Details

Time bar (total: 31.1s)

sample275.0ms

Algorithm
intervals
Results
150.0ms97×body1280valid
53.0ms54×body640valid
21.0ms75×body80valid
14.0ms21×body320valid
4.0ms9×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03250
17450
219247
369747
4290747
done500147

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.2b
(- (cos x) (cos y))

rewrite151.0ms

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:
24.0ms
(/ (/ (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)))
92.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (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)))
133.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
94.0ms
(- (cos x) (cos y))

simplify2.5s

Counts
260 → 260
Iterations

Useful iterations: done (2.5s)

IterNodesCost
065811736
1139410851
238959139
done50009131

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize103.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
2.2b
(- (cos x) (cos y))

rewrite14.0ms

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:
1.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
9.0ms
(- (cos x) (cos y))

series73.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
73.0ms
(- (cos x) (cos y))

simplify2.6s

Counts
74 → 74
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0124888
1246765
2552583
31846522
done5000513

prune943.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize49.0ms

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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.2b
(- (cos x) (cos y))

rewrite317.0ms

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:
129.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
22.0ms
(/ (/ (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)))
126.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms
(- (cos x) (cos y))

series2.4s

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
2.0s
(/ (/ (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)))
133.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
80.0ms
(- (cos x) (cos y))

simplify2.5s

Counts
280 → 280
Iterations

Useful iterations: done (2.5s)

IterNodesCost
068713457
1148612539
2455310707
done500010705

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize40.0ms

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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.2b
(- (cos x) (cos y))

rewrite680.0ms

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:
537.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
100.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series607.0ms

Counts
4 → 10
Calls
4 calls:
381.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
156.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
69.0ms
(- (cos x) (cos y))

simplify987.0ms

Counts
262 → 262
Iterations

Useful iterations: done (965.0ms)

IterNodesCost
05909605
114268446
done50017068

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes249.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04082
14682
done4682

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.4s2783×body1280valid
1.8s1879×body640valid
490.0ms732×body320valid
469.0ms2284×body80valid
141.0ms322×body160valid