Details

Time bar (total: 12.1s)

analyze2.7s (22.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.5%0.5%0
0%99.5%0.5%1
0%99.5%0.5%2
0%99.5%0.5%3
0%99.5%0.5%4
0%99.5%0.5%5
0%99.5%0.5%6
0%99.5%0.5%7
0%99.5%0.5%8
0%99.5%0.5%9
0%99.5%0.5%10
0%99.5%0.5%11
0%99.5%0.5%12
0%99.5%0.5%13
0%99.5%0.5%14
Compiler

Compiled 42 to 30 computations (28.6% saved)

sample3.8s (31.4%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results
1.9s8482×body128invalid
1.8s8256×body128valid
Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify335.0ms (2.8%)

Algorithm
egg-herbie
Rules
6437×fma-neg_binary64
684×unsub-neg_binary64
621×distribute-rgt-neg-in_binary64
515×distribute-rgt-in_binary64
434×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02943
17737
225535
377335
4171135
5277735
6347435
7347035
8349335
9351635
10353435
11353435
12352635
13354935
14354935
15354935
16363935
17413135
18367535
19367535
20367535
21938435

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
5.9b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
3.9b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
Compiler

Compiled 218 to 148 computations (32.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
0.1b
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
3.1b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
3.9b
(*.f64 y (*.f64 z t))

series134.0ms (1.1%)

Counts
4 → 252
Calls

4 calls:

100.0ms
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
15.0ms
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
10.0ms
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
8.0ms
(*.f64 y (*.f64 z t))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
4 → 50
Calls

4 calls:

3.0ms
(*.f64 y (*.f64 z t))
0.0ms
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
0.0ms
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
0.0ms
(fma.f64 -27 (*.f64 j k) (*.f64 b c))

simplify194.0ms (1.6%)

Algorithm
egg-herbie
Rules
856×fma-neg_binary64
688×associate-*l*_binary64
535×associate-*r*_binary64
523×cancel-sign-sub-inv_binary64
490×exp-prod_binary64
Counts
302 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01356517
13115980
29245783
328655781
448605781
551495781

prune163.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1156121
Fresh011
Picked101
Done000
Total1167123
Error
0.0b
Counts
123 → 7
Alt Table
StatusErrorProgram
17.1b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.3b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
34.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
5.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c)))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
8.1b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
5.9b
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))
4.3b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
Compiler

Compiled 3975 to 1895 computations (52.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))
0.2b
(*.f64 18 (*.f64 z x))
1.9b
(fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4))
2.7b
(fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4)))

series111.0ms (0.9%)

Counts
4 → 192
Calls

4 calls:

77.0ms
(fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4)))
13.0ms
(fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))
13.0ms
(fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4))
8.0ms
(*.f64 18 (*.f64 z x))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
4 → 50
Calls

4 calls:

3.0ms
(*.f64 18 (*.f64 z x))
1.0ms
(fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4))
0.0ms
(fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4)))
0.0ms
(fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))

simplify150.0ms (1.2%)

Algorithm
egg-herbie
Rules
929×fma-neg_binary64
652×associate-*l*_binary64
583×cancel-sign-sub-inv_binary64
508×associate-*r*_binary64
450×exp-prod_binary64
Counts
242 → 116
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01295320
13034771
28204617
326784617
445984617
554114617

prune178.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1133116
Fresh246
Picked011
Done000
Total1158123
Error
0.0b
Counts
123 → 8
Alt Table
StatusErrorProgram
8.1b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
4.3b
(fma.f64 c b (-.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j))))))
17.1b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.3b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
34.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
5.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c)))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
6.1b
(fma.f64 c b (fma.f64 t (fma.f64 x (*.f64 18 (*.f64 y z)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
18.6b
(fma.f64 c b (fma.f64 k (*.f64 j -27) (*.f64 (*.f64 t a) -4)))
Compiler

Compiled 3887 to 1994 computations (48.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
0.2b
(*.f64 27 (*.f64 k j))
2.8b
(*.f64 t (*.f64 z x))
7.5b
(*.f64 y (*.f64 t (*.f64 z x)))

series47.0ms (0.4%)

Counts
4 → 0
Calls

4 calls:

19.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
16.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
8.0ms
(*.f64 t (*.f64 z x))
4.0ms
(*.f64 27 (*.f64 k j))

rewrite24.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube_binary64
37×add-exp-log_binary64
37×pow1_binary64
22×cbrt-unprod_binary64
22×prod-exp_binary64
Counts
4 → 89
Calls

4 calls:

6.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
5.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
3.0ms
(*.f64 t (*.f64 z x))
3.0ms
(*.f64 27 (*.f64 k j))

simplify67.0ms (0.6%)

Algorithm
egg-herbie
Rules
620×unswap-sqr_binary64
594×*-commutative_binary64
389×associate-/l/_binary64
385×sqr-pow_binary64
333×associate-/r/_binary64
Counts
89 → 95
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01311275
1288990
21009990
31695990
42239990
53346990
65183990

prune196.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New92395
Fresh066
Picked101
Done011
Total9310103
Error
0.0b
Counts
103 → 10
Alt Table
StatusErrorProgram
6.1b
(fma.f64 c b (fma.f64 t (fma.f64 x (*.f64 18 (*.f64 y z)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
4.4b
(fma.f64 c b (-.f64 (*.f64 18 (*.f64 (*.f64 y t) (*.f64 z x))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j))))))
17.1b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.3b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
11.3b
(fma.f64 c b (-.f64 (*.f64 18 (expm1.f64 (log1p.f64 (*.f64 y (*.f64 t (*.f64 z x)))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j))))))
34.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
4.4b
(fma.f64 c b (-.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (*.f64 27 k) j)))))
5.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c)))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
8.1b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
18.6b
(fma.f64 c b (fma.f64 k (*.f64 j -27) (*.f64 (*.f64 t a) -4)))
Compiler

Compiled 4257 to 2008 computations (52.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
0.2b
(*.f64 (*.f64 27 k) j)
2.8b
(*.f64 t (*.f64 z x))
7.5b
(*.f64 y (*.f64 t (*.f64 z x)))

series7.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

7.0ms
(*.f64 (*.f64 27 k) j)

rewrite4.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
associate-*r*_binary64
cbrt-unprod_binary64
Counts
1 → 20
Calls

1 calls:

4.0ms
(*.f64 (*.f64 27 k) j)

simplify69.0ms (0.6%)

Algorithm
egg-herbie
Rules
537×associate-*l*_binary64
367×associate-*r*_binary64
353×*-commutative_binary64
340×cube-div_binary64
340×log-div_binary64
Counts
44 → 27
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
044380
197344
2352344
3971344
41135344
51335344
61591344
72659344
84026344
94880344

prune170.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1002102
Fresh178
Picked101
Done011
Total10210112
Error
0.0b
Counts
112 → 10
Alt Table
StatusErrorProgram
6.1b
(fma.f64 c b (fma.f64 t (fma.f64 x (*.f64 18 (*.f64 y z)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
4.4b
(fma.f64 c b (-.f64 (*.f64 18 (*.f64 (*.f64 y t) (*.f64 z x))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j))))))
4.3b
(fma.f64 c b (fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 (*.f64 k j) -27 (*.f64 (*.f64 x i) -4))))
11.3b
(fma.f64 c b (-.f64 (*.f64 18 (expm1.f64 (log1p.f64 (*.f64 y (*.f64 t (*.f64 z x)))))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j))))))
3.7b
(fma.f64 c b (-.f64 (*.f64 18 (*.f64 y (*.f64 (*.f64 t z) x))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (*.f64 27 k) j)))))
18.6b
(fma.f64 c b (fma.f64 k (*.f64 j -27) (*.f64 (*.f64 t a) -4)))
34.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) (sqrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
5.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c)))))) (cbrt.f64 (fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
8.1b
(fma.f64 x (fma.f64 18 (*.f64 (*.f64 y z) t) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
47.8b
(fma.f64 c b (-.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 (*.f64 (*.f64 27 k) (sqrt.f64 j)) (sqrt.f64 j))))))
Compiler

Compiled 4124 to 1954 computations (52.6% saved)

regimes3.1s (25.8%)

Accuracy

Total 1.8b remaining (99%)

Threshold costs 0b (0%)

Counts
96 → 3
Compiler

Compiled 55696 to 38996 computations (30% saved)

bsearch41.0ms (0.3%)

Steps
ItersRangePoint
2
7.3843687535750805e-87
4.278005309268114e-81
1.607584982652585e-82
2
-6.77063386401871e+38
-9.783205654041762e+35
-4.921965120671141e+36
Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
051117
168117
267117

end443.0ms (3.7%)

Remove

(sort j k)

(sort b c)

Compiler

Compiled 1360 to 843 computations (38% saved)

Profiling

Loading profile data...