Details

Time bar (total: 36.5s)

sample422.0ms

Algorithm
intervals
Results
169.0ms90×body1280valid
106.0ms51×body640valid
77.0ms78×body80valid
25.0ms21×body320valid
9.0ms16×body160valid

simplify1.6s

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: 0.4b

localize54.0ms

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))
2.2b
(- (cos x) (cos y))

rewrite286.0ms

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:
169.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
87.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms
(- 3.0 (sqrt 5.0))
14.0ms
(- (cos x) (cos y))

series410.0ms

Counts
4 → 10
Calls
4 calls:
195.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
117.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
97.0ms
(- (cos x) (cos y))

simplify1.4s

Counts
104 → 104
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02381837
16221770
221871621
done50021619

prune852.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize55.0ms

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)))
2.2b
(- (cos x) (cos y))

rewrite387.0ms

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:
105.0ms
(/ (+ 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)))))
145.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
116.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms
(- (cos x) (cos y))

series3.0s

Counts
4 → 12
Calls
4 calls:
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)))))
205.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
133.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
81.0ms
(- (cos x) (cos y))

simplify3.1s

Counts
118 → 118
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
03664085
110713978
242833480
done50023480

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize139.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.2b
(- (cos x) (cos y))
2.2b
(- (cos x) (cos y))
2.2b
(- (cos x) (cos y))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×*-un-lft-identity
10×add-log-exp
7×add-cube-cbrt
6×pow1 add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×sub-neg difference-of-squares
4×flip3-- sqrt-prod 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 → 76
Calls
4 calls:
90.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
15.0ms
(- (cos x) (cos y))
15.0ms
(- (cos x) (cos y))
32.0ms
(- (cos x) (cos y))

series402.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
105.0ms
(- (cos x) (cos y))
97.0ms
(- (cos x) (cos y))
68.0ms
(- (cos x) (cos y))

simplify1.5s

Counts
88 → 88
Iterations

Useful iterations: 3 (620.0ms)

IterNodesCost
0123986
1271961
2754899
32051890
done5002890

prune970.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.6b
(cbrt (- (sin y) (/ (sin x) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.2b
(- (cos x) (cos y))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
14×*-un-lft-identity
12×cbrt-prod
8×add-log-exp
7×difference-of-squares
6×add-cube-cbrt
4×pow1 add-exp-log cbrt-div flip3-- add-cbrt-cube flip-- distribute-lft-out--
2×sub-neg times-frac pow1/3 diff-log
1×sqrt-prod diff-cos
Counts
4 → 62
Calls
4 calls:
22.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
11.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
7.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series527.0ms

Counts
4 → 10
Calls
4 calls:
230.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
219.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
78.0ms
(- (cos x) (cos y))

simplify2.5s

Counts
72 → 72
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
0155957
1316926
2638876
31315860
43162836
done5001836

prune731.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes368.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
039110
149110
done49110

end0.0ms

sample16.5s

Algorithm
intervals
Results
9.3s2747×body1280valid
4.1s1854×body640valid
1.3s745×body320valid
878.0ms2316×body80valid
337.0ms338×body160valid