Details

Time bar (total: 41.2s)

sample336.0ms

Algorithm
intervals
Results
130.0ms78×body1280valid
102.0ms57×body640valid
41.0ms11×body160valid
22.0ms33×body320valid
16.0ms77×body80valid

simplify2.3s

Counts
1 → 1
Iterations
IterNodes
done5004
43022
3657
2188
174
032

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
0.4b
(* (- (cos x) (cos y)) (sqrt 2.0))
1.0b
(- 3.0 (sqrt 5.0))
2.3b
(- (cos x) (cos y))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×*-un-lft-identity
29×add-cube-cbrt
27×prod-diff
14×sqrt-prod
11×add-cbrt-cube add-exp-log
8×add-log-exp
6×pow1 fma-neg associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×times-frac flip3-- flip-- associate-/l* distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-*l/ prod-exp cbrt-unprod diff-cos unswap-sqr
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv
Counts
4 → 119
Calls
4 calls:
6.0ms
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
21.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
7.0ms
(- 3.0 (sqrt 5.0))
14.0ms
(- (cos x) (cos y))

series1.7s

Counts
4 → 10
Calls
4 calls:
1.5s
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
125.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms
(- 3.0 (sqrt 5.0))
78.0ms
(- (cos x) (cos y))

simplify1.9s

Counts
129 → 129
Iterations
IterNodes
done5000
22471
1798
0328

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
0.3b
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
0.4b
(* (- (cos x) (cos y)) (sqrt 2.0))
2.3b
(- (cos x) (cos y))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity
17×add-cube-cbrt
16×add-cbrt-cube add-exp-log
12×associate-*l*
11×pow1
10×associate-*l/
9×prod-diff
8×flip3-- flip--
7×associate-*r*
6×add-log-exp
5×prod-exp cbrt-unprod
4×expm1-log1p-u frac-times times-frac pow-prod-down sqrt-prod log1p-expm1-u difference-of-squares
3×fma-neg associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp associate-*r/ *-commutative diff-cos unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-inv
Counts
4 → 112
Calls
4 calls:
69.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
6.0ms
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
30.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
7.0ms
(- (cos x) (cos y))

series2.1s

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
1.8s
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
112.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
59.0ms
(- (cos x) (cos y))

simplify3.3s

Counts
124 → 124
Iterations
IterNodes
done5000
23049
1870
0327

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize117.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (* (* (- (cos x) (cos y)) (sqrt 2.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (* (- (cos x) (cos y)) (sqrt 2.0))))
2.3b
(- (cos x) (cos y))
2.3b
(- (cos x) (cos y))
2.3b
(- (cos x) (cos y))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
68×associate-*l/
31×add-sqr-sqrt *-un-lft-identity
30×flip3-- flip--
28×frac-times
27×prod-diff
26×cbrt-div
25×add-cube-cbrt
10×add-log-exp
9×fma-neg
8×associate-*r/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×sub-neg diff-log diff-cos distribute-lft-out-- difference-of-squares
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 125
Calls
4 calls:
365.0ms
(cbrt (* (* (* (- (cos x) (cos y)) (sqrt 2.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (* (- (cos x) (cos y)) (sqrt 2.0))))
13.0ms
(- (cos x) (cos y))
11.0ms
(- (cos x) (cos y))
7.0ms
(- (cos x) (cos y))

series411.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (* (* (* (- (cos x) (cos y)) (sqrt 2.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (* (- (cos x) (cos y)) (sqrt 2.0))))
99.0ms
(- (cos x) (cos y))
102.0ms
(- (cos x) (cos y))
67.0ms
(- (cos x) (cos y))

simplify2.2s

Counts
137 → 137
Iterations
IterNodes
done5000
21906
1499
0191

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize109.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
0.3b
(* (- (cos x) (cos y)) (sqrt (sqrt 2.0)))
2.3b
(- (cos x) (cos y))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×*-un-lft-identity
20×add-cbrt-cube add-exp-log
18×add-cube-cbrt
16×associate-*l/
15×pow1
12×associate-*l* sqrt-prod
10×associate-*r*
9×prod-diff
8×flip3-- prod-exp cbrt-unprod flip--
7×pow-prod-down
6×add-log-exp
4×expm1-log1p-u frac-times times-frac log1p-expm1-u difference-of-squares
3×fma-neg associate-/l* distribute-lft-out-- unswap-sqr
2×cbrt-undiv div-exp associate-*r/ *-commutative diff-cos
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-inv
Counts
4 → 119
Calls
4 calls:
234.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
12.0ms
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
55.0ms
(* (- (cos x) (cos y)) (sqrt (sqrt 2.0)))
13.0ms
(- (cos x) (cos y))

series2.6s

Counts
4 → 12
Calls
4 calls:
198.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
2.1s
(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
172.0ms
(* (- (cos x) (cos y)) (sqrt (sqrt 2.0)))
101.0ms
(- (cos x) (cos y))

simplify2.8s

Counts
131 → 131
Iterations
IterNodes
done5002
23373
1942
0347

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes387.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done40
140
035

end0.0ms

sample14.0s

Algorithm
intervals
Results
8.0s2762×body1280valid
3.3s1807×body640valid
1.5s807×body320valid
797.0ms2287×body80valid
197.0ms337×body160valid