Details

Time bar (total: 48.0s)

sample232.0ms

Algorithm
intervals
Results
120.0ms94×body1280valid
49.0ms57×body640valid
19.0ms25×body320valid
17.0ms69×body80valid
5.0ms11×body160valid

simplify22.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0495550
1495550

prune17.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 2

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
0.4b
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.0b
(- (cos x) (cos y))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
25×*-un-lft-identity
22×associate-*r*
19×times-frac
15×add-cube-cbrt
10×add-log-exp
9×add-exp-log add-cbrt-cube difference-of-squares
6×pow1
5×distribute-lft-out--
4×sqrt-prod
3×associate-*r/ associate-*l*
2×sub-neg flip3-- diff-log prod-exp flip-- cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative flip3-+ div-exp pow-prod-down frac-add sum-log *-commutative flip-+ div-inv diff-cos
Counts
4 → 83
Calls
4 calls:
12.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
11.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
4.0ms
(- 3.0 (sqrt 5.0))
5.0ms
(- (cos x) (cos y))

series53.0ms

Counts
4 → 10
Calls
4 calls:
7.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
35.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
0.0ms
(- 3.0 (sqrt 5.0))
10.0ms
(- (cos x) (cos y))

simplify35.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
050671203

prune367.0ms

Filtered
67 candidates to 93 candidates (-38.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New791493
Fresh101
Picked101
Done000
Total811495

Merged error: 0.2b

Counts
95 → 14

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
0.3b
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
0.4b
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
2.0b
(- (cos x) (cos y))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
43×associate-*r/
36×add-sqr-sqrt
28×frac-times flip3-- flip--
25×*-un-lft-identity
24×distribute-rgt-in distribute-lft-in
23×associate-*r*
19×times-frac
18×add-exp-log add-cbrt-cube
17×add-cube-cbrt
15×pow1
9×sub-neg associate-*l*
8×associate-*l/ prod-exp cbrt-unprod add-log-exp
7×pow-prod-down difference-of-squares
6×sqrt-prod
4×distribute-lft-out--
2×*-commutative unswap-sqr
1×cbrt-undiv +-commutative flip3-+ diff-log div-exp frac-add sum-log flip-+ div-inv diff-cos
Counts
4 → 134
Calls
4 calls:
30.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
12.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
11.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
5.0ms
(- (cos x) (cos y))

series89.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
7.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
30.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
10.0ms
(- (cos x) (cos y))

simplify74.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050043409

prune577.0ms

Filtered
99 candidates to 146 candidates (-47.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1424146
Fresh5813
Picked101
Done000
Total14812160

Merged error: 0.1b

Counts
160 → 12

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.4b
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
2.2b
(+ (* (cos x) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))) (* (neg (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
262×associate-*r/
98×flip3-- flip--
65×frac-add
64×frac-times
52×distribute-rgt-in distribute-lft-in
32×associate-*l/
28×add-sqr-sqrt
20×sub-neg
16×associate-+l+ associate-+r+
14×*-un-lft-identity
12×associate-*r* associate-*l*
10×add-cube-cbrt
8×pow1 add-exp-log sqrt-prod add-cbrt-cube add-log-exp
4×difference-of-squares unswap-sqr
2×+-commutative distribute-lft-neg-out flip3-+ times-frac pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ distribute-lft-out--
1×distribute-rgt-out unsub-neg
Counts
4 → 184
Calls
4 calls:
12.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
38.0ms
(+ (* (cos x) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))) (* (neg (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))))

series197.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
15.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
27.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
141.0ms
(+ (* (cos x) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))) (* (neg (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))))

simplify123.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
0498911546
1498911546

prune1.8s

Filtered
151 candidates to 196 candidates (-29.8%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1942196
Fresh01111
Picked011
Done000
Total19414208

Merged error: 0.1b

Counts
208 → 14

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (sin x) (/ (sin y) 16.0)))
0.6b
(cbrt (- (sin x) (/ (sin y) 16.0)))
0.6b
(cbrt (- (sin x) (/ (sin y) 16.0)))
6.1b
(+ (* (cos x) (* (- (sin y) (/ (sin x) 16.0)) (* (* (sqrt 2.0) (* (cbrt (- (sin x) (/ (sin y) 16.0))) (cbrt (- (sin x) (/ (sin y) 16.0))))) (cbrt (- (sin x) (/ (sin y) 16.0)))))) (* (neg (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
2896×associate-*r/
1408×frac-times
1347×flip3-- flip--
1302×cbrt-div
640×frac-add
512×associate-*l/
24×distribute-rgt-in distribute-lft-in
22×add-sqr-sqrt
18×cbrt-prod
16×associate-+r+
13×*-un-lft-identity
8×sub-neg
7×add-cube-cbrt
6×add-log-exp difference-of-squares
4×pow1 add-exp-log add-cbrt-cube
3×times-frac pow1/3 distribute-lft-out--
2×distribute-lft-neg-out
1×+-commutative flip3-+ unsub-neg sum-log flip-+
Counts
4 → 717
Calls
4 calls:
14.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
7.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
7.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
83.0ms
(+ (* (cos x) (* (- (sin y) (/ (sin x) 16.0)) (* (* (sqrt 2.0) (* (cbrt (- (sin x) (/ (sin y) 16.0))) (cbrt (- (sin x) (/ (sin y) 16.0))))) (cbrt (- (sin x) (/ (sin y) 16.0)))))) (* (neg (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))))

series230.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
27.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
27.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
147.0ms
(+ (* (cos x) (* (- (sin y) (/ (sin x) 16.0)) (* (* (sqrt 2.0) (* (cbrt (- (sin x) (/ (sin y) 16.0))) (cbrt (- (sin x) (/ (sin y) 16.0))))) (cbrt (- (sin x) (/ (sin y) 16.0)))))) (* (neg (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))))

simplify615.0ms

Algorithm
egg-herbie
Counts
729 → 729
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
05546143556

prune36.1s

Filtered
713 candidates to 729 candidates (-2.2%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New7290729
Fresh01212
Picked011
Done011
Total72914743

Merged error: 0.1b

Counts
743 → 14

regimes271.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify21.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
071475
171475

end0.0ms

sample6.6s

Algorithm
intervals
Results
3.5s2745×body1280valid
1.7s1790×body640valid
451.0ms772×body320valid
435.0ms2361×body80valid
126.0ms332×body160valid

Profiling

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