Details

Time bar (total: 34.3s)

sample298.0ms

Algorithm
intervals
Results
157.0ms85×body1280valid
71.0ms63×body640valid
22.0ms33×body320valid
12.0ms63×body80valid
6.0ms12×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03250
17450
218150
365350
4266450
done500050

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize66.0ms

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))
2.0b
(- (cos x) (cos y))

rewrite278.0ms

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:
167.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
89.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series426.0ms

Counts
4 → 10
Calls
4 calls:
186.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
139.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
100.0ms
(- (cos x) (cos y))

simplify1.4s

Counts
104 → 104
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02381837
16221770
221871621
done50021619

prune929.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×pow1 add-exp-log associate-*r/ add-cbrt-cube
14×*-un-lft-identity
10×distribute-rgt-in distribute-lft-in associate-*l* sqrt-prod
9×flip3-- pow-prod-down prod-exp flip-- cbrt-unprod
8×add-cube-cbrt sub-neg add-log-exp
7×associate-*r*
5×difference-of-squares
4×frac-times
3×distribute-lft-out--
2×diff-log associate-*l/ *-commutative
1×times-frac diff-cos
Counts
4 → 100
Calls
4 calls:
96.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
430.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
14.0ms
(- 3.0 (sqrt 5.0))
17.0ms
(- (cos x) (cos y))

series463.0ms

Counts
4 → 10
Calls
4 calls:
155.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
231.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
77.0ms
(- (cos x) (cos y))

simplify1.5s

Counts
110 → 110
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02382402
16181929
222911684
done50001682

prune913.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
1.0b
(- 3.0 (sqrt 5.0))
2.0b
(- (cos x) (cos y))
3.7b
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
12×associate-*r/
11×add-exp-log add-cbrt-cube
9×add-cube-cbrt
8×add-log-exp
6×pow1 associate-*l* frac-sub sin-mult
5×sqrt-prod associate-/l/
4×sub-neg flip3-- times-frac associate-*r* associate-/r* flip-- difference-of-squares
2×cbrt-undiv distribute-rgt-in frac-times distribute-lft-in diff-log div-exp associate-*l/ prod-exp associate-/r/ cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
1×frac-2neg flip3-+ pow-prod-down clear-num *-commutative flip-+ div-inv diff-cos associate-/l*
Counts
4 → 92
Calls
4 calls:
68.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
15.0ms
(- 3.0 (sqrt 5.0))
12.0ms
(- (cos x) (cos y))
99.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

series478.0ms

Counts
4 → 10
Calls
4 calls:
156.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
0.0ms
(- 3.0 (sqrt 5.0))
79.0ms
(- (cos x) (cos y))
242.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

simplify2.0s

Counts
102 → 102
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02442225
16142007
221131750
done50021568

prune911.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
2.0b
(- (cos x) (cos y))
3.7b
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-exp-log add-cbrt-cube
16×associate-*l*
14×associate-*r/
12×add-cube-cbrt
10×associate-*r*
9×times-frac
8×pow1
6×prod-exp frac-sub cbrt-unprod sin-mult add-log-exp
5×sub-neg flip3-- flip-- associate-/l/
4×cbrt-undiv distribute-rgt-in frac-times distribute-lft-in div-exp associate-/r* sqrt-prod associate-/r/ difference-of-squares
3×associate-*l/ distribute-lft-out unswap-sqr
2×flip3-+ pow-prod-down *-commutative flip-+ div-inv distribute-lft-out--
1×frac-2neg diff-log clear-num diff-cos associate-/l*
Counts
4 → 118
Calls
4 calls:
191.0ms
(* (/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
67.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
8.0ms
(- (cos x) (cos y))
63.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

series867.0ms

Counts
4 → 12
Calls
4 calls:
356.0ms
(* (/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
162.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
74.0ms
(- (cos x) (cos y))
275.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

simplify2.8s

Counts
130 → 130
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02813960
17653617
230213113
done50012513

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes283.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03455
14455
done4455

end0.0ms

sample16.3s

Algorithm
intervals
Results
9.0s2741×body1280valid
4.5s1829×body640valid
1.2s786×body320valid
1.0s2309×body80valid
213.0ms335×body160valid