Details

Time bar (total: 47.5s)

sample383.0ms

Algorithm
intervals
Results
188.0ms100×body1280valid
59.0ms48×body640valid
53.0ms6×body160valid
23.0ms25×body320valid
21.0ms77×body80valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
0321087
1741087
21771087
36221087
427521087
done50001087

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize146.0ms

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))
2.7b
(- (cos x) (cos y))

rewrite178.0ms

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 distribute-lft-out--
2×times-frac diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 94
Calls
4 calls:
113.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
51.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms
(- 3.0 (sqrt 5.0))
6.0ms
(- (cos x) (cos y))

series373.0ms

Counts
4 → 10
Calls
4 calls:
181.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
114.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
78.0ms
(- (cos x) (cos y))

simplify2.3s

Counts
104 → 104
Iterations

Useful iterations: done (2.3s)

IterNodesCost
024144339
165239943
2210839823
done502739623

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize117.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (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 (sqrt 5.0)) 2.0) (cos y)))))
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))
2.7b
(- (cos x) (cos y))

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cbrt-cube associate-*r/ add-exp-log
13×pow1 *-un-lft-identity
8×flip3-- flip-- add-log-exp
7×prod-exp add-cube-cbrt cbrt-unprod
6×associate-*r* pow-prod-down
5×difference-of-squares
4×frac-times sub-neg times-frac associate-*l/ associate-/r/
3×flip3-+ flip-+ associate-/l* distribute-lft-out--
2×distribute-rgt-in cbrt-undiv distribute-lft-in diff-log div-exp frac-add associate-/l/
1×clear-num associate-/r* frac-2neg associate-*l* *-commutative sqrt-prod div-inv diff-cos
Counts
4 → 93
Calls
4 calls:
110.0ms
(/ (+ 2.0 (* (* (* (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 (sqrt 5.0)) 2.0) (cos y)))))
354.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
6.0ms
(- 3.0 (sqrt 5.0))
6.0ms
(- (cos x) (cos y))

series2.4s

Counts
4 → 10
Calls
4 calls:
2.1s
(/ (+ 2.0 (* (* (* (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 (sqrt 5.0)) 2.0) (cos y)))))
223.0ms
(* (* (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))
104.0ms
(- (cos x) (cos y))

simplify5.2s

Counts
103 → 103
Iterations

Useful iterations: 2 (2.7s)

IterNodesCost
037176729
1112365542
2473064702
done500964702

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize572.0ms

Local error

Found 4 expressions with local error:

1.0b
(- 3.0 (sqrt 5.0))
2.7b
(- (cos x) (cos y))
2.7b
(- (cos x) (cos y))
2.7b
(- (cos x) (cos y))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-log-exp
5×difference-of-squares
4×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt flip-- distribute-lft-out--
3×diff-cos
1×sqrt-prod
Counts
4 → 60
Calls
4 calls:
6.0ms
(- 3.0 (sqrt 5.0))
6.0ms
(- (cos x) (cos y))
6.0ms
(- (cos x) (cos y))
12.0ms
(- (cos x) (cos y))

series255.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(- 3.0 (sqrt 5.0))
84.0ms
(- (cos x) (cos y))
94.0ms
(- (cos x) (cos y))
77.0ms
(- (cos x) (cos y))

simplify2.5s

Counts
70 → 70
Iterations

Useful iterations: 3 (750.0ms)

IterNodesCost
010421072
122517932
254217852
3196417692
done500017692

prune998.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize127.0ms

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)))
2.7b
(- (cos x) (cos y))

rewrite240.0ms

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
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 → 106
Calls
4 calls:
53.0ms
(/ (+ 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)))))
127.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
50.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms
(- (cos x) (cos y))

series2.9s

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)))))
155.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
104.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
80.0ms
(- (cos x) (cos y))

simplify6.1s

Counts
118 → 118
Iterations

Useful iterations: done (6.0s)

IterNodesCost
038282071
1115776081
2466175480
done500675320

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes541.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify21.0ms

Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
0381327
1481327
done481327

end0.0ms

sample15.1s

Algorithm
intervals
Results
8.0s2753×body1280valid
4.6s1821×body640valid
1.1s765×body320valid
797.0ms2313×body80valid
212.0ms348×body160valid