Details

Time bar (total: 18.1s)

sample184.0ms

Algorithm
intervals
Results
92.0ms79×body1280valid
47.0ms67×body640valid
11.0ms77×body80valid
10.0ms22×body320valid
4.0ms11×body160valid

simplify767.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
03250
17450
218747
358747
4193547
done500047

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

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))
1.5b
(- (cos x) (cos y))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
184×add-sqr-sqrt
183×prod-diff
172×*-un-lft-identity
164×add-cube-cbrt
110×times-frac
82×distribute-rgt-in distribute-lft-in
14×sqrt-prod
12×associate-*r* div-inv
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
8×add-log-exp
7×associate-*l* difference-of-squares
6×sub-neg fma-neg
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod log1p-expm1-u distribute-lft-out--
2×diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 291
Calls
4 calls:
64.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
35.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series295.0ms

Counts
4 → 10
Calls
4 calls:
143.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
61.0ms
(- (cos x) (cos y))

simplify622.0ms

Counts
301 → 301
Iterations

Useful iterations: done (607.0ms)

IterNodesCost
073212252
1168810920
done500010032

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.5b
(- (cos x) (cos y))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
9×cbrt-prod prod-diff
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg pow1/3
1×sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 68
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
4.0ms
(- (cos x) (cos y))

series52.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
52.0ms
(- (cos x) (cos y))

simplify1.3s

Counts
74 → 74
Iterations

Useful iterations: 3 (356.0ms)

IterNodesCost
0125933
1258807
2700646
32980576
done5001576

prune612.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
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)))
1.5b
(- (cos x) (cos y))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
209×add-sqr-sqrt
199×*-un-lft-identity
193×add-cube-cbrt
185×times-frac
165×prod-diff
82×distribute-rgt-in distribute-lft-in
17×div-inv
16×add-exp-log add-cbrt-cube
13×associate-/l*
12×associate-*r*
11×pow1
10×associate-*r/
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg difference-of-squares
4×expm1-log1p-u frac-times pow-prod-down prod-exp sqrt-prod cbrt-unprod log1p-expm1-u
3×cbrt-undiv fma-neg div-exp associate-/r* distribute-lft-out--
2×associate-*l/ *-commutative unswap-sqr
1×frac-2neg diff-log clear-num diff-cos associate-/l/
Counts
4 → 325
Calls
4 calls:
5.0ms
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
62.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
180.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- (cos x) (cos y))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
136.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
59.0ms
(- (cos x) (cos y))

simplify755.0ms

Counts
337 → 337
Iterations

Useful iterations: done (735.0ms)

IterNodesCost
088018227
1209317028
done500016985

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

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))) (- (cos x) (cos y)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.5b
(- (cos x) (cos y))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
123×prod-diff
116×*-un-lft-identity
108×add-cube-cbrt
55×times-frac
52×distribute-rgt-in distribute-lft-in
30×flip3-- flip--
28×frac-times associate-*r/
15×pow1 add-exp-log add-cbrt-cube
14×associate-*l/ sqrt-prod
12×associate-*r*
8×add-log-exp
7×associate-*l* pow-prod-down prod-exp cbrt-unprod
6×sub-neg fma-neg div-inv difference-of-squares
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
2×diff-log *-commutative diff-cos unswap-sqr
Counts
4 → 252
Calls
4 calls:
159.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
35.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series377.0ms

Counts
4 → 10
Calls
4 calls:
230.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
54.0ms
(- (cos x) (cos y))

simplify522.0ms

Counts
262 → 262
Iterations

Useful iterations: done (510.0ms)

IterNodesCost
05909605
114388446
done50027975

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04297
15697
26097
36297
done6297

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.1s2767×body1280valid
1.3s1856×body640valid
359.0ms730×body320valid
332.0ms2330×body80valid
101.0ms317×body160valid