Details

Time bar (total: 15.9s)

sample118.0ms

Algorithm
intervals
Results
38.0ms89×body1280valid
20.0ms70×body640valid
16.0ms264×body80valid
9.0ms42×body320valid
3.0ms20×body160valid

simplify139.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612513
713913
done13913

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.4b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×flip3-+ associate-*r* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
3 → 98
Calls
3 calls:
15.0ms
(+ (* a1 a1) (* a2 a2))
56.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
14.0ms
(/ (cos th) (sqrt 2.0))

series365.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* a1 a1) (* a2 a2))
259.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
77.0ms
(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts
107 → 107
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01581536
14801469
215991325
done50001322

prune485.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow a1 2) (cos th))
0.2b
(* (cos th) (pow a2 2))
0.3b
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))
0.3b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
30×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×times-frac prod-exp associate-/r* sqrt-prod
11×associate-*r* associate-*l*
8×unpow-prod-down div-exp unswap-sqr
4×pow1 cbrt-undiv pow-to-exp pow-exp cbrt-unprod unpow2 add-log-exp sqr-pow
2×frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 112
Calls
4 calls:
30.0ms
(* (pow a1 2) (cos th))
15.0ms
(* (cos th) (pow a2 2))
15.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))
27.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series407.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (pow a1 2) (cos th))
57.0ms
(* (cos th) (pow a2 2))
145.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))
136.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify1.6s

Counts
124 → 124
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01801380
14001260
214991116
done50011114

prune540.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a2 (cos th)) a2)
0.1b
(* a2 (cos th))
0.3b
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))
0.3b
(/ (* (* a2 (cos th)) a2) (sqrt 2.0))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
25×add-cbrt-cube
17×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×times-frac associate-/r* sqrt-prod
11×pow1
10×prod-exp
8×cbrt-unprod
7×div-exp
6×associate-*r*
5×cbrt-undiv
4×associate-*l* pow-prod-down add-log-exp
2×frac-2neg clear-num *-commutative div-inv associate-/l*
1×pow-to-exp pow-exp unswap-sqr
Counts
4 → 94
Calls
4 calls:
43.0ms
(* (* a2 (cos th)) a2)
17.0ms
(* a2 (cos th))
29.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))
45.0ms
(/ (* (* a2 (cos th)) a2) (sqrt 2.0))

series410.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* a2 (cos th)) a2)
56.0ms
(* a2 (cos th))
143.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))
159.0ms
(/ (* (* a2 (cos th)) a2) (sqrt 2.0))

simplify1.6s

Counts
106 → 106
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01561162
13711081
21432941
done5000939

prune464.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* a2 (cos th))
0.2b
(/ (/ (* (* a2 (cos th)) a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.2b
(/ (* (* a2 (cos th)) a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
66×add-exp-log
62×times-frac
42×add-cbrt-cube
40×add-sqr-sqrt
38×add-cube-cbrt *-un-lft-identity
36×cbrt-prod
24×sqrt-prod
23×div-exp
22×prod-exp
21×cbrt-undiv
20×cbrt-unprod
16×associate-/r*
13×div-inv
7×associate-/l*
6×pow1
4×add-log-exp
3×frac-2neg associate-*r* associate-*l* clear-num
1×pow-to-exp pow-prod-down pow-exp *-commutative associate-/l/ unswap-sqr
Counts
4 → 156
Calls
4 calls:
18.0ms
(* a2 (cos th))
48.0ms
(/ (/ (* (* a2 (cos th)) a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
56.0ms
(/ (* (* a2 (cos th)) a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
21.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
56.0ms
(* a2 (cos th))
554.0ms
(/ (/ (* (* a2 (cos th)) a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
475.0ms
(/ (* (* a2 (cos th)) a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
157.0ms
(/ (* (pow a1 2) (cos th)) (sqrt 2.0))

simplify1.6s

Counts
168 → 168
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02653637
16243223
223322777
done50012763

prune682.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes415.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02241
12941
done2941

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s2521×body1280valid
709.0ms2120×body640valid
626.0ms7985×body80valid
239.0ms1005×body320valid
85.0ms511×body160valid