Details

Time bar (total: 24.0s)

sample192.0ms

Algorithm
intervals
Results
91.0ms84×body1280valid
46.0ms61×body640valid
17.0ms80×body80valid
11.0ms23×body320valid
2.0ms8×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
03250
17450
219247
369747
4290747
done500147

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
152×add-sqr-sqrt
143×*-un-lft-identity
137×add-cube-cbrt
130×times-frac
105×prod-diff
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
13×associate-/l*
11×add-exp-log add-cbrt-cube div-inv
8×add-log-exp
6×pow1 fma-neg associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip-- distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos associate-/l/
Counts
4 → 250
Calls
4 calls:
11.0ms
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
63.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series1.2s

Counts
4 → 10
Calls
4 calls:
1.0s
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
95.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
65.0ms
(- (cos x) (cos y))

simplify1.6s

Counts
260 → 260
Iterations

Useful iterations: done (1.6s)

IterNodesCost
065811736
1139410851
238959139
done50009131

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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))
3.0b
(- (cos x) (cos y))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
105×prod-diff
103×*-un-lft-identity
97×add-cube-cbrt
58×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
11×add-exp-log add-cbrt-cube
8×add-log-exp
7×div-inv
6×pow1 fma-neg associate-*r/ associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg associate-/r/ log1p-expm1-u
3×flip3-- flip3-+ flip-- flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative diff-cos
Counts
4 → 207
Calls
4 calls:
67.0ms
(/ (+ 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)))))
62.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series1.5s

Counts
4 → 10
Calls
4 calls:
1.4s
(/ (+ 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)))))
94.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
64.0ms
(- (cos x) (cos y))

simplify1.9s

Counts
217 → 217
Iterations

Useful iterations: done (1.8s)

IterNodesCost
06028074
113927196
247765380
done50005376

prune840.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.6b
(+ (cos x) (cos y))
1.0b
(- 3.0 (sqrt 5.0))
3.2b
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
97×prod-diff
95×*-un-lft-identity
89×add-cube-cbrt
55×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
10×add-log-exp
6×pow1 add-exp-log associate-*r* associate-*l* add-cbrt-cube div-inv
5×difference-of-squares
4×expm1-log1p-u sub-neg fma-neg cos-mult log1p-expm1-u
3×flip3-- fma-def flip--
2×sqr-cos diff-log associate-*r/ distribute-lft-out-- unswap-sqr
1×+-commutative flip3-+ sum-cos pow-prod-down prod-exp associate--l+ sum-log *-commutative frac-sub cbrt-unprod flip-+ distribute-lft-out associate--r+ sub-div
Counts
4 → 188
Calls
4 calls:
61.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(+ (cos x) (cos y))
8.0ms
(- 3.0 (sqrt 5.0))
21.0ms
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

series220.0ms

Counts
4 → 10
Calls
4 calls:
97.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
41.0ms
(+ (cos x) (cos y))
0.0ms
(- 3.0 (sqrt 5.0))
81.0ms
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

simplify1.6s

Counts
198 → 198
Iterations

Useful iterations: done (1.6s)

IterNodesCost
04645852
19365068
225043665
done50002959

prune789.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize47.0ms

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 x)) (* (cos y) (cos y))) (+ (cos x) (cos y))))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ (sqrt 5.0) 3.0)) 2.0) (cos y)))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.6b
(+ (cos x) (cos y))
3.2b
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
82×*-un-lft-identity
79×prod-diff
78×add-cube-cbrt
58×times-frac
41×distribute-rgt-in distribute-lft-in
11×add-exp-log add-cbrt-cube
8×add-log-exp
7×div-inv
6×pow1 associate-*r/ associate-*r* associate-*l*
4×expm1-log1p-u flip3-+ sqrt-prod associate-/r/ cos-mult flip-+ log1p-expm1-u
3×sub-neg fma-def associate-/l* difference-of-squares
2×cbrt-undiv sqr-cos flip3-- div-exp associate-*l/ frac-add prod-exp flip-- cbrt-unprod associate-/l/ unswap-sqr
1×+-commutative frac-2neg sum-cos fma-neg diff-log pow-prod-down associate--l+ clear-num associate-/r* sum-log *-commutative frac-sub distribute-lft-out associate--r+ distribute-lft-out-- sub-div
Counts
4 → 179
Calls
4 calls:
67.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (/ (- (* (cos x) (cos x)) (* (cos y) (cos y))) (+ (cos x) (cos y))))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ (sqrt 5.0) 3.0)) 2.0) (cos y)))))
62.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(+ (cos x) (cos y))
18.0ms
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

series2.8s

Counts
4 → 12
Calls
4 calls:
2.5s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (/ (- (* (cos x) (cos x)) (* (cos y) (cos y))) (+ (cos x) (cos y))))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ (sqrt 5.0) 3.0)) 2.0) (cos y)))))
94.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
48.0ms
(+ (cos x) (cos y))
83.0ms
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

simplify1.8s

Counts
191 → 191
Iterations

Useful iterations: 2 (814.0ms)

IterNodesCost
05718277
114067547
248735770
done50005770

prune879.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.4b 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
03968
15068
done5068

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.0s2723×body1280valid
1.3s1847×body640valid
378.0ms789×body320valid
331.0ms2299×body80valid
111.0ms342×body160valid