Details

Time bar (total: 35.6s)

sample411.0ms

Algorithm
intervals
Results
197.0ms83×body1280valid
80.0ms55×body640valid
67.0ms84×body80valid
28.0ms29×body320valid
4.0ms5×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03250
17450
218150
365650
4315750
done500050

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize60.0ms

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 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
3.4b
(- (cos x) (cos y))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
15×*-un-lft-identity
11×add-exp-log add-cbrt-cube
9×add-cube-cbrt
8×add-log-exp
6×pow1 associate-*r/ associate-*r* associate-*l*
5×sqrt-prod difference-of-squares
4×sub-neg times-frac associate-/r/
3×flip3-- flip3-+ flip-- flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv distribute-rgt-in distribute-lft-in diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative div-inv diff-cos
Counts
4 → 88
Calls
4 calls:
105.0ms
(/ (+ 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 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
87.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series2.0s

Counts
4 → 10
Calls
4 calls:
1.8s
(/ (+ 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 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
163.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
87.0ms
(- (cos x) (cos y))

simplify2.3s

Counts
98 → 98
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03112970
18752901
238912547
done50002545

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

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)))
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 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.4b
(- (cos x) (cos y))

rewrite398.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
16×add-exp-log *-un-lft-identity add-cbrt-cube
14×associate-*r/
12×associate-*r*
11×pow1
10×add-cube-cbrt
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg times-frac prod-exp cbrt-unprod difference-of-squares
4×distribute-rgt-in frac-times distribute-lft-in pow-prod-down associate-*l/ sqrt-prod associate-/r/
3×flip3-+ flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp frac-add *-commutative associate-/l/ unswap-sqr
1×frac-2neg diff-log clear-num associate-/r* div-inv diff-cos
Counts
4 → 106
Calls
4 calls:
154.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
122.0ms
(/ (+ 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 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
109.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- (cos x) (cos y))

series3.0s

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
2.5s
(/ (+ 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 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
168.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
80.0ms
(- (cos x) (cos y))

simplify745.0ms

Counts
118 → 118
Iterations

Useful iterations: done (736.0ms)

IterNodesCost
03664085
111103990
done50013495

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (- (sin y) (/ (sin x) 16.0)) 3)
0.5b
(pow (- (sin x) (/ (sin y) 16.0)) 3)
3.4b
(- (cos x) (cos y))
7.6b
(cbrt (* (sqrt 2.0) (* 2.0 (* (pow (- (sin x) (/ (sin y) 16.0)) 3) (pow (- (sin y) (/ (sin x) 16.0)) 3)))))

rewrite757.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
20×*-un-lft-identity
18×associate-*r/
16×cube-div
12×unpow-prod-down cube-prod
10×add-cube-cbrt
9×flip3-- flip-- difference-of-squares
8×cbrt-div
6×pow1 add-exp-log pow-unpow add-cbrt-cube add-log-exp
5×distribute-lft-out--
4×frac-times times-frac
2×cube-mult pow-to-exp pow-pow unpow3 associate-*l/ pow-exp rem-cube-cbrt sqr-pow
1×cbrt-prod sub-neg pow1/3 diff-log diff-cos
Counts
4 → 94
Calls
4 calls:
24.0ms
(pow (- (sin y) (/ (sin x) 16.0)) 3)
47.0ms
(pow (- (sin x) (/ (sin y) 16.0)) 3)
14.0ms
(- (cos x) (cos y))
668.0ms
(cbrt (* (sqrt 2.0) (* 2.0 (* (pow (- (sin x) (/ (sin y) 16.0)) 3) (pow (- (sin y) (/ (sin x) 16.0)) 3)))))

series736.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(pow (- (sin y) (/ (sin x) 16.0)) 3)
113.0ms
(pow (- (sin x) (/ (sin y) 16.0)) 3)
106.0ms
(- (cos x) (cos y))
429.0ms
(cbrt (* (sqrt 2.0) (* 2.0 (* (pow (- (sin x) (/ (sin y) 16.0)) 3) (pow (- (sin y) (/ (sin x) 16.0)) 3)))))

simplify2.0s

Counts
106 → 106
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02562126
18021965
234901823
done50011820

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.6b
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.6b
(cbrt (- (sin y) (/ (sin x) 16.0)))
3.4b
(- (cos x) (cos y))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×cbrt-prod
15×*-un-lft-identity
7×add-cube-cbrt difference-of-squares
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-- add-cbrt-cube flip-- distribute-lft-out--
3×times-frac pow1/3
1×sub-neg diff-log diff-cos
Counts
4 → 63
Calls
4 calls:
12.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
13.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
18.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
14.0ms
(- (cos x) (cos y))

series797.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
224.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
239.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
90.0ms
(- (cos x) (cos y))

simplify1.1s

Counts
75 → 75
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01201119
12481088
25821030
317391010
done5001974

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes663.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04063
15163
done5163

end0.0ms

sample13.2s

Algorithm
intervals
Results
7.6s2797×body1280valid
3.2s1848×body640valid
891.0ms721×body320valid
830.0ms2288×body80valid
260.0ms346×body160valid