Details

Time bar (total: 41.8s)

sample395.0ms

Algorithm
intervals
Results
178.0ms88×body1280valid
138.0ms61×body640valid
19.0ms23×body320valid
18.0ms72×body80valid
7.0ms12×body160valid

simplify2.2s

Counts
1 → 1
Iterations
IterNodes
done5000
43141
3655
2181
174
032

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize100.0ms

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))
1.7b
(- (cos x) (cos y))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
15×*-un-lft-identity
11×add-cbrt-cube add-exp-log
9×add-cube-cbrt
8×add-log-exp
6×pow1 associate-*r* associate-*l* associate-*r/
5×sqrt-prod difference-of-squares
4×sub-neg times-frac associate-/r/
3×flip3-+ flip3-- flip-+ flip-- associate-/l* distribute-lft-out--
2×distribute-rgt-in cbrt-undiv distribute-lft-in diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod unswap-sqr associate-/l/
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv diff-cos
Counts
4 → 88
Calls
4 calls:
59.0ms
(/ (+ 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)))))
74.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms
(- 3.0 (sqrt 5.0))
12.0ms
(- (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)))))
109.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
73.0ms
(- (cos x) (cos y))

simplify2.7s

Counts
98 → 98
Iterations
IterNodes
done5000
24129
1918
0324

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
16×*-un-lft-identity
13×sqrt-prod
11×add-cbrt-cube add-exp-log
10×add-cube-cbrt
9×associate-*l*
8×add-log-exp
6×pow1 associate-*r* associate-*r/
5×difference-of-squares
4×sub-neg times-frac associate-/r/
3×flip3-+ flip3-- flip-+ flip-- associate-/l* distribute-lft-out-- unswap-sqr
2×distribute-rgt-in cbrt-undiv distribute-lft-in diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod associate-/l/
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv diff-cos
Counts
4 → 92
Calls
4 calls:
74.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
88.0ms
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (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)))))
5.0ms
(- 3.0 (sqrt 5.0))
6.0ms
(- (cos x) (cos y))

series2.1s

Counts
4 → 10
Calls
4 calls:
159.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
1.9s
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (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)))))
0.0ms
(- 3.0 (sqrt 5.0))
86.0ms
(- (cos x) (cos y))

simplify2.9s

Counts
102 → 102
Iterations
IterNodes
done5000
24086
1923
0330

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize147.0ms

Local error

Found 4 expressions with local error:

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

rewrite293.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
18×associate-*l*
17×*-un-lft-identity
16×add-cbrt-cube add-exp-log
13×add-cube-cbrt
11×pow1
10×distribute-rgt-in distribute-lft-in associate-*r/
7×sub-neg associate-*r*
6×add-log-exp
5×prod-exp cbrt-unprod
4×times-frac pow-prod-down associate-/r/
3×flip3-+ flip3-- flip-+ flip-- associate-/l* difference-of-squares unswap-sqr
2×cbrt-undiv div-exp associate-*l/ frac-add *-commutative distribute-lft-out-- associate-/l/
1×clear-num associate-/r* frac-2neg diff-log div-inv diff-cos
Counts
4 → 111
Calls
4 calls:
84.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
72.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
118.0ms
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (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)))))
12.0ms
(- (cos x) (cos y))

series3.0s

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
168.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
2.6s
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (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)))))
90.0ms
(- (cos x) (cos y))

simplify2.2s

Counts
123 → 123
Iterations
IterNodes
done5000
11021
0348

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize123.0ms

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
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))

rewrite366.0ms

Algorithm
rewrite-expression-head
Rules
30×flip3-- flip--
28×frac-times associate-*r/
25×add-sqr-sqrt
16×*-un-lft-identity
15×pow1 add-cbrt-cube add-exp-log
14×associate-*l/
12×associate-*r*
8×add-cube-cbrt add-log-exp
7×associate-*l* pow-prod-down prod-exp cbrt-unprod
6×sub-neg difference-of-squares
5×sqrt-prod
4×distribute-rgt-in distribute-lft-in distribute-lft-out--
2×diff-log *-commutative diff-cos unswap-sqr
1×times-frac
Counts
4 → 115
Calls
4 calls:
299.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
46.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms
(- 3.0 (sqrt 5.0))
6.0ms
(- (cos x) (cos y))

series524.0ms

Counts
4 → 10
Calls
4 calls:
299.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
122.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
103.0ms
(- (cos x) (cos y))

simplify2.9s

Counts
125 → 125
Iterations
IterNodes
done5001
24624
1871
0278

prune1.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes430.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done48
148
037

end0.0ms

sample12.9s

Algorithm
intervals
Results
6.6s2697×body1280valid
3.2s1941×body640valid
1.5s732×body320valid
1.1s2244×body80valid
209.0ms386×body160valid