Details

Time bar (total: 38.6s)

sample379.0ms

Algorithm
intervals
Results
185.0ms80×body1280valid
110.0ms58×body640valid
26.0ms28×body320valid
20.0ms80×body80valid
5.0ms10×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03250
17450
218150
365350
4266450
done500050

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.4b
(- (cos x) (cos y))

rewrite132.0ms

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:
44.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
59.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
16.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series364.0ms

Counts
4 → 10
Calls
4 calls:
132.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
144.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
88.0ms
(- (cos x) (cos y))

simplify1.2s

Counts
112 → 112
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02471369
15841330
216891232
done50001221

prune744.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.3b
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.4b
(- (cos x) (cos y))

rewrite224.0ms

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:
81.0ms
(/ (+ 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)))))
49.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
76.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms
(- (cos x) (cos y))

series2.4s

Counts
4 → 12
Calls
4 calls:
2.1s
(/ (+ 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)))))
92.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
107.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
83.0ms
(- (cos x) (cos y))

simplify2.1s

Counts
126 → 126
Iterations

Useful iterations: 2 (667.0ms)

IterNodesCost
03723617
110273530
237323107
done50013107

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

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
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.4b
(- (cos x) (cos y))

rewrite626.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
31×*-un-lft-identity
29×associate-*l*
21×times-frac
19×add-cube-cbrt
16×add-exp-log add-cbrt-cube
15×associate-*r*
13×pow1
11×difference-of-squares
10×associate-*r/
8×flip3-- flip--
7×sqrt-prod
6×prod-exp cbrt-unprod distribute-lft-out-- add-log-exp
5×sub-neg pow-prod-down
4×distribute-rgt-in frac-times distribute-lft-in unswap-sqr
3×associate-*l/ *-commutative
1×cbrt-undiv diff-log div-exp div-inv diff-cos
Counts
4 → 120
Calls
4 calls:
156.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
53.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
401.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- (cos x) (cos y))

series457.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
94.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
109.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
66.0ms
(- (cos x) (cos y))

simplify1.4s

Counts
132 → 132
Iterations

Useful iterations: 2 (457.0ms)

IterNodesCost
02842218
17502147
226741958
done50021958

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (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)))))
0.3b
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.4b
(- (cos x) (cos y))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
77×add-sqr-sqrt
45×times-frac
44×*-un-lft-identity
41×associate-*l*
33×add-exp-log
32×add-cube-cbrt
26×associate-*r*
23×add-cbrt-cube
11×prod-exp
10×pow1 unswap-sqr
9×div-exp difference-of-squares
7×sqrt-prod cbrt-unprod
6×add-log-exp
5×cbrt-undiv distribute-lft-out--
4×associate-*l/ associate-/r/
3×sub-neg associate-*r/ pow-prod-down *-commutative div-inv
2×distribute-rgt-in rec-exp flip3-- distribute-lft-in flip3-+ 1-exp frac-add flip-- flip-+
1×frac-times diff-log diff-cos
Counts
4 → 147
Calls
4 calls:
149.0ms
(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (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)))))
76.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
104.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
16.0ms
(- (cos x) (cos y))

series3.1s

Counts
4 → 12
Calls
4 calls:
2.7s
(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (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)))))
131.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
152.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
82.0ms
(- (cos x) (cos y))

simplify2.6s

Counts
159 → 159
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
04336075
111915892
240045201
done50015201

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes376.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03758
15058
done5058

end0.0ms

sample16.5s

Algorithm
intervals
Results
9.3s2636×body1280valid
4.2s1918×body640valid
1.4s780×body320valid
1.0s2375×body80valid
196.0ms291×body160valid