Details

Time bar (total: 40.1s)

sample367.0ms

Algorithm
intervals
Results
200.0ms81×body1280valid
83.0ms63×body640valid
21.0ms27×body320valid
19.0ms72×body80valid
7.0ms13×body160valid

simplify2.6s

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize93.0ms

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
(* (- (cos x) (cos y)) (sqrt 2.0))
1.0b
(- 3.0 (sqrt 5.0))
1.8b
(- (cos x) (cos y))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
36×*-un-lft-identity
28×add-cube-cbrt
27×prod-diff
14×sqrt-prod
12×associate-*l*
11×pow1 add-cbrt-cube add-exp-log
10×associate-*l/
9×flip3-- flip--
8×add-log-exp
7×associate-*r*
6×fma-neg difference-of-squares
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out--
2×sub-neg diff-log associate-*r/ *-commutative diff-cos unswap-sqr
1×times-frac
Counts
4 → 131
Calls
4 calls:
118.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
43.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
13.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series374.0ms

Counts
4 → 10
Calls
4 calls:
182.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
112.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms
(- 3.0 (sqrt 5.0))
79.0ms
(- (cos x) (cos y))

simplify2.2s

Counts
141 → 141
Iterations
IterNodes
done5000
21967
1654
0273

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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))
0.3b
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
0.3b
(* (- (cos x) (cos y)) (sqrt 2.0))
1.8b
(- (cos x) (cos y))

rewrite231.0ms

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 insert-posit16 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 → 116
Calls
4 calls:
10.0ms
(/ (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))
153.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
54.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
10.0ms
(- (cos x) (cos y))

series2.4s

Counts
4 → 12
Calls
4 calls:
2.0s
(/ (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))
166.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
112.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
76.0ms
(- (cos x) (cos y))

simplify2.7s

Counts
128 → 128
Iterations
IterNodes
done5000
23057
1875
0331

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)))
0.3b
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
0.3b
(* (- (cos x) (cos y)) (sqrt 2.0))
1.8b
(- (cos x) (cos y))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
29×*-un-lft-identity
23×add-cube-cbrt
13×add-cbrt-cube add-exp-log
12×associate-*l*
11×pow1
10×times-frac associate-*l/
9×prod-diff
8×flip3-- flip--
7×associate-*r*
6×add-log-exp
4×expm1-log1p-u frac-times pow-prod-down prod-exp sqrt-prod cbrt-unprod insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* fma-neg associate-/l* distribute-lft-out--
2×associate-*r/ *-commutative diff-cos unswap-sqr
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
4 → 122
Calls
4 calls:
5.0ms
(/ (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)))
123.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
61.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
13.0ms
(- (cos x) (cos y))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.9s
(/ (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)))
172.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
146.0ms
(* (- (cos x) (cos y)) (sqrt 2.0))
83.0ms
(- (cos x) (cos y))

simplify2.3s

Counts
134 → 134
Iterations
IterNodes
done5001
22836
1829
0325

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize212.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sin x) (/ (sin y) 16.0)) (+ (sin x) (/ (sin y) 16.0)))
0.3b
(* (- (* (cos x) (* (cos x) (cos x))) (* (cos y) (* (cos y) (cos y)))) (sqrt 2.0))
0.4b
(+ (* (cos y) (cos y)) (* (cos x) (cos y)))
1.6b
(- (* (cos x) (* (cos x) (cos x))) (* (cos y) (* (cos y) (cos y))))

rewrite514.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*r* associate-*l* associate-*r/ cos-mult
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log add-log-exp
6×associate-*l/
5×sqr-cos flip3-- flip--
4×expm1-log1p-u frac-times flip3-+ cube-unmult sqrt-prod flip-+ insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in unswap-sqr
2×difference-cubes pow-prod-down prod-exp associate--l+ *-commutative frac-sub cbrt-unprod associate--r+ sub-div difference-of-squares
1×+-commutative associate-+l+ sum-log sub-neg fma-def times-frac distribute-rgt-out fma-neg diff-log prod-diff frac-add distribute-lft-out distribute-lft-out--
Counts
4 → 107
Calls
4 calls:
145.0ms
(* (- (sin x) (/ (sin y) 16.0)) (+ (sin x) (/ (sin y) 16.0)))
243.0ms
(* (- (* (cos x) (* (cos x) (cos x))) (* (cos y) (* (cos y) (cos y)))) (sqrt 2.0))
28.0ms
(+ (* (cos y) (cos y)) (* (cos x) (cos y)))
95.0ms
(- (* (cos x) (* (cos x) (cos x))) (* (cos y) (* (cos y) (cos y))))

series596.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (- (sin x) (/ (sin y) 16.0)) (+ (sin x) (/ (sin y) 16.0)))
185.0ms
(* (- (* (cos x) (* (cos x) (cos x))) (* (cos y) (* (cos y) (cos y)))) (sqrt 2.0))
102.0ms
(+ (* (cos y) (cos y)) (* (cos x) (cos y)))
118.0ms
(- (* (cos x) (* (cos x) (cos x))) (* (cos y) (* (cos y) (cos y))))

simplify2.0s

Counts
119 → 119
Iterations
IterNodes
done5009
22675
1742
0260

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes501.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify12.0ms

Iterations
IterNodes
done54
154
043

end0.0ms

sample13.7s

Algorithm
intervals
Results
6.9s2706×body1280valid
3.9s1814×body640valid
1.4s780×body320valid
716.0ms2334×body80valid
676.0ms366×body160valid