Details

Time bar (total: 4.9s)

analyze165.0ms (3.3%)

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%53.1%22%7
25%46.8%28.2%8
25%33.6%41.5%9
28.1%18%54%10
31.6%12.1%56.3%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.3s (25.6%)

Results
1.2s8256×body128valid
1.0msbody128invalid
Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify57.0ms (1.2%)

Algorithm
egg-herbie
Rules
620×fma-def_binary64
556×cancel-sign-sub-inv_binary64
552×unswap-sqr_binary64
357×unsub-neg_binary64
344×+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01939
15737
216837
349237
4160433
5289133
6430933
7521433

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 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
Compiler

Compiled 166 to 104 computations (37.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.0b
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.1b
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
0.3b
(*.f64 (*.f64 b b) (+.f64 a 3))

series89.0ms (1.8%)

Counts
4 → 96
Calls

4 calls:

35.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
33.0ms
(pow.f64 (hypot.f64 a b) 4)
13.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))

rewrite18.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-exp-log_binary64
10×pow1_binary64
add-cube-cbrt_binary64
Counts
4 → 78
Calls

4 calls:

8.0ms
(*.f64 (*.f64 b b) (+.f64 a 3))
4.0ms
(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))
2.0ms
(pow.f64 (hypot.f64 a b) 4)
0.0ms
(fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3)))

simplify82.0ms (1.7%)

Algorithm
egg-herbie
Rules
574×associate-+l+_binary64
469×distribute-rgt-in_binary64
453×distribute-lft-in_binary64
338×associate--l+_binary64
219×cancel-sign-sub-inv_binary64
Counts
174 → 162
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01743413
14643143
215563045
350743045

prune224.0ms (4.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1584162
Fresh101
Picked101
Done000
Total1604164
Error
0b
Counts
164 → 4
Alt Table
StatusErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
0.1b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.3b
(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
Compiler

Compiled 5038 to 2969 computations (41.1% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 4 (*.f64 a (pow.f64 b 2)))
0.2b
(*.f64 a (pow.f64 b 2))
0.3b
(*.f64 12 (pow.f64 b 2))
1.8b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series39.0ms (0.8%)

Counts
4 → 0
Calls

4 calls:

16.0ms
(*.f64 4 (*.f64 a (pow.f64 b 2)))
12.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
8.0ms
(*.f64 a (pow.f64 b 2))
2.0ms
(*.f64 12 (pow.f64 b 2))

rewrite25.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
36×add-exp-log_binary64
25×associate-*r*_binary64
24×unswap-sqr_binary64
22×unpow-prod-down_binary64
Counts
4 → 132
Calls

4 calls:

6.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
5.0ms
(*.f64 a (pow.f64 b 2))
4.0ms
(*.f64 12 (pow.f64 b 2))
4.0ms
(*.f64 4 (*.f64 a (pow.f64 b 2)))

simplify93.0ms (1.9%)

Algorithm
egg-herbie
Rules
893×fma-def_binary64
369×*-commutative_binary64
303×sqr-pow_binary64
237×associate-/l/_binary64
230×exp-prod_binary64
Counts
132 → 186
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01621455
12951266
28591241
315671178
426161178
548041178
649411178

prune364.0ms (7.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1860186
Fresh033
Picked011
Done000
Total1864190
Error
0b
Counts
190 → 4
Alt Table
StatusErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
0.1b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.3b
(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
Compiler

Compiled 9647 to 7437 computations (22.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.0b
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
0.0b
(fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4))
0.3b
(*.f64 (+.f64 3 a) (*.f64 b b))

series61.0ms (1.2%)

Counts
3 → 72
Calls

3 calls:

41.0ms
(fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4))
12.0ms
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
8.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite23.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64
36×prod-diff_binary64
33×*-un-lft-identity_binary64
29×add-cube-cbrt_binary64
13×cube-prod_binary64
Counts
3 → 104
Calls

3 calls:

8.0ms
(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))
6.0ms
(*.f64 (+.f64 3 a) (*.f64 b b))
0.0ms
(fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4))

simplify180.0ms (3.6%)

Algorithm
egg-herbie
Rules
548×distribute-rgt-in_binary64
515×fma-neg_binary64
502×exp-prod_binary64
458×cancel-sign-sub-inv_binary64
247×unswap-sqr_binary64
Counts
176 → 163
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02214043
14473644
216993331
342743318
448693318
549533318
649063318

prune302.0ms (6.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1950195
Fresh022
Picked011
Done011
Total1954199
Error
0b
Counts
199 → 4
Alt Table
StatusErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
0.1b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.3b
(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
Compiler

Compiled 6780 to 4077 computations (39.9% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.0b
(*.f64 a (+.f64 4 (*.f64 2 a)))
0.1b
(*.f64 (pow.f64 a 3) (-.f64 a 4))
1.2b
(*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a)))))

series54.0ms (1.1%)

Counts
4 → 72
Calls

4 calls:

30.0ms
(+.f64 (*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
18.0ms
(*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a)))))
3.0ms
(*.f64 (pow.f64 a 3) (-.f64 a 4))
2.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))

rewrite37.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
25×add-cube-cbrt_binary64
18×prod-diff_binary64
16×associate-*l*_binary64
Counts
4 → 133
Calls

4 calls:

8.0ms
(+.f64 (*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
7.0ms
(*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a)))))
7.0ms
(*.f64 (pow.f64 a 3) (-.f64 a 4))
7.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))

simplify143.0ms (2.9%)

Algorithm
egg-herbie
Rules
510×fma-neg_binary64
496×associate-*l*_binary64
455×associate-*r*_binary64
333×fma-def_binary64
235×unswap-sqr_binary64
Counts
205 → 239
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03094913
18443754
238123736
349803730
449493730

prune352.0ms (7.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2390239
Fresh011
Picked011
Done022
Total2394243
Error
0b
Counts
243 → 4
Alt Table
StatusErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (*.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
0.1b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (+.f64 12 (*.f64 b b)) (*.f64 a (+.f64 4 (*.f64 2 a))))) (fma.f64 (*.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
0.0b
(+.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.3b
(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
Compiler

Compiled 10179 to 6500 computations (36.1% saved)

regimes1.1s (23.2%)

Accuracy

Total 0.0b remaining (72.8%)

Threshold costs 0.0b (72.8%)

Counts
190 → 1
Compiler

Compiled 27561 to 19297 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×+-commutative_binary64
10×*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02767
14467
25267
36467
46967
57267
67367
77067

end138.0ms (2.8%)

Compiler

Compiled 228 to 174 computations (23.7% saved)

Profiling

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