Details

Time bar (total: 7.2s)

analyze198.0ms (2.8%)

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)

sample1.4s (19.1%)

Results
1.3s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify60.0ms (0.8%)

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

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
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 106 to 66 computations (37.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (hypot.f64 a b) 4)
0.1b
(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))
0.6b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series98.0ms (1.4%)

Counts
4 → 96
Calls

4 calls:

36.0ms
(pow.f64 (hypot.f64 a b) 4)
35.0ms
(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))
16.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
11.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

rewrite11.0ms (0.1%)

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:

4.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
1.0ms
(pow.f64 (hypot.f64 a b) 4)
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 (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))

simplify117.0ms (1.6%)

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

prune160.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1364140
Fresh000
Picked101
Done000
Total1374141
Error
0.0b
Counts
141 → 4
Alt Table
StatusErrorProgram
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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)
13.5b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a -12))) -1)
0.6b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4))) -1)
1.1b
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 4209 to 2316 computations (45% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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))))
0.6b
(*.f64 (cbrt.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))) (cbrt.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))))
0.6b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
10.1b
(cbrt.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)))

series668.0ms (9.3%)

Counts
3 → 72
Calls

3 calls:

463.0ms
(*.f64 (cbrt.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))) (cbrt.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))))
165.0ms
(cbrt.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)))
39.0ms
(*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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))))

rewrite25.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

8.0ms
(*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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))))
4.0ms
(*.f64 (cbrt.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))) (cbrt.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))))
1.0ms
(cbrt.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)))

simplify236.0ms (3.3%)

Algorithm
egg-herbie
Rules
507×associate-+l+_binary64
310×*-commutative_binary64
201×+-commutative_binary64
185×associate--l+_binary64
181×fma-def_binary64
Counts
165 → 192
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
078213856
1247012464
2495712460
3505012460

prune1.2s (16.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3992401
Fresh033
Picked101
Done000
Total4005405
Error
0.0b
Counts
405 → 5
Alt Table
StatusErrorProgram
0.5b
(+.f64 (*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (*.f64 (cbrt.f64 (sqrt.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)))) (cbrt.f64 (sqrt.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)
0.6b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4))) -1)
18.5b
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (*.f64 a a) (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4))) 2)) (cbrt.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)
13.5b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a -12))) -1)
1.1b
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 42215 to 25752 computations (39% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (sqrt.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))))
0.6b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
9.5b
(sqrt.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)))
10.1b
(cbrt.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)))

series229.0ms (3.2%)

Counts
2 → 48
Calls

2 calls:

158.0ms
(cbrt.f64 (sqrt.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))))
71.0ms
(sqrt.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)))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
cbrt-prod_binary64
sqrt-prod_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 31
Calls

2 calls:

1.0ms
(cbrt.f64 (sqrt.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))))
1.0ms
(sqrt.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)))

simplify100.0ms (1.4%)

Algorithm
egg-herbie
Rules
624×fma-def_binary64
565×associate-*r*_binary64
433×associate-*l*_binary64
300×associate-+l+_binary64
169×*-commutative_binary64
Counts
79 → 97
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04796504
114976055
251976055

prune1.5s (21.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New4411442
Fresh044
Picked101
Done000
Total4425447
Error
0.0b
Counts
447 → 5
Alt Table
StatusErrorProgram
1.3b
(+.f64 (*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (*.f64 (cbrt.f64 (sqrt.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)))) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.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)
0.6b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4))) -1)
18.5b
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (*.f64 a a) (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4))) 2)) (cbrt.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)
13.5b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a -12))) -1)
1.1b
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 59114 to 34840 computations (41.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4)))
0.3b
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4))
0.6b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
0.8b
(pow.f64 (sqrt.f64 (hypot.f64 a b)) 4)

series146.0ms (2%)

Counts
3 → 56
Calls

3 calls:

76.0ms
(pow.f64 (sqrt.f64 (hypot.f64 a b)) 4)
35.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4)))
35.0ms
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4))

rewrite18.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
50×unpow-prod-down_binary64
46×add-sqr-sqrt_binary64
25×sqrt-prod_binary64
18×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
Counts
3 → 107
Calls

3 calls:

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

simplify118.0ms (1.7%)

Algorithm
egg-herbie
Rules
605×fma-def_binary64
417×fma-neg_binary64
406×associate--l+_binary64
404×associate-+l+_binary64
383×unswap-sqr_binary64
Counts
163 → 161
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01493249
13172800
29702504
325782450
447302424
550752424

prune359.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2370237
Fresh044
Picked011
Done000
Total2375242
Error
0.0b
Counts
242 → 5
Alt Table
StatusErrorProgram
1.3b
(+.f64 (*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (*.f64 (cbrt.f64 (sqrt.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)))) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.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)
0.6b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4))) -1)
18.5b
(+.f64 (*.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (*.f64 a a) (fma.f64 4 (pow.f64 a 3) (pow.f64 a 4))) 2)) (cbrt.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)
13.5b
(+.f64 (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a -12))) -1)
1.1b
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 8625 to 4271 computations (50.5% saved)

regimes326.0ms (4.5%)

Accuracy

Total 0.1b remaining (71.5%)

Threshold costs 0.1b (71.5%)

Counts
51 → 1
Compiler

Compiled 8211 to 5304 computations (35.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01225
11325
21325

end170.0ms (2.4%)

Compiler

Compiled 248 to 151 computations (39.1% saved)

Profiling

Loading profile data...