Details

Time bar (total: 20.9s)

sample192.0ms

Algorithm
intervals
Results
97.0ms88×body1280valid
48.0ms61×body640valid
14.0ms28×body320valid
10.0ms69×body80valid
3.0ms10×body160valid

simplify1.0s

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: 0.5b

localize40.0ms

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

rewrite92.0ms

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))

series286.0ms

Counts
4 → 10
Calls
4 calls:
137.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
58.0ms
(- (cos x) (cos y))

simplify877.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (232.0ms)

IterNodesCost
02381837
16231770
222041621
done50011621

prune544.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

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

rewrite112.0ms

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:
23.0ms
(/ (+ 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)))
28.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- (cos x) (cos y))

series2.1s

Counts
4 → 12
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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
135.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
90.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
57.0ms
(- (cos x) (cos y))

simplify1.2s

Counts
118 → 118
Iterations

Useful iterations: 2 (430.0ms)

IterNodesCost
03664085
110663978
242453480
done50003480

prune757.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (log (exp (* (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)))
1.7b
(- (cos x) (cos y))
4.0b
(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
14×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt
7×pow1 log-prod add-log-exp
6×associate-*r/ associate-*r* associate-*l*
5×sub-neg
4×distribute-rgt-in distribute-lft-in times-frac exp-sum sqrt-prod associate-/r/
3×flip3-+ log-pow flip-+ associate-/l* difference-of-squares
2×cbrt-undiv flip3-- div-exp associate-*l/ frac-add prod-exp flip-- cbrt-unprod associate-/l/ distribute-lft-out-- unswap-sqr
1×exp-prod exp-to-pow frac-2neg diff-log rem-log-exp pow-prod-down clear-num associate-/r* *-commutative div-inv diff-cos
Counts
4 → 91
Calls
4 calls:
27.0ms
(/ (+ 2.0 (* (* (log (exp (* (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)))))
26.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- (cos x) (cos y))
3.0ms
(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

series2.2s

Counts
4 → 12
Calls
4 calls:
2.0s
(/ (+ 2.0 (* (* (log (exp (* (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)))))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
53.0ms
(- (cos x) (cos y))
93.0ms
(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

simplify960.0ms

Counts
103 → 103
Iterations

Useful iterations: 2 (325.0ms)

IterNodesCost
03213474
18553293
230772873
done50012873

prune694.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (log (exp (* (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)))))
0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
1.7b
(- (cos x) (cos y))
4.0b
(log (exp (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
16×distribute-rgt-in distribute-lft-in
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
11×log-prod
10×pow1 add-cube-cbrt
9×sub-neg associate-*l* sqrt-prod
8×associate-*r/ exp-sum
7×add-log-exp
4×prod-exp associate-/r/ cbrt-unprod
3×flip3-+ times-frac pow-prod-down log-pow flip-+ associate-/l*
2×cbrt-undiv flip3-- div-exp associate-*l/ frac-add flip-- associate-/l/
1×exp-prod exp-to-pow frac-2neg diff-log rem-log-exp associate-*r* clear-num associate-/r* *-commutative div-inv diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 98
Calls
4 calls:
29.0ms
(/ (+ 2.0 (* (* (log (exp (* (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)))))
36.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
3.0ms
(- (cos x) (cos y))
4.0ms
(log (exp (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
1.7s
(/ (+ 2.0 (* (* (log (exp (* (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)))))
97.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
54.0ms
(- (cos x) (cos y))
95.0ms
(log (exp (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))))

simplify971.0ms

Counts
110 → 110
Iterations

Useful iterations: 2 (333.0ms)

IterNodesCost
03364168
18903430
231522968
done50012968

prune636.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes233.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03963
15063
done5063

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.3s2801×body1280valid
1.4s1817×body640valid
378.0ms726×body320valid
349.0ms2321×body80valid
110.0ms335×body160valid