Details

Time bar (total: 39.8s)

sample498.0ms

Algorithm
intervals
Results
314.0ms97×body1280valid
89.0ms57×body640valid
24.0ms24×body320valid
19.0ms65×body80valid
10.0ms13×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03250
17450
218150
365350
4266450
done500050

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
30×*-un-lft-identity
28×associate-*l*
20×times-frac
18×add-cube-cbrt
11×add-exp-log add-cbrt-cube difference-of-squares
9×associate-*r*
8×pow1 sqrt-prod add-log-exp
6×distribute-lft-out--
4×sub-neg unswap-sqr
3×flip3-- prod-exp flip-- cbrt-unprod
2×distribute-rgt-in distribute-lft-in diff-log associate-*r/ pow-prod-down *-commutative
1×cbrt-undiv div-exp associate-*l/ div-inv diff-cos
Counts
4 → 102
Calls
4 calls:
85.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
84.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series337.0ms

Counts
4 → 10
Calls
4 calls:
131.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
121.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
85.0ms
(- (cos x) (cos y))

simplify1.3s

Counts
112 → 112
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02471369
15841330
216891232
done50001221

prune826.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize78.0ms

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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.3b
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.7b
(- (cos x) (cos y))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
30×*-un-lft-identity
28×associate-*l*
23×times-frac
20×add-cube-cbrt
16×add-exp-log add-cbrt-cube
9×associate-*r* difference-of-squares
8×pow1
7×sqrt-prod
6×associate-*r/ add-log-exp
5×distribute-lft-out--
4×prod-exp associate-/r/ cbrt-unprod unswap-sqr
3×cbrt-undiv sub-neg flip3-+ div-exp associate-*l/ flip-+ associate-/l*
2×distribute-rgt-in flip3-- distribute-lft-in pow-prod-down frac-add *-commutative flip-- div-inv associate-/l/
1×frac-2neg diff-log clear-num associate-/r* diff-cos
Counts
4 → 114
Calls
4 calls:
137.0ms
(/ (+ 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)))))
63.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
82.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms
(- (cos x) (cos y))

series3.4s

Counts
4 → 12
Calls
4 calls:
2.6s
(/ (+ 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)))))
530.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
163.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
97.0ms
(- (cos x) (cos y))

simplify2.3s

Counts
126 → 126
Iterations

Useful iterations: 2 (769.0ms)

IterNodesCost
03723617
110273530
237323107
done50013107

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 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)))
1.0b
(/ 1 (sqrt 2.0))
1.7b
(- (cos x) (cos y))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
28×*-un-lft-identity
24×add-cube-cbrt
22×times-frac
16×sqrt-prod
15×add-exp-log
13×add-cbrt-cube
8×pow1
7×associate-/r*
6×associate-*r/ associate-*r* associate-*l* associate-/l* add-log-exp
4×div-exp associate-/r/
3×cbrt-undiv sub-neg pow-flip flip3-+ flip-+ difference-of-squares
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in associate-*l/ frac-add prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- unswap-sqr
1×rec-exp sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down *-commutative diff-cos inv-pow
Counts
4 → 118
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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
92.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(/ 1 (sqrt 2.0))
8.0ms
(- (cos x) (cos y))

series4.2s

Counts
4 → 10
Calls
4 calls:
4.0s
(/ (+ 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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
134.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(/ 1 (sqrt 2.0))
101.0ms
(- (cos x) (cos y))

simplify2.3s

Counts
128 → 128
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03583755
19523549
234983040
done50002976

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

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
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(/ 1 (sqrt 2.0))
1.7b
(- (cos x) (cos y))

rewrite634.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
29×flip3-- *-un-lft-identity flip--
28×frac-times associate-*r/
23×add-cube-cbrt
19×add-exp-log times-frac
17×pow1 add-cbrt-cube
16×sqrt-prod
14×associate-*l/
12×associate-*r*
7×associate-*l* pow-prod-down prod-exp cbrt-unprod
6×associate-/r* add-log-exp
5×sub-neg
4×distribute-rgt-in distribute-lft-in difference-of-squares
3×pow-flip associate-/l* distribute-lft-out--
2×div-exp *-commutative diff-cos unswap-sqr
1×cbrt-undiv rec-exp frac-2neg sqrt-pow1 pow1/2 diff-log 1-exp clear-num div-inv inv-pow
Counts
4 → 145
Calls
4 calls:
472.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
119.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
15.0ms
(/ 1 (sqrt 2.0))
16.0ms
(- (cos x) (cos y))

series528.0ms

Counts
4 → 10
Calls
4 calls:
320.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
129.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(/ 1 (sqrt 2.0))
78.0ms
(- (cos x) (cos y))

simplify2.5s

Counts
155 → 155
Iterations

Useful iterations: 2 (819.0ms)

IterNodesCost
02913534
18393305
239433079
done50013079

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes323.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03862
15062
done5062

end0.0ms

sample14.2s

Algorithm
intervals
Results
7.7s2727×body1280valid
3.3s1787×body640valid
1.6s853×body320valid
773.0ms2248×body80valid
374.0ms385×body160valid