Details

Time bar (total: 13.5s)

analyze2.8s (21.1%)

Algorithm
1×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 (28.1%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results
1.9s8614×body128invalid
1.8s8256×body128valid
Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify343.0ms (2.5%)

Algorithm
1×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
0.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶6.4b
(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))))
6.8b
(-.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))
✓3.8b
(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))))
✓7.2b
(*.f64 y (*.f64 z t))

series150.0ms (1.1%)

Counts
4 → 252
Calls

4 calls:

108.0ms
(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))))
19.0ms
(fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4))
12.0ms
(fma.f64 -27 (*.f64 j k) (*.f64 b c))
11.0ms
(*.f64 y (*.f64 z t))

rewrite81.0ms (0.6%)

Algorithm
2×batch-egg-rewrite
Rules
75×egg-rr
Counts
4 → 75
Calls

2 calls:

77.0ms
((*.f64 y (*.f64 z t)) (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)))) (fma.f64 -27 (*.f64 j k) (*.f64 b c)) (fma.f64 18 (*.f64 y (*.f64 z t)) (*.f64 i -4)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02467
147967
2489367
3503967
000
100

simplify688.0ms (5.1%)

Algorithm
1×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

prune183.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1104114
Fresh011
Picked011
Done000
Total1106116
Error
0.0b
Counts
116 → 6
Alt Table
StatusErrorProgram
10.4b
(fma.f64 k (*.f64 j -27) (fma.f64 -4 (fma.f64 t a (*.f64 x i)) (*.f64 c b)))
6.8b
(-.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))
5.1b
(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
(-.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)))))
✓6.4b
(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))))
44.9b
(*.f64 (-.f64 (*.f64 18 (*.f64 y (*.f64 z x))) (*.f64 4 a)) t)
Compiler

Compiled 3441 to 1662 computations (51.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
✓0.3b
(*.f64 27 (*.f64 k j))
✓4.5b
(*.f64 t (*.f64 z x))
✓5.2b
(*.f64 y (*.f64 t (*.f64 z x)))

series58.0ms (0.4%)

Counts
4 → 0
Calls

4 calls:

22.0ms
(*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))
21.0ms
(*.f64 y (*.f64 t (*.f64 z x)))
11.0ms
(*.f64 t (*.f64 z x))
5.0ms
(*.f64 27 (*.f64 k j))

rewrite74.0ms (0.6%)

Algorithm
2×batch-egg-rewrite
Rules
68×egg-rr
Counts
4 → 68
Calls

2 calls:

72.0ms
((*.f64 y (*.f64 t (*.f64 z x))) (*.f64 t (*.f64 z x)) (*.f64 27 (*.f64 k j)) (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01537
130437
2353737
3597637
000
100

simplify45.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
100

prune112.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New66268
Fresh044
Picked101
Done011
Total67774
Error
0.0b
Counts
74 → 7
Alt Table
StatusErrorProgram
10.4b
(fma.f64 k (*.f64 j -27) (fma.f64 -4 (fma.f64 t a (*.f64 x i)) (*.f64 c b)))
6.8b
(-.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))
▶5.0b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
5.1b
(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))))
✓6.4b
(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))))
28.9b
(-.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)) (pow.f64 (sqrt.f64 (*.f64 27 (*.f64 k j))) 2))))
44.9b
(*.f64 (-.f64 (*.f64 18 (*.f64 y (*.f64 z x))) (*.f64 4 a)) t)
Compiler

Compiled 2905 to 1415 computations (51.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.6b
(pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3)
4.5b
(*.f64 t (*.f64 z x))
5.2b
(*.f64 y (*.f64 t (*.f64 z x)))
✓17.6b
(cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x))))

series2.4s (18.1%)

Counts
2 → 96
Calls

2 calls:

1.3s
(pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3)
1.2s
(cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x))))

rewrite57.0ms (0.4%)

Algorithm
2×batch-egg-rewrite
Rules
72×egg-rr
Counts
2 → 72
Calls

2 calls:

55.0ms
((cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) (pow.f64 (cbrt.f64 (*.f64 y (*.f64 t (*.f64 z x)))) 3))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
120922
2240022
3551022
000
100

simplify119.0ms (0.9%)

Algorithm
1×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

prune218.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1352137
Fresh145
Picked101
Done011
Total1377144
Error
0.0b
Counts
144 → 7
Alt Table
StatusErrorProgram
10.4b
(fma.f64 k (*.f64 j -27) (fma.f64 -4 (fma.f64 t a (*.f64 x i)) (*.f64 c b)))
6.8b
(-.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))
6.6b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 t (*.f64 (*.f64 z x) y)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
5.1b
(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))))
✓6.4b
(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))))
28.9b
(-.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)) (pow.f64 (sqrt.f64 (*.f64 27 (*.f64 k j))) 2))))
▶4.1b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 (*.f64 (*.f64 y t) x) z))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
Compiler

Compiled 5771 to 2769 computations (52% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 18 (*.f64 (*.f64 (*.f64 y t) x) z))
0.3b
(*.f64 27 (*.f64 k j))
✓5.4b
(*.f64 (*.f64 (*.f64 y t) x) z)
✓5.6b
(*.f64 (*.f64 y t) x)

series51.0ms (0.4%)

Counts
3 → 132
Calls

3 calls:

22.0ms
(*.f64 18 (*.f64 (*.f64 (*.f64 y t) x) z))
17.0ms
(*.f64 (*.f64 (*.f64 y t) x) z)
12.0ms
(*.f64 (*.f64 y t) x)

rewrite55.0ms (0.4%)

Algorithm
2×batch-egg-rewrite
Rules
59×egg-rr
Counts
3 → 59
Calls

2 calls:

54.0ms
((*.f64 (*.f64 y t) x) (*.f64 (*.f64 (*.f64 y t) x) z) (*.f64 18 (*.f64 (*.f64 (*.f64 y t) x) z)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01030
120330
2240330
3525230
000
100

simplify44.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
141×associate-*l*_binary64
87×associate-*r*_binary64
54×*-commutative_binary64
Counts
191 → 64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0121356
1251356
2621356
31441356
41881356
51861356
61861356

prune137.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New80080
Fresh055
Picked011
Done011
Total80787
Error
0.0b
Counts
87 → 7
Alt Table
StatusErrorProgram
10.4b
(fma.f64 k (*.f64 j -27) (fma.f64 -4 (fma.f64 t a (*.f64 x i)) (*.f64 c b)))
6.8b
(-.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))
6.6b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 t (*.f64 (*.f64 z x) y)))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
5.1b
(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))))
✓6.4b
(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))))
28.9b
(-.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)) (pow.f64 (sqrt.f64 (*.f64 27 (*.f64 k j))) 2))))
✓4.1b
(-.f64 (+.f64 (*.f64 c b) (*.f64 18 (*.f64 (*.f64 (*.f64 y t) x) z))) (+.f64 (*.f64 4 (*.f64 i x)) (+.f64 (*.f64 4 (*.f64 a t)) (*.f64 27 (*.f64 k j)))))
Compiler

Compiled 3091 to 1467 computations (52.5% saved)

regimes1.4s (10.3%)

Accuracy

Total 1.7b remaining (98.1%)

Threshold costs 0b (0%)

Counts
53 → 3
Compiler

Compiled 29125 to 21329 computations (26.8% saved)

bsearch111.0ms (0.8%)

Steps
ItersRangePoint
7
6.010692223912497e-118
9.664301330820853e-117
9.16768781234981e-117
6
-4.312001500700976e+41
-1.069052298946026e+41
-1.0827335004684045e+41
Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify9.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
29×*-commutative_binary64
20×+-commutative_binary64
16×sub-neg_binary64
14×neg-sub0_binary64
14×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042150
164150
274150
393150
4124150
5152150
6171150
7183150
8187150
9185150

end396.0ms (2.9%)

Remove

(sort j k)

(sort b c)

Compiler

Compiled 1373 to 804 computations (41.4% saved)

Profiling

Loading profile data...