Details

Time bar (total: 40.1s)

analyze740.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
50%50%0.1%4
74.9%25%0.1%5
74.9%25%0.1%6
74.9%25%0.1%7
74.9%25%0.1%8
74.9%25%0.1%9
74.9%25%0.1%10
74.9%25%0.1%11
74.9%25%0.1%12
74.9%25%0.1%13
74.9%25%0.1%14

sample217.0ms

Algorithm
intervals
Results
122.0ms92×body1280valid
53.0ms64×body640valid
14.0ms74×body80valid
11.0ms18×body320valid
3.0ms8×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0158948
1158948

prune15.0ms

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: 0.4b

Counts
2 → 2

localize30.0ms

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)))))
0.5b
(+ (* (cos x) (- (sqrt 5.0) 1.0)) (* (cos y) (- 3.0 (sqrt 5.0))))
1.0b
(- 3.0 (sqrt 5.0))
1.4b
(- (cos x) (cos y))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
48×associate-*r/
33×flip3-- flip--
28×frac-times
14×distribute-rgt-in sub-neg distribute-lft-in
13×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
8×associate-*l/
6×add-cube-cbrt associate-*l* pow-prod-down prod-exp cbrt-unprod
4×frac-add sqrt-prod
3×difference-of-squares
2×associate-+l+ associate-+r+ diff-log distribute-lft-out--
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ diff-cos
Counts
4 → 105
Calls
4 calls:
27.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
10.0ms
(+ (* (cos x) (- (sqrt 5.0) 1.0)) (* (cos y) (- 3.0 (sqrt 5.0))))
4.0ms
(- 3.0 (sqrt 5.0))
5.0ms
(- (cos x) (cos y))

series69.0ms

Counts
4 → 10
Calls
4 calls:
38.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
22.0ms
(+ (* (cos x) (- (sqrt 5.0) 1.0)) (* (cos y) (- 3.0 (sqrt 5.0))))
0.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

simplify45.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
050752769

prune394.0ms

Filtered
89 candidates to 115 candidates (-29.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10510115
Fresh101
Picked101
Done000
Total10710117

Merged error: 0.2b

Counts
117 → 10

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))) (* 3.0 (+ 1.0 (/ (/ (+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0)))) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (+ (sqrt 5.0) 1.0))) 2.0))))
0.3b
(+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0))))
0.3b
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
1.4b
(- (cos x) (cos y))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
202×associate-*r/
92×frac-times
76×flip3-- flip--
64×frac-add
51×flip3-+ flip-+
40×associate-*l/
20×distribute-rgt-in distribute-lft-in
18×add-exp-log add-cbrt-cube
13×pow1 sub-neg
12×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt add-log-exp
7×prod-exp cbrt-unprod
6×associate-*l* pow-prod-down
4×associate-+l+ associate-+r+ times-frac associate-/l*
3×sqrt-prod
2×cbrt-undiv div-exp associate-/r/ associate-/l/ distribute-lft-out
1×+-commutative frac-2neg diff-log associate-*r* clear-num associate-/r* sum-log *-commutative div-inv diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 182
Calls
4 calls:
28.0ms
(/ (+ 2.0 (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))) (* 3.0 (+ 1.0 (/ (/ (+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0)))) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (+ (sqrt 5.0) 1.0))) 2.0))))
16.0ms
(+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0))))
24.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
4.0ms
(- (cos x) (cos y))

series637.0ms

Counts
4 → 12
Calls
4 calls:
551.0ms
(/ (+ 2.0 (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))) (* 3.0 (+ 1.0 (/ (/ (+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0)))) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (+ (sqrt 5.0) 1.0))) 2.0))))
42.0ms
(+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0))))
35.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
9.0ms
(- (cos x) (cos y))

simplify103.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0523713051

prune2.7s

Filtered
165 candidates to 194 candidates (-17.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1868194
Fresh819
Picked101
Done000
Total1959204

Merged error: 0.0b

Counts
204 → 9

localize49.0ms

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)) (cbrt (pow (- (cos x) (cos y)) 3)))))
0.4b
(cbrt (pow (- (cos x) (cos y)) 3))
0.6b
(pow (- (cos x) (cos y)) 3)
1.4b
(- (cos x) (cos y))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
40×associate-*r/
30×flip3-- flip--
28×frac-times
22×cube-div add-sqr-sqrt *-un-lft-identity
20×cbrt-div
18×cbrt-prod
14×pow1 add-exp-log
13×add-cbrt-cube
12×add-cube-cbrt unpow-prod-down cube-prod
8×associate-*l/
6×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
5×diff-cos distribute-lft-out-- difference-of-squares
3×pow-unpow sqrt-prod
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg pow-pow pow1/3 diff-log associate-*r* pow-exp *-commutative rem-cbrt-cube rem-cube-cbrt
Counts
4 → 124
Calls
4 calls:
27.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (cbrt (pow (- (cos x) (cos y)) 3)))))
5.0ms
(cbrt (pow (- (cos x) (cos y)) 3))
5.0ms
(pow (- (cos x) (cos y)) 3)
5.0ms
(- (cos x) (cos y))

series72.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (cbrt (pow (- (cos x) (cos y)) 3)))))
14.0ms
(cbrt (pow (- (cos x) (cos y)) 3))
13.0ms
(pow (- (cos x) (cos y)) 3)
9.0ms
(- (cos x) (cos y))

simplify59.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050362376

prune687.0ms

Filtered
89 candidates to 136 candidates (-52.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1360136
Fresh088
Picked011
Done000
Total1369145

Merged error: 0.0b

Counts
145 → 9

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))) (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))))
1.4b
(- (cos x) (cos y))
1.4b
(- (cos x) (cos y))
1.4b
(- (cos x) (cos y))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
2188×frac-times
2186×associate-*r/
1461×flip3-- flip--
458×associate-*l/
254×pow1
166×pow-prod-down
84×add-exp-log add-cbrt-cube
64×prod-exp cbrt-unprod
32×distribute-rgt-in distribute-lft-in
19×sub-neg
16×pow-sqr pow-prod-up
10×add-sqr-sqrt *-un-lft-identity add-log-exp
4×add-cube-cbrt pow-plus
3×diff-log diff-cos distribute-lft-out-- difference-of-squares
1×pow2 swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 882
Calls
4 calls:
68.0ms
(* (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))) (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))))
4.0ms
(- (cos x) (cos y))
4.0ms
(- (cos x) (cos y))
5.0ms
(- (cos x) (cos y))

series118.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))) (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))))
9.0ms
(- (cos x) (cos y))
9.0ms
(- (cos x) (cos y))
9.0ms
(- (cos x) (cos y))

simplify416.0ms

Algorithm
egg-herbie
Counts
894 → 894
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0633792280

prune25.8s

Filtered
812 candidates to 894 candidates (-10.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New8940894
Fresh077
Picked011
Done011
Total8949903

Merged error: 0.0b

Counts
903 → 9

regimes224.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06284
16284

end0.0ms

analyze741.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
50%50%0.1%4
74.9%25%0.1%5
74.9%25%0.1%6
74.9%25%0.1%7
74.9%25%0.1%8
74.9%25%0.1%9
74.9%25%0.1%10
74.9%25%0.1%11
74.9%25%0.1%12
74.9%25%0.1%13
74.9%25%0.1%14

sample6.4s

Algorithm
intervals
Results
3.6s2763×body1280valid
1.6s1833×body640valid
458.0ms2329×body80valid
446.0ms741×body320valid
137.0ms334×body160valid

Profiling

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