Details

Time bar (total: 20.8s)

analyze2.8s (13.5%)

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 (18.4%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results
1.9s8300×body128invalid
1.8s8256×body128valid
Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify342.0ms (1.6%)

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

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
4.6b
(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))))
6.2b
(-.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))
Compiler

Compiled 218 to 148 computations (32.1% saved)

localize17.0ms (0.1%)

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))
2.8b
(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))))
4.7b
(*.f64 y (*.f64 z t))

series131.0ms (0.6%)

Counts
4 → 252
Calls

4 calls:

98.0ms
(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))))
13.0ms
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
11.0ms
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
8.0ms
(*.f64 y (*.f64 z t))

rewrite76.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
242×add-sqr-sqrt_binary64
222×add-log-exp_binary64
222×log1p-expm1-u_binary64
222×expm1-log1p-u_binary64
221×add-cube-cbrt_binary64
Counts
4 → 75
Calls

4 calls:

74.0ms
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
74.0ms
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
74.0ms
(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))))
74.0ms
(*.f64 y (*.f64 z t))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02467
147967
2489367
3503967
000
100

simplify712.0ms (3.4%)

Algorithm
egg-herbie
Rules
6691×fma-neg_binary64
864×unsub-neg_binary64
611×sub-neg_binary64
523×distribute-rgt-neg-in_binary64
518×cancel-sign-sub-inv_binary64
Counts
327 → 114
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0635548
11915103
25494906
314534904
429574904
535274904
638504904
737394904
837564904
937584904
1038034904
1139234904
1239934904
1339994904
1439994904
1540934904
1646854904
1741574904
1841574904
1941574904
2041574904
2198324904

prune151.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1077114
Fresh011
Picked101
Done000
Total1088116
Error
0.0b
Counts
116 → 8
Alt Table
StatusErrorProgram
4.9b
(fma.f64 x (pow.f64 (cbrt.f64 (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))) 3) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
8.4b
(fma.f64 k (*.f64 j -27) (fma.f64 -4 (fma.f64 t a (*.f64 x i)) (*.f64 c b)))
19.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.4b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 y (*.f64 18 (*.f64 t (*.f64 z x))) (fma.f64 c b (*.f64 (*.f64 k j) -27))))
5.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (pow.f64 (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) 2) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
46.3b
(cbrt.f64 (pow.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)))) 3))
14.2b
(fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
6.2b
(-.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))
Compiler

Compiled 3646 to 1798 computations (50.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 18 (*.f64 t (*.f64 z x)))
0.3b
(*.f64 (*.f64 k j) -27)
2.4b
(fma.f64 y (*.f64 18 (*.f64 t (*.f64 z x))) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
6.1b
(*.f64 t (*.f64 z x))

series74.0ms (0.4%)

Counts
4 → 120
Calls

4 calls:

51.0ms
(fma.f64 y (*.f64 18 (*.f64 t (*.f64 z x))) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
11.0ms
(*.f64 18 (*.f64 t (*.f64 z x)))
8.0ms
(*.f64 t (*.f64 z x))
4.0ms
(*.f64 (*.f64 k j) -27)

rewrite82.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
329×log1p-udef_binary64
281×prod-diff_binary64
183×add-sqr-sqrt_binary64
173×associate-*r*_binary64
168×add-log-exp_binary64
Counts
4 → 65
Calls

4 calls:

80.0ms
(*.f64 18 (*.f64 t (*.f64 z x)))
80.0ms
(*.f64 (*.f64 k j) -27)
80.0ms
(fma.f64 y (*.f64 18 (*.f64 t (*.f64 z x))) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
80.0ms
(*.f64 t (*.f64 z x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01848
136248
2417948
3523248
000
100

simplify359.0ms (1.7%)

Algorithm
egg-herbie
Rules
1453×fma-def_binary64
895×fma-neg_binary64
532×distribute-rgt-neg-in_binary64
338×unsub-neg_binary64
314×cancel-sign-sub-inv_binary64
Counts
185 → 77
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0242318
1552162
21252162
33072162
45602162
510212162
615192162
723852162
823572162
924112162
1024052162
1124052162
1234342162
1333672162
1434432162
1534532162
1634532162
1734532162
1834532162
1934532162
2034532162
2132922162

prune223.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New76177
Fresh167
Picked011
Done000
Total77885
Error
0.0b
Counts
85 → 8
Alt Table
StatusErrorProgram
19.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.4b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 y (*.f64 18 (*.f64 t (*.f64 z x))) (fma.f64 c b (*.f64 (*.f64 k j) -27))))
4.9b
(fma.f64 x (pow.f64 (cbrt.f64 (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))) 3) (fma.f64 a (*.f64 t -4) (fma.f64 -27 (*.f64 j k) (*.f64 b c))))
5.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (pow.f64 (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) 2) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
46.3b
(cbrt.f64 (pow.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)))) 3))
14.2b
(fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.4b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))))))
6.2b
(-.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))
Compiler

Compiled 2739 to 1227 computations (55.2% saved)

localize47.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))))
0.2b
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
4.3b
(*.f64 y (*.f64 t (*.f64 z x)))
6.1b
(*.f64 t (*.f64 z x))

series226.0ms (1.1%)

Counts
3 → 96
Calls

3 calls:

120.0ms
(fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))))
78.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
29.0ms
(*.f64 y (*.f64 t (*.f64 z x)))

rewrite102.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
336×prod-diff_binary64
329×log1p-udef_binary64
183×add-sqr-sqrt_binary64
182×associate-*r*_binary64
168×add-log-exp_binary64
Counts
3 → 52
Calls

3 calls:

98.0ms
(fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))))
97.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
97.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01847
136247
2419947
3538947
000
100

simplify562.0ms (2.7%)

Algorithm
egg-herbie
Rules
1453×fma-def_binary64
895×fma-neg_binary64
532×distribute-rgt-neg-in_binary64
338×unsub-neg_binary64
314×cancel-sign-sub-inv_binary64
Counts
148 → 64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0242150
1551994
21251994
33071994
45601994
510211994
615191994
723851994
823571994
924111994
1024051994
1124051994
1234341994
1333671994
1434431994
1534531994
1634531994
1734531994
1834531994
1934531994
2034531994
2132921994

prune247.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New77279
Fresh246
Picked101
Done011
Total80787
Error
0.0b
Counts
87 → 7
Alt Table
StatusErrorProgram
37.2b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (cbrt.f64 (pow.f64 (fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 (*.f64 y (*.f64 t (*.f64 z x))) 18))) 3)))
5.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (pow.f64 (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) 2) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
19.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.4b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 y (*.f64 18 (*.f64 t (*.f64 z x))) (fma.f64 c b (*.f64 (*.f64 k j) -27))))
14.2b
(fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.4b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3)))))
6.2b
(-.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))
Compiler

Compiled 2721 to 1215 computations (55.3% saved)

localize49.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3)
4.3b
(*.f64 y (*.f64 t (*.f64 z x)))
6.1b
(*.f64 t (*.f64 z x))
18.8b
(cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x))))

series3.7s (17.6%)

Counts
2 → 96
Calls

2 calls:

2.1s
(cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x))))
1.6s
(pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3)

rewrite98.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
907×log1p-expm1-u_binary64
907×expm1-log1p-u_binary64
111×associate-*r*_binary64
101×add-sqr-sqrt_binary64
94×add-cbrt-cube_binary64
Counts
2 → 72
Calls

2 calls:

95.0ms
(pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3)
95.0ms
(cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
120922
2240022
3551022
000
100

simplify169.0ms (0.8%)

Algorithm
egg-herbie
Rules
743×fma-def_binary64
686×fma-neg_binary64
367×distribute-rgt-in_binary64
303×exp-sum_binary64
294×exp-prod_binary64
Counts
168 → 101
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0972176
12772176
25461952
317301264
440161264
549911264
650571264

prune443.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1283131
Fresh145
Picked101
Done011
Total1308138
Error
0.0b
Counts
138 → 8
Alt Table
StatusErrorProgram
37.2b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (cbrt.f64 (pow.f64 (fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 (*.f64 y (*.f64 t (*.f64 z x))) 18))) 3)))
5.2b
(fma.f64 x (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)) (fma.f64 a (*.f64 t -4) (*.f64 (pow.f64 (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))) 2) (cbrt.f64 (fma.f64 -27 (*.f64 j k) (*.f64 b c))))))
19.6b
(fma.f64 x (fma.f64 y (*.f64 (*.f64 t z) 18) (*.f64 i -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.4b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 y (*.f64 18 (*.f64 t (*.f64 z x))) (fma.f64 c b (*.f64 (*.f64 k j) -27))))
4.5b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (*.f64 (*.f64 t z) (*.f64 x y))))))
14.2b
(fma.f64 t (fma.f64 y (*.f64 18 (*.f64 z x)) (*.f64 a -4)) (fma.f64 c b (*.f64 (*.f64 k j) -27)))
4.6b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (*.f64 (*.f64 (*.f64 y t) x) z)))))
4.6b
(fma.f64 -4 (fma.f64 t a (*.f64 x i)) (fma.f64 k (*.f64 j -27) (fma.f64 c b (*.f64 18 (*.f64 (*.f64 y (*.f64 t z)) x)))))
Compiler

Compiled 4502 to 1977 computations (56.1% saved)

regimes5.7s (27.2%)

Accuracy

Total 2.4b remaining (98.8%)

Threshold costs 0b (0%)

Counts
111 → 3
Compiler

Compiled 61824 to 43097 computations (30.3% saved)

bsearch106.0ms (0.5%)

Steps
ItersRangePoint
5
1.6672518404253175e-130
3.671217662317056e-130
3.5401247757472833e-130
6
-7.446951786899849e-19
-6.185513563956728e-21
-2.946096318727387e-20
Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify10.0ms (0%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
051122
173120
289120
3105120
4115120
5121120
6123120
7122120

end596.0ms (2.9%)

Remove

(sort b c)

Compiler

Compiled 1426 to 863 computations (39.5% saved)

Profiling

Loading profile data...