Details

Time bar (total: 43.4s)

sample453.0ms

Algorithm
intervals
Results
194.0ms90×body1280valid
104.0ms51×body640valid
70.0ms16×body160valid
27.0ms78×body80valid
20.0ms21×body320valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03250
17450
219247
369747
4290747
done500147

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.2b
(- (cos x) (cos y))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
152×add-sqr-sqrt
143×*-un-lft-identity
137×add-cube-cbrt
130×times-frac
105×prod-diff
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
13×associate-/l*
11×add-exp-log add-cbrt-cube div-inv
8×add-log-exp
6×pow1 fma-neg associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip-- distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos associate-/l/
Counts
4 → 250
Calls
4 calls:
28.0ms
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
98.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms
(- 3.0 (sqrt 5.0))
18.0ms
(- (cos x) (cos y))

series1.6s

Counts
4 → 10
Calls
4 calls:
1.4s
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
138.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
95.0ms
(- (cos x) (cos y))

simplify2.4s

Counts
260 → 260
Iterations

Useful iterations: done (2.3s)

IterNodesCost
065811736
1139410851
238959139
done50009131

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.3b
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.2b
(- (cos x) (cos y))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
158×add-sqr-sqrt
146×*-un-lft-identity
138×add-cube-cbrt
131×times-frac
105×prod-diff
52×distribute-rgt-in distribute-lft-in
13×add-exp-log add-cbrt-cube associate-/l*
12×associate-*r* associate-*l*
11×div-inv
8×pow1 flip3-- flip--
6×add-log-exp difference-of-squares
5×sub-neg
4×expm1-log1p-u frac-times associate-*r/ sqrt-prod log1p-expm1-u distribute-lft-out--
3×cbrt-undiv fma-neg div-exp associate-/r* unswap-sqr
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
1×frac-2neg diff-log clear-num associate-/l/
Counts
4 → 268
Calls
4 calls:
115.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
19.0ms
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 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)))
120.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms
(- (cos x) (cos y))

series2.3s

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
1.9s
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 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)))
163.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
78.0ms
(- (cos x) (cos y))

simplify2.8s

Counts
280 → 280
Iterations

Useful iterations: done (2.7s)

IterNodesCost
068713457
1148612539
2455310707
done500010705

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (fma (log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.2b
(- (cos x) (cos y))
4.7b
(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
204×add-sqr-sqrt
197×*-un-lft-identity
193×add-cube-cbrt
184×times-frac
165×prod-diff
85×log-prod
82×distribute-rgt-in distribute-lft-in exp-sum
17×div-inv
13×associate-/l*
11×add-exp-log add-cbrt-cube
7×pow1 add-log-exp
6×associate-*r* associate-*l*
5×sub-neg
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×cbrt-undiv fma-neg div-exp associate-/r* log-pow difference-of-squares
2×flip3-- associate-*r/ flip-- distribute-lft-out-- unswap-sqr
1×exp-prod exp-to-pow frac-2neg diff-log rem-log-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos associate-/l/
Counts
4 → 310
Calls
4 calls:
23.0ms
(/ (/ (fma (log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 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)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
17.0ms
(- (cos x) (cos y))
46.0ms
(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
2.1s
(/ (/ (fma (log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 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)))
121.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
80.0ms
(- (cos x) (cos y))
127.0ms
(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

simplify2.7s

Counts
322 → 322
Iterations

Useful iterations: done (2.7s)

IterNodesCost
083716816
1169015078
2434312200
done500012193

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize93.0ms

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))
2.2b
(- (cos x) (cos y))

rewrite336.0ms

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:
183.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
86.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms
(- 3.0 (sqrt 5.0))
20.0ms
(- (cos x) (cos y))

series398.0ms

Counts
4 → 10
Calls
4 calls:
179.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
145.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
74.0ms
(- (cos x) (cos y))

simplify1.5s

Counts
301 → 301
Iterations

Useful iterations: done (1.5s)

IterNodesCost
073512255
1168210923
done50018176

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes334.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03455
13755
done3755

end0.0ms

sample15.9s

Algorithm
intervals
Results
8.8s2747×body1280valid
3.6s1854×body640valid
1.5s2316×body80valid
889.0ms745×body320valid
655.0ms338×body160valid