Details

Time bar (total: 56.9s)

sample424.0ms

Algorithm
intervals
Results
242.0ms100×body1280valid
99.0ms48×body640valid
23.0ms25×body320valid
21.0ms77×body80valid
4.0ms6×body160valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0321087
1741087
21881012
36571012
430221012
done50041012

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize84.0ms

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))

rewrite226.0ms

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-cbrt-cube add-exp-log
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:
103.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
80.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
14.0ms
(- (cos x) (cos y))

series365.0ms

Counts
4 → 10
Calls
4 calls:
169.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
124.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
72.0ms
(- (cos x) (cos y))

simplify3.3s

Counts
301 → 301
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0735237851
11991219592
done5000198823

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

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) (* (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
(* (* (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))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
165×prod-diff
159×*-un-lft-identity
153×add-cube-cbrt
113×times-frac
82×distribute-rgt-in distribute-lft-in
16×add-cbrt-cube add-exp-log
13×div-inv
12×associate-*r*
11×pow1
10×associate-*r/
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg prod-exp cbrt-unprod difference-of-squares
4×expm1-log1p-u frac-times pow-prod-down sqrt-prod log1p-expm1-u
3×fma-neg associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp associate-*l/ *-commutative unswap-sqr
1×clear-num associate-/r* frac-2neg diff-log diff-cos
Counts
4 → 276
Calls
4 calls:
10.0ms
(/ (fma (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)) 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))
130.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
63.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
26.0ms
(- (cos x) (cos y))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.9s
(/ (fma (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)) 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))
164.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
97.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
77.0ms
(- (cos x) (cos y))

simplify3.7s

Counts
288 → 288
Iterations

Useful iterations: done (3.5s)

IterNodesCost
0781258066
12181241679
done5002221490

prune3.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

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) (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
(* (* (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))

rewrite243.0ms

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-cbrt-cube add-exp-log
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 associate-/r* fma-neg div-exp distribute-lft-out--
2×associate-*l/ *-commutative unswap-sqr
1×clear-num frac-2neg diff-log diff-cos associate-/l/
Counts
4 → 325
Calls
4 calls:
17.0ms
(/ (/ (fma (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)) 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)
134.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
62.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(- (cos x) (cos y))

series2.6s

Counts
4 → 12
Calls
4 calls:
2.2s
(/ (/ (fma (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)) 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
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
167.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
87.0ms
(- (cos x) (cos y))

simplify4.6s

Counts
337 → 337
Iterations

Useful iterations: done (4.5s)

IterNodesCost
0882349815
12403331284
done5001312030

prune4.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (fma (* (sqrt 2.0) (* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y))))) (- (cos x) (cos y)) 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 y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y))))
0.4b
(* (sqrt 2.0) (* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y)))))
2.7b
(- (cos x) (cos y))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
67×add-sqr-sqrt
65×*-un-lft-identity
63×add-cube-cbrt
27×prod-diff
25×distribute-rgt-in distribute-lft-in
16×add-cbrt-cube add-exp-log
13×flip3-- flip-- associate-/l*
12×associate-*r/
11×pow1
9×associate-*l*
8×frac-times
7×sub-neg
6×add-log-exp
5×div-inv
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ prod-exp cbrt-unprod log1p-expm1-u
3×cbrt-undiv associate-/r* fma-neg div-exp sqrt-prod
2×*-commutative
1×clear-num frac-2neg diff-log diff-cos distribute-lft-out-- difference-of-squares unswap-sqr associate-/l/
Counts
4 → 190
Calls
4 calls:
9.0ms
(/ (/ (fma (* (sqrt 2.0) (* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y))))) (- (cos x) (cos y)) 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)
36.0ms
(* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y))))
72.0ms
(* (sqrt 2.0) (* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y)))))
7.0ms
(- (cos x) (cos y))

series2.8s

Counts
4 → 12
Calls
4 calls:
2.4s
(/ (/ (fma (* (sqrt 2.0) (* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y))))) (- (cos x) (cos y)) 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)
152.0ms
(* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y))))
209.0ms
(* (sqrt 2.0) (* (- (sin y) (* 0.0625 (sin x))) (- (sin x) (* 0.0625 (sin y)))))
73.0ms
(- (cos x) (cos y))

simplify5.6s

Counts
202 → 202
Iterations

Useful iterations: done (5.5s)

IterNodesCost
0473197846
11222188341
24188184512
done5000184352

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes588.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0321132
1371132
done371132

end0.0ms

sample13.3s

Algorithm
intervals
Results
7.3s2753×body1280valid
3.5s1821×body640valid
1.3s2313×body80valid
711.0ms765×body320valid
191.0ms348×body160valid