Details

Time bar (total: 2.1m)

sample609.0ms

Algorithm
intervals
Results
370.0ms90×body1280valid
104.0ms46×body640valid
46.0ms30×body320valid
34.0ms76×body80valid
14.0ms14×body160valid

simplify2.0s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize81.0ms

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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.9b
(- (cos x) (cos y))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
16×*-un-lft-identity
12×associate-*r*
11×pow1 add-cbrt-cube add-exp-log
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 insert-posit16 distribute-lft-out--
2×times-frac diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 98
Calls
4 calls:
96.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
48.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series431.0ms

Counts
4 → 10
Calls
4 calls:
199.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
129.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
103.0ms
(- (cos x) (cos y))

simplify1.7s

Counts
108 → 108
Iterations
IterNodes
done5002
22926
1657
0245

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize113.0ms

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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.9b
(- (cos x) (cos y))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
16×*-un-lft-identity add-cbrt-cube add-exp-log
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/ associate-/r/ sqrt-prod insert-posit16
3×flip3-+ flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp frac-add *-commutative unswap-sqr associate-/l/
1×clear-num associate-/r* frac-2neg diff-log div-inv diff-cos
Counts
4 → 110
Calls
4 calls:
62.0ms
(/ (+ 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)))))
91.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
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:
2.7s
(/ (+ 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)))))
224.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
136.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
91.0ms
(- (cos x) (cos y))

simplify2.0s

Counts
122 → 122
Iterations
IterNodes
done5000
11163
0386

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize194.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (+ (* (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))) 2.0) 3.0) (+ (* (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))) (* (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))))) (* (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0) (* (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0) (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0))))) (+ (* (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (+ 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)) (* (/ (/ (- (* 3.0 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))))))
0.5b
(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
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))))
1.9b
(- (cos x) (cos y))

rewrite5.9s

Algorithm
rewrite-expression-head
Rules
978×associate-*l/
957×associate-*r/
819×frac-times
522×flip3-+ flip-+
486×frac-add
255×frac-sub
246×associate-*l*
184×associate-/r/
92×times-frac
70×add-sqr-sqrt
54×*-un-lft-identity
50×add-cube-cbrt
34×sub-div
26×cube-unmult
19×flip3-- flip--
15×add-cbrt-cube add-exp-log
13×sum-cubes
9×associate-*r*
8×pow1 add-log-exp
5×div-inv unswap-sqr
4×prod-exp sqrt-prod cbrt-unprod insert-posit16
3×cbrt-undiv div-exp difference-of-squares
2×sub-neg diff-log pow-prod-down *-commutative distribute-lft-out--
1×distribute-rgt-in distribute-lft-in distribute-rgt-out-- diff-cos
Counts
4 → 648
Calls
4 calls:
5.6s
(* (/ (/ (+ (* (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))) 2.0) 3.0) (+ (* (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))) (* (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))))) (* (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0) (* (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0) (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0))))) (+ (* (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (+ 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)) (* (/ (/ (- (* 3.0 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))))))
54.0ms
(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
177.0ms
(- (* (* (/ (/ (- (* 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))))
12.0ms
(- (cos x) (cos y))

series45.1s

Counts
4 → 12
Calls
4 calls:
43.5s
(* (/ (/ (+ (* (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))) 2.0) 3.0) (+ (* (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))) (* (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ 3.0 (sqrt 5.0))))))) (* (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0) (* (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0) (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) 1.0))))) (+ (* (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (+ 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)) (* (/ (/ (- (* 3.0 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))))))
167.0ms
(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
1.3s
(- (* (* (/ (/ (- (* 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))))
140.0ms
(- (cos x) (cos y))

simplify18.8s

Counts
660 → 660
Iterations
IterNodes
done5001
01663

prune15.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize205.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)))
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))))
1.9b
(- (cos x) (cos y))
7.2b
(cbrt (* (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))))

rewrite784.0ms

Algorithm
rewrite-expression-head
Rules
127×associate-*l/
43×frac-times pow1
35×flip3-- flip--
26×cbrt-div
21×associate-*r/
17×pow-prod-down
16×add-cbrt-cube add-exp-log
15×frac-sub
8×prod-exp cbrt-unprod add-log-exp
6×add-sqr-sqrt *-un-lft-identity flip3-+ flip-+
4×pow-sqr pow-prod-up add-cube-cbrt insert-posit16
2×sub-neg pow-plus diff-log sub-div
1×cbrt-prod pow2 distribute-rgt-out-- pow1/3 swap-sqr associate-*r* associate-*l* pow3 *-commutative rem-cbrt-cube diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 127
Calls
4 calls:
145.0ms
(* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)))
215.0ms
(- (* (* (/ (/ (- (* 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))))
7.0ms
(- (cos x) (cos y))
412.0ms
(cbrt (* (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
181.0ms
(* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)))
1.0s
(- (* (* (/ (/ (- (* 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))))
76.0ms
(- (cos x) (cos y))
132.0ms
(cbrt (* (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))) (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))))

simplify1.5s

Counts
139 → 139
Iterations
IterNodes
done5000
11177
0381

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes361.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify21.0ms

Iterations
IterNodes
done80
380
276
171
053

end0.0ms

sample19.3s

Algorithm
intervals
Results
10.2s2724×body1280valid
6.0s1901×body640valid
1.5s766×body320valid
1.1s2244×body80valid
355.0ms365×body160valid