Details

Time bar (total: 2.9s)

analyze99.0ms (3.5%)

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)

sample144.0ms (5%)

Algorithm
intervals
Results
13.0ms256×body128valid
Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify43.0ms (1.5%)

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
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series93.0ms (3.3%)

Counts
3 → 72
Calls

3 calls:

45.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
35.0ms
(pow.f64 (hypot.f64 a b) 4)
13.0ms
(hypot.f64 a b)

rewrite8.0ms (0.3%)

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)

simplify100.0ms (3.5%)

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 → 113
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01302123
13432010
29791901
340701899
449221899
549441899

prune93.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1112113
Fresh101
Picked011
Done000
Total1123115
Error
0b
Counts
115 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
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))
0.2b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
Compiler

Compiled 2363 to 1515 computations (35.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
0.0b
(hypot.f64 a b)
0.0b
(pow.f64 (hypot.f64 a b) 2)
0.3b
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

series120.0ms (4.2%)

Counts
3 → 72
Calls

3 calls:

48.0ms
(pow.f64 (hypot.f64 a b) 2)
38.0ms
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
34.0ms
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

rewrite16.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
25×unpow-prod-down_binary64
14×*-un-lft-identity_binary64
12×fma-def_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
Counts
3 → 77
Calls

3 calls:

8.0ms
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
3.0ms
(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
1.0ms
(pow.f64 (hypot.f64 a b) 2)

simplify147.0ms (5.2%)

Algorithm
egg-herbie
Rules
444×log-prod_binary64
413×exp-prod_binary64
342×cancel-sign-sub-inv_binary64
321×fma-def_binary64
284×fma-neg_binary64
Counts
149 → 127
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01112194
12521935
26401839
323921834
441091834
544731828
649711828
749241828

prune145.0ms (5.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1700170
Fresh011
Picked011
Done011
Total1703173
Error
0b
Counts
173 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
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))
0.2b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
Compiler

Compiled 3808 to 2588 computations (32% saved)

localize10.0ms (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)))
19.1b
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

series417.0ms (14.6%)

Counts
3 → 72
Calls

3 calls:

243.0ms
(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))
92.0ms
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
82.0ms
(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

rewrite18.0ms (0.6%)

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:

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))
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))

simplify148.0ms (5.2%)

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

prune362.0ms (12.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New3530353
Fresh000
Picked011
Done022
Total3533356
Error
0b
Counts
356 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
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))
0.2b
(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
Compiler

Compiled 12038 to 7453 computations (38.1% saved)

regimes172.0ms (6%)

Accuracy

Total 0.0b remaining (26.3%)

Threshold costs 0.0b (26.3%)

Counts
27 → 1
Compiler

Compiled 3146 to 2274 computations (27.7% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
11217
21217

end1.0ms (0%)

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample697.0ms (24.4%)

Algorithm
intervals
Results
422.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 95 to 66 computations (30.5% saved)

Profiling

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