Details

Time bar (total: 33.7s)

sample377.0ms

Algorithm
intervals
Results
157.0ms86×body1280valid
123.0ms56×body640valid
26.0ms26×body320valid
21.0ms79×body80valid
5.0ms9×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
03250
17450
219247
369947
4339047
done500147

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize54.0ms

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))

rewrite125.0ms

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:
14.0ms
(/ (/ (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)))
75.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms
(- 3.0 (sqrt 5.0))
10.0ms
(- (cos x) (cos y))

series1.5s

Counts
4 → 10
Calls
4 calls:
1.3s
(/ (/ (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)))
107.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
63.0ms
(- (cos x) (cos y))

simplify1.1s

Counts
260 → 260
Iterations

Useful iterations: done (1.1s)

IterNodesCost
065811736
1157010876
done50009459

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize93.0ms

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))

rewrite20.0ms

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)
15.0ms
(- (cos x) (cos y))

series80.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
80.0ms
(- (cos x) (cos y))

simplify927.0ms

Counts
74 → 74
Iterations

Useful iterations: done (924.0ms)

IterNodesCost
0121864
1251738
2827598
done5001528

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0))
1.0b
(- 3.0 (sqrt 5.0))
2.2b
(- (cos x) (cos y))
3.1b
(/ (* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0)) (+ (sin x) (/ (sin y) 16.0)))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
37×*-un-lft-identity
29×add-cube-cbrt
27×prod-diff
14×sqrt-prod
11×add-exp-log add-cbrt-cube
8×add-log-exp
7×associate-*l* difference-of-squares
6×pow1 fma-neg associate-*r*
4×expm1-log1p-u flip3-- times-frac associate-*l/ associate-/r* flip-- log1p-expm1-u
2×cbrt-undiv sub-neg diff-log div-exp prod-exp associate-/r/ cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out-- unswap-sqr
1×unpow-prod-down frac-2neg flip3-+ pow-prod-down clear-num *-commutative flip-+ div-inv diff-cos associate-/l* unpow2 sqr-pow
Counts
4 → 126
Calls
4 calls:
65.0ms
(* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0))
9.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))
77.0ms
(/ (* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0)) (+ (sin x) (/ (sin y) 16.0)))

series470.0ms

Counts
4 → 10
Calls
4 calls:
145.0ms
(* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0))
0.0ms
(- 3.0 (sqrt 5.0))
84.0ms
(- (cos x) (cos y))
242.0ms
(/ (* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0)) (+ (sin x) (/ (sin y) 16.0)))

simplify1.9s

Counts
136 → 136
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03012933
17342546
232862078
done50002036

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (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))
2.2b
(- (cos x) (cos y))

rewrite301.0ms

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:
167.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
85.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms
(- 3.0 (sqrt 5.0))
16.0ms
(- (cos x) (cos y))

series469.0ms

Counts
4 → 10
Calls
4 calls:
222.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
153.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
94.0ms
(- (cos x) (cos y))

simplify1.3s

Counts
301 → 301
Iterations

Useful iterations: done (1.3s)

IterNodesCost
073512255
1200510968
done50009307

prune2.6s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0b

regimes542.0ms

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
03774
14374
done4374

end0.0ms

sample14.9s

Algorithm
intervals
Results
8.2s2672×body1280valid
3.7s1854×body640valid
1.3s2381×body80valid
964.0ms754×body320valid
218.0ms339×body160valid