Details

Time bar (total: 4.4s)

analyze163.0ms (3.7%)

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)

sample75.0ms (1.7%)

Algorithm
intervals
Results
21.0ms256×body128valid
Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify60.0ms (1.4%)

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)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a -3 1)
0.0b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.1b
(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))
0.7b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series58.0ms (1.3%)

Counts
4 → 84
Calls

4 calls:

33.0ms
(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))
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))
1.0ms
(fma.f64 a -3 1)

rewrite7.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
add-sqr-sqrt_binary64
fma-udef_binary64
Counts
4 → 53
Calls

4 calls:

4.0ms
(*.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))
0.0ms
(fma.f64 a -3 1)
0.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))

simplify101.0ms (2.3%)

Algorithm
egg-herbie
Rules
786×fma-def_binary64
528×fma-neg_binary64
415×associate-+l+_binary64
313×cancel-sign-sub-inv_binary64
229×associate-+r+_binary64
Counts
137 → 125
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01252754
13182352
29692192
331842169
448182143
549832143

prune197.0ms (4.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1223125
Fresh011
Picked101
Done000
Total1234127
Error
0.0b
Counts
127 → 4
Alt Table
StatusErrorProgram
0.0b
(+.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (*.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
12.0b
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
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)
3.0b
(+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 3665 to 2075 computations (43.4% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))
0.2b
(*.f64 12 (*.f64 a (pow.f64 b 2)))
0.7b
(*.f64 a (pow.f64 b 2))
2.8b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series56.0ms (1.3%)

Counts
4 → 15
Calls

4 calls:

24.0ms
(+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))
11.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
11.0ms
(*.f64 a (pow.f64 b 2))
10.0ms
(*.f64 12 (*.f64 a (pow.f64 b 2)))

rewrite35.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64
31×add-exp-log_binary64
20×unswap-sqr_binary64
19×prod-exp_binary64
18×unpow-prod-down_binary64
Counts
4 → 121
Calls

4 calls:

16.0ms
(+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))
6.0ms
(*.f64 (pow.f64 a 2) (pow.f64 b 2))
4.0ms
(*.f64 12 (*.f64 a (pow.f64 b 2)))
4.0ms
(*.f64 a (pow.f64 b 2))

simplify67.0ms (1.5%)

Algorithm
egg-herbie
Rules
721×distribute-rgt-in_binary64
689×distribute-lft-in_binary64
537×fma-def_binary64
217×associate-*l*_binary64
214×unswap-sqr_binary64
Counts
136 → 188
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01842295
14091991
215071840
354931840

prune389.0ms (8.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1862188
Fresh123
Picked101
Done000
Total1884192
Error
0b
Counts
192 → 4
Alt Table
StatusErrorProgram
0.1b
(+.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))))) (*.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
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)
3.0b
(+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 (hypot.f64 a b) 4)) -1)
25.4b
(+.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (-.f64 (*.f64 (*.f64 4 (pow.f64 a 3)) (*.f64 4 (pow.f64 a 3))) (*.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (-.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))))))) (*.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
Compiler

Compiled 9916 to 7583 computations (23.5% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (pow.f64 a 3) (+.f64 4 a))
0.2b
(*.f64 12 (*.f64 a (pow.f64 b 2)))
0.7b
(*.f64 a (pow.f64 b 2))
2.8b
(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series3.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

3.0ms
(*.f64 (pow.f64 a 3) (+.f64 4 a))

rewrite8.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×associate-*l*_binary64
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-exp-log_binary64
add-cube-cbrt_binary64
Counts
1 → 38
Calls

1 calls:

6.0ms
(*.f64 (pow.f64 a 3) (+.f64 4 a))

simplify68.0ms (1.5%)

Algorithm
egg-herbie
Rules
971×fma-def_binary64
348×sqr-pow_binary64
340×*-commutative_binary64
308×associate-+l+_binary64
297×associate-+r+_binary64
Counts
50 → 47
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
069623
1178591
2818591
32091567
44420567
55174567

prune392.0ms (8.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1930193
Fresh033
Picked011
Done000
Total1934197
Error
0b
Counts
197 → 4
Alt Table
StatusErrorProgram
0.1b
(+.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))))) (*.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
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)
3.0b
(+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 (hypot.f64 a b) 4)) -1)
25.4b
(+.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (/.f64 (-.f64 (*.f64 (*.f64 4 (pow.f64 a 3)) (*.f64 4 (pow.f64 a 3))) (*.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (-.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))))))) (*.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
Compiler

Compiled 9768 to 7451 computations (23.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.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))))))
0.0b
(*.f64 (*.f64 a a) (+.f64 1 a))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.7b
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))

series54.0ms (1.2%)

Counts
4 → 84
Calls

4 calls:

28.0ms
(+.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))))))
12.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
10.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
4.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))

rewrite30.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
15×add-exp-log_binary64
15×pow1_binary64
14×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
14×add-cbrt-cube_binary64
Counts
4 → 102
Calls

4 calls:

8.0ms
(*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))
8.0ms
(+.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))))))
6.0ms
(*.f64 (*.f64 a a) (+.f64 1 a))
3.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

simplify90.0ms (2%)

Algorithm
egg-herbie
Rules
870×distribute-rgt-in_binary64
807×distribute-lft-in_binary64
278×cancel-sign-sub-inv_binary64
257×associate-*l*_binary64
213×associate-*r*_binary64
Counts
186 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02093661
15773211
219973007
358193007

prune280.0ms (6.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1891190
Fresh112
Picked011
Done011
Total1904194
Error
0b
Counts
194 → 4
Alt Table
StatusErrorProgram
0.1b
(+.f64 (-.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))))) (*.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
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)
0.5b
(-.f64 (+.f64 (*.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))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
3.0b
(+.f64 (fma.f64 4 (pow.f64 a 3) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 7158 to 4058 computations (43.3% saved)

regimes1.2s (26.8%)

Accuracy

Total 0.0b remaining (56.5%)

Threshold costs 0.0b (56.5%)

Counts
197 → 1
Compiler

Compiled 31256 to 21754 computations (30.4% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01732
12232
22132

end1.0ms (0%)

Compiler

Compiled 25 to 16 computations (36% saved)

sample1.0s (23.2%)

Algorithm
intervals
Results
662.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 197 to 138 computations (29.9% saved)

Profiling

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