counts
124 → 114
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01302123
13432010
29791901
340701899
449221899
549441899

prune121.0ms (3.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1122114
Fresh101
Picked101
Done000
Total1142116
Error
0b
Counts
116 → 2
Alt Table
StatusErrorProgram
0.5b
(fma.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)) (fma.f64 b (*.f64 b 4) -1))
0.0b
(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))))
Compiler

Compiled 2362 to 1513 computations (35.9% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 -1 (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4)))
1.2b
(fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))

series39.0ms (1.2%)

Counts
2 → 48
Calls

2 calls:

21.0ms
(fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))
18.0ms
(+.f64 -1 (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4)))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-log-exp_binary64
fma-def_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 28
Calls

2 calls:

2.0ms
(+.f64 -1 (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4)))
0.0ms
(fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))

simplify80.0ms (2.5%)

Algorithm
egg-herbie
Rules
458×exp-prod_binary64
416×cancel-sign-sub-inv_binary64
390×fma-neg_binary64
203×distribute-rgt-in_binary64
196×distribute-neg-in_binary64
Counts
76 → 62
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0591712
11331435
23381431
318191431
441711431
549711431

prune61.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New62062
Fresh011
Picked011
Done000
Total62264
Error
0b
Counts
64 → 2
Alt Table
StatusErrorProgram
0.5b
(fma.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)) (fma.f64 b (*.f64 b 4) -1))
0.0b
(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))))
Compiler

Compiled 1682 to 1042 computations (38% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.1b
(fma.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)) (fma.f64 b (*.f64 b 4) -1))
0.4b
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
17.9b
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

series316.0ms (9.7%)

Counts
3 → 72
Calls

3 calls:

213.0ms
(fma.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)) (fma.f64 b (*.f64 b 4) -1))
57.0ms
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
46.0ms
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

rewrite17.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
59×cbrt-prod_binary64
41×add-sqr-sqrt_binary64
23×unpow-prod-down_binary64
17×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
Counts
3 → 93
Calls

3 calls:

9.0ms
(*.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))
0.0ms
(fma.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)) (fma.f64 b (*.f64 b 4) -1))

simplify154.0ms (4.7%)

Algorithm
egg-herbie
Rules
514×fma-def_binary64
498×unswap-sqr_binary64
312×*-commutative_binary64
275×fma-neg_binary64
227×cancel-sign-sub-inv_binary64
Counts
165 → 175
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02014579
14614352
212873938
327743911
448493847
549203847

prune437.0ms (13.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New3530353
Fresh000
Picked011
Done011
Total3532355
Error
0b
Counts
355 → 2
Alt Table
StatusErrorProgram
0.5b
(fma.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)) (fma.f64 b (*.f64 b 4) -1))
0.0b
(+.f64 (pow.f64 a 4) (+.f64 -1 (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))))
Compiler

Compiled 12028 to 7445 computations (38.1% saved)

regimes590.0ms (18.2%)

Accuracy

Total 0.0b remaining (33.4%)

Threshold costs 0.0b (33.4%)

Counts
98 → 1
Compiler

Compiled 10988 to 8010 computations (27.1% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01735
12335
22335

end79.0ms (2.4%)

Compiler

Compiled 101 to 73 computations (27.7% saved)

Profiling

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