Details

Time bar (total: 2.8s)

sample20.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
3.0ms256×pre80true

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (14.0ms)

IterNodesCost
0257
1617
21717
33687
48496
526306
650026

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 62.0b

Counts
2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

62.0b
(- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
999×add-sqr-sqrt
720×prod-diff
504×associate-*r*
477×associate-*l*
415×*-un-lft-identity
331×add-cube-cbrt
300×unswap-sqr
150×unpow-prod-down
118×*-commutative
114×difference-of-squares
112×swap-sqr
94×associate--r+
78×sqr-pow
47×distribute-rgt-in distribute-lft-in
42×distribute-lft-out--
18×fma-neg
3×sub-neg add-log-exp
1×pow1 add-exp-log expm1-log1p-u flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u
Counts
1 → 786
Calls
1 calls:
65.0ms
(- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0)))

series176.0ms

Counts
1 → 3
Calls
1 calls:
176.0ms
(- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0)))

simplify201.0ms

Algorithm
egg-herbie
Counts
789 → 789
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0217020376
1500213585

prune374.0ms

Filtered
789 candidates to 130 candidates (16.5%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New7881789
Fresh000
Picked101
Done000
Total7891790

Merged error: 52.0b

Counts
790 → 1

localize12.0ms

Local error

Found 1 expressions with local error:

23.0b
(fma (pow x 4.0) 9.0 (- (pow y 4)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (pow x 4.0) 9.0 (- (pow y 4)))

series323.0ms

Counts
1 → 3
Calls
1 calls:
323.0ms
(fma (pow x 4.0) 9.0 (- (pow y 4)))

simplify81.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (16.0ms)

IterNodesCost
05677
113468
247068
3200363
4500263

prune30.0ms

Filtered
13 candidates to 12 candidates (92.3%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New12113
Fresh000
Picked101
Done000
Total13114

Merged error: 52.0b

Counts
14 → 1

localize21.0ms

Local error

Found 2 expressions with local error:

1.0b
(cbrt (pow (fma (pow x 4.0) 9.0 (- (pow y 4))) 3))
23.0b
(fma (pow x 4.0) 9.0 (- (pow y 4)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod
5×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt
3×unpow-prod-down
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube rem-cbrt-cube log1p-expm1-u add-log-exp
1×pow-unpow pow1/3 unpow3 fma-udef sqr-pow
Counts
2 → 30
Calls
2 calls:
2.0ms
(cbrt (pow (fma (pow x 4.0) 9.0 (- (pow y 4))) 3))
1.0ms
(fma (pow x 4.0) 9.0 (- (pow y 4)))

series655.0ms

Counts
2 → 6
Calls
2 calls:
327.0ms
(cbrt (pow (fma (pow x 4.0) 9.0 (- (pow y 4))) 3))
328.0ms
(fma (pow x 4.0) 9.0 (- (pow y 4)))

simplify46.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0107224
1297221
21088221
35001211

prune81.0ms

Filtered
36 candidates to 28 candidates (77.8%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New36036
Fresh000
Picked011
Done000
Total36137

Merged error: 52.0b

Counts
37 → 1

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12410
22810
32810

end0.0ms

sample491.0ms

Algorithm
intervals
Results
262.0ms8000×body80valid
96.0ms8000×pre80true