Details

Time bar (total: 43.2s)

sample374.0ms

Algorithm
intervals
Results
214.0ms88×body1280valid
66.0ms52×body640valid
43.0ms28×body320valid
20.0ms80×body80valid
5.0ms8×body160valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5000
42752
3622
2177
174
032

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize129.0ms

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)))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.9b
(- (cos x) (cos y))

rewrite153.0ms

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/ insert-posit16
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 → 92
Calls
4 calls:
79.0ms
(/ (+ 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)))))
61.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
7.0ms
(- (cos x) (cos y))

series2.1s

Counts
4 → 10
Calls
4 calls:
1.9s
(/ (+ 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)))))
136.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
75.0ms
(- (cos x) (cos y))

simplify3.1s

Counts
102 → 102
Iterations
IterNodes
done5001
23449
1920
0328

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize143.0ms

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)))
0.3b
(/ (+ 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)))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.9b
(- (cos x) (cos y))

rewrite423.0ms

Algorithm
rewrite-expression-head
Rules
32×associate-*r/
29×flip3-- flip--
28×frac-times
23×add-sqr-sqrt
20×add-cbrt-cube add-exp-log
16×*-un-lft-identity associate-*l/
15×pow1
12×associate-*r*
10×add-cube-cbrt
8×prod-exp cbrt-unprod
7×associate-*l* pow-prod-down
6×add-log-exp
5×sub-neg
4×distribute-rgt-in distribute-lft-in times-frac associate-/r/ sqrt-prod insert-posit16 difference-of-squares
3×flip3-+ flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp frac-add *-commutative diff-cos unswap-sqr associate-/l/
1×clear-num associate-/r* frac-2neg diff-log div-inv
Counts
4 → 131
Calls
4 calls:
256.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
110.0ms
(/ (+ 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)))))
48.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(- (cos x) (cos y))

series3.1s

Counts
4 → 12
Calls
4 calls:
337.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
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)))))
132.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
92.0ms
(- (cos x) (cos y))

simplify3.0s

Counts
143 → 143
Iterations
IterNodes
done5000
11374
0423

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize131.0ms

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)))) (/ 1 (* 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))) (- (cos x) (cos y)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.9b
(- (cos x) (cos y))

rewrite524.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
33×associate-*r/
30×frac-times
29×flip3-- flip--
26×add-sqr-sqrt
24×add-cbrt-cube
23×associate-*r*
18×associate-*l/
17×pow1 *-un-lft-identity prod-exp
11×add-cube-cbrt cbrt-unprod
10×associate-*l*
8×pow-prod-down
6×add-log-exp
5×sub-neg
4×distribute-rgt-in distribute-lft-in flip3-+ times-frac div-exp associate-/r/ sqrt-prod flip-+ insert-posit16 difference-of-squares
3×*-commutative distribute-lft-out-- unswap-sqr
2×cbrt-undiv rec-exp 1-exp frac-add diff-cos
1×diff-log un-div-inv div-inv
Counts
4 → 144
Calls
4 calls:
162.0ms
(* (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (/ 1 (* 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))))))
299.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
51.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms
(- (cos x) (cos y))

series3.5s

Counts
4 → 12
Calls
4 calls:
3.0s
(* (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (/ 1 (* 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))))))
304.0ms
(* (* (* (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)))
72.0ms
(- (cos x) (cos y))

simplify3.3s

Counts
156 → 156
Iterations
IterNodes
done5003
11507
0460

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize144.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.9b
(- (cos x) (cos y))
1.9b
(- (cos x) (cos y))
1.9b
(- (cos x) (cos y))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×*-un-lft-identity
10×add-log-exp
7×add-cube-cbrt
6×pow1 add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×sub-neg difference-of-squares
4×flip3-- sqrt-prod insert-posit16 flip-- distribute-lft-out--
3×diff-log diff-cos
2×distribute-rgt-in distribute-lft-in associate-*r/ unswap-sqr
1×times-frac pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 80
Calls
4 calls:
48.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms
(- (cos x) (cos y))
9.0ms
(- (cos x) (cos y))
9.0ms
(- (cos x) (cos y))

series326.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
74.0ms
(- (cos x) (cos y))
84.0ms
(- (cos x) (cos y))
58.0ms
(- (cos x) (cos y))

simplify1.6s

Counts
92 → 92
Iterations
IterNodes
done5005
32599
2757
1283
0125

prune929.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes337.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations
IterNodes
done49
149
039

end0.0ms

sample13.0s

Algorithm
intervals
Results
8.0s2720×body1280valid
3.0s1809×body640valid
856.0ms756×body320valid
684.0ms2359×body80valid
236.0ms356×body160valid