Details

Time bar (total: 43.9s)

sample385.0ms

Algorithm
intervals
Results
204.0ms76×body1280valid
85.0ms61×body640valid
31.0ms90×body80valid
18.0ms18×body320valid
8.0ms11×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
03250
17450
219247
369747
4290747
done500147

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (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))
2.0b
(- (cos x) (cos y))

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
133×add-sqr-sqrt
123×prod-diff
119×*-un-lft-identity
109×add-cube-cbrt
56×times-frac
52×distribute-rgt-in distribute-lft-in
14×sqrt-prod
12×associate-*r* associate-*l*
9×flip3-- flip--
8×pow1 add-exp-log add-cbrt-cube add-log-exp difference-of-squares
6×sub-neg fma-neg div-inv
5×distribute-lft-out--
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×unswap-sqr
2×diff-log pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
Counts
4 → 234
Calls
4 calls:
120.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
99.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
16.0ms
(- 3.0 (sqrt 5.0))
27.0ms
(- (cos x) (cos y))

series341.0ms

Counts
4 → 10
Calls
4 calls:
131.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
122.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
88.0ms
(- (cos x) (cos y))

simplify2.2s

Counts
244 → 244
Iterations

Useful iterations: done (2.2s)

IterNodesCost
05387482
110736428
232314816
done50003982

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (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)))
0.2b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.0b
(- (cos x) (cos y))

rewrite277.0ms

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:
20.0ms
(/ (/ (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)))
94.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
113.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
29.0ms
(- (cos x) (cos y))

series2.3s

Counts
4 → 12
Calls
4 calls:
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)))
112.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
110.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
64.0ms
(- (cos x) (cos y))

simplify3.0s

Counts
280 → 280
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
068713457
1148512539
2454710707
done500010707

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)) (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0))
0.2b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.0b
(- (cos x) (cos y))

rewrite760.0ms

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 associate-/r* add-cbrt-cube
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-/l* unswap-sqr
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
1×frac-2neg diff-log clear-num associate-/r/
Counts
4 → 268
Calls
4 calls:
18.0ms
(/ (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)) (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0))
561.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
139.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms
(- (cos x) (cos y))

series2.4s

Counts
4 → 12
Calls
4 calls:
2.1s
(/ (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)) (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0))
132.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
148.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
90.0ms
(- (cos x) (cos y))

simplify2.9s

Counts
280 → 280
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
068013465
1144712535
2469410697
done500010697

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)) (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (* 0.0625 (sin x))) (- (cos x) (cos y))) 2.0) 3.0))
0.2b
(* (- (sin y) (* 0.0625 (sin x))) (- (cos x) (cos y)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.0b
(- (cos x) (cos y))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
153×add-sqr-sqrt
144×*-un-lft-identity
138×add-cube-cbrt
130×times-frac
105×prod-diff
52×distribute-rgt-in distribute-lft-in
13×add-exp-log associate-/r* add-cbrt-cube
12×associate-*r*
11×div-inv
9×associate-*l*
8×pow1 flip3-- flip--
6×add-log-exp
5×sub-neg
4×expm1-log1p-u frac-times associate-*r/ sqrt-prod log1p-expm1-u difference-of-squares
3×cbrt-undiv fma-neg div-exp associate-/l* distribute-lft-out-- unswap-sqr
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
1×frac-2neg diff-log clear-num associate-/r/
Counts
4 → 265
Calls
4 calls:
10.0ms
(/ (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)) (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (* 0.0625 (sin x))) (- (cos x) (cos y))) 2.0) 3.0))
86.0ms
(* (- (sin y) (* 0.0625 (sin x))) (- (cos x) (cos y)))
89.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
14.0ms
(- (cos x) (cos y))

series2.6s

Counts
4 → 12
Calls
4 calls:
2.2s
(/ (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)) (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (* 0.0625 (sin x))) (- (cos x) (cos y))) 2.0) 3.0))
181.0ms
(* (- (sin y) (* 0.0625 (sin x))) (- (cos x) (cos y)))
153.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
77.0ms
(- (cos x) (cos y))

simplify2.8s

Counts
277 → 277
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
067113421
1143312488
2468510649
done500010649

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes638.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03555
14155
done4155

end0.0ms

sample13.0s

Algorithm
intervals
Results
7.2s2725×body1280valid
3.3s1816×body640valid
1.1s2343×body80valid
739.0ms760×body320valid
313.0ms356×body160valid