Details

Time bar (total: 35.2s)

sample198.0ms

Algorithm
intervals
Results
96.0ms87×body1280valid
47.0ms56×body640valid
12.0ms24×body320valid
11.0ms72×body80valid
5.0ms17×body160valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03250
17450
217650
354250
4170050
done500050

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize42.0ms

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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.7b
(- (cos x) (cos y))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
16×*-un-lft-identity
12×associate-*r*
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
8×add-cube-cbrt add-log-exp
7×associate-*l* difference-of-squares
6×sub-neg
5×sqrt-prod
4×distribute-rgt-in frac-times distribute-lft-in pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
2×times-frac diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 94
Calls
4 calls:
55.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
28.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- (cos x) (cos y))

series322.0ms

Counts
4 → 10
Calls
4 calls:
157.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
103.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
61.0ms
(- (cos x) (cos y))

simplify943.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (245.0ms)

IterNodesCost
02381837
16231770
222041621
done50011621

prune574.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

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 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.7b
(- (cos x) (cos y))

rewrite116.0ms

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:
25.0ms
(/ (+ 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)))))
55.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
27.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- (cos x) (cos y))

series2.3s

Counts
4 → 12
Calls
4 calls:
2.0s
(/ (+ 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 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
155.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
104.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
65.0ms
(- (cos x) (cos y))

simplify1.5s

Counts
118 → 118
Iterations

Useful iterations: 2 (524.0ms)

IterNodesCost
03664085
110663978
242453480
done50003480

prune814.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3))))
0.5b
(* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3)))
0.6b
(- (* (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))) (* (+ 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))))
2.7b
(- (cos x) (cos y))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
49×associate-*l/
19×associate-*r/
15×frac-sub
12×add-sqr-sqrt *-un-lft-identity
11×add-exp-log frac-times flip3-+ add-cbrt-cube flip-+
8×cube-div add-cube-cbrt add-log-exp
6×pow1
5×associate-*r*
4×frac-add associate-/r/
3×times-frac associate-*l* associate-/l*
2×cbrt-undiv sub-neg flip3-- diff-log div-exp prod-exp flip-- cbrt-unprod associate-/l/ sub-div
1×distribute-rgt-in distribute-rgt-out-- frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* sum-cubes *-commutative div-inv diff-cos distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 98
Calls
4 calls:
37.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3))))
73.0ms
(* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3)))
97.0ms
(- (* (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))) (* (+ 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))))
3.0ms
(- (cos x) (cos y))

series8.8s

Counts
4 → 12
Calls
4 calls:
6.4s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3))))
1.5s
(* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3)))
917.0ms
(- (* (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))) (* (+ 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))))
60.0ms
(- (cos x) (cos y))

simplify494.0ms

Counts
110 → 110
Iterations

Useful iterations: done (484.0ms)

IterNodesCost
04527576
113666948
done50006802

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3))))
0.5b
(* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3)))
0.6b
(- (* (* (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0)))) (pow (cos y) 2)) (* 2.0 (* (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) (cos y)))))
2.7b
(- (cos x) (cos y))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
36×associate-*r/
15×frac-sub
12×add-sqr-sqrt *-un-lft-identity
11×add-exp-log frac-times flip3-+ add-cbrt-cube flip-+
8×cube-div add-cube-cbrt add-log-exp
6×pow1
5×associate-*r*
4×frac-add associate-/r/
3×times-frac associate-*l* associate-/l*
2×cbrt-undiv sub-neg flip3-- diff-log div-exp prod-exp flip-- cbrt-unprod associate-/l/ sub-div
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* sum-cubes *-commutative div-inv diff-cos distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 97
Calls
4 calls:
36.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3))))
75.0ms
(* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3)))
72.0ms
(- (* (* (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0)))) (pow (cos y) 2)) (* 2.0 (* (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) (cos y)))))
3.0ms
(- (cos x) (cos y))

series8.7s

Counts
4 → 12
Calls
4 calls:
6.3s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3))))
1.5s
(* 3.0 (+ (pow (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) 3) (pow (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)) 3)))
924.0ms
(- (* (* (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0)))) (pow (cos y) 2)) (* 2.0 (* (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) (cos y)))))
67.0ms
(- (cos x) (cos y))

simplify506.0ms

Counts
109 → 109
Iterations

Useful iterations: done (498.0ms)

IterNodesCost
04657449
114237089
done50026913

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes260.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
054209
174209
done74209

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.1s2704×body1280valid
1.4s1861×body640valid
388.0ms756×body320valid
338.0ms2299×body80valid
128.0ms380×body160valid