Details

Time bar (total: 19.4s)

sample139.0ms

Algorithm
intervals
Results
66.0ms77×body1280valid
21.0ms65×body640valid
18.0ms252×body80valid
6.0ms25×body320valid
2.0ms12×body160valid

simplify140.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612613
714213
done14213

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
34.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
38.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
12.0ms
(/ (cos th) (sqrt 2.0))
12.0ms
(/ (cos th) (sqrt 2.0))

series454.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
160.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
79.0ms
(/ (cos th) (sqrt 2.0))
82.0ms
(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts
180 → 180
Iterations

Useful iterations: 2 (458.0ms)

IterNodesCost
01812118
15412012
228441832
done50011832

prune671.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.3b
(/ (pow a1 2) (sqrt 2.0))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
142×times-frac
121×add-sqr-sqrt
94×add-cube-cbrt *-un-lft-identity
77×sqrt-prod
53×associate-*r*
41×unpow-prod-down
33×add-exp-log
25×associate-*l* add-cbrt-cube
15×unpow2 sqr-pow
12×associate-/r* unswap-sqr
11×pow1 associate-/l*
10×prod-exp
9×div-exp
8×cbrt-unprod
5×cbrt-undiv
4×pow-prod-down div-inv add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num *-commutative
1×associate-*r/ associate-*l/
Counts
4 → 240
Calls
4 calls:
48.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
19.0ms
(/ (pow a1 2) (sqrt 2.0))
59.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
27.0ms
(/ (cos th) (sqrt 2.0))

series495.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
112.0ms
(/ (pow a1 2) (sqrt 2.0))
128.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
82.0ms
(/ (cos th) (sqrt 2.0))

simplify593.0ms

Counts
252 → 252
Iterations

Useful iterations: done (586.0ms)

IterNodesCost
03003180
17562865
done50012556

prune937.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
110×times-frac
101×add-sqr-sqrt
73×add-cube-cbrt *-un-lft-identity
61×sqrt-prod
60×associate-*r*
45×unpow-prod-down
34×add-exp-log
18×add-cbrt-cube
17×unpow2 sqr-pow
13×unswap-sqr
12×associate-/r*
10×div-exp prod-exp
9×associate-/l*
6×pow1 associate-*l*
4×cbrt-undiv pow-to-exp pow-exp cbrt-unprod add-log-exp
3×div-inv
2×frac-2neg clear-num *-commutative
1×associate-*r/ pow-prod-down
Counts
4 → 212
Calls
4 calls:
41.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
15.0ms
(* (cos th) (pow a2 2))
11.0ms
(/ (pow a1 2) (sqrt 2.0))
16.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series498.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
53.0ms
(* (cos th) (pow a2 2))
83.0ms
(/ (pow a1 2) (sqrt 2.0))
170.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify546.0ms

Counts
224 → 224
Iterations

Useful iterations: done (534.0ms)

IterNodesCost
02772813
16552493
done50012175

prune931.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
202×times-frac
90×add-sqr-sqrt
84×add-cube-cbrt *-un-lft-identity
78×cbrt-prod
53×add-exp-log
45×sqrt-prod
40×unpow-prod-down
23×div-exp
21×associate-/l*
18×add-cbrt-cube
16×associate-/r*
14×unpow2 sqr-pow
13×div-inv
12×prod-exp
9×cbrt-undiv
8×associate-*r*
6×pow-to-exp pow-exp
4×pow1 cbrt-unprod add-log-exp unswap-sqr
3×frac-2neg associate-*l* clear-num
1×*-commutative associate-/l/
Counts
4 → 241
Calls
4 calls:
29.0ms
(* (cos th) (pow a2 2))
22.0ms
(/ (pow a1 2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
43.0ms
(/ (/ (pow a1 2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
15.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series924.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (cos th) (pow a2 2))
549.0ms
(/ (pow a1 2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
106.0ms
(/ (/ (pow a1 2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
177.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify3.0s

Counts
253 → 253
Iterations

Useful iterations: 2 (1.6s)

IterNodesCost
03535004
17714476
244904038
done50004038

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes370.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01728
12028
done2028

end0.0ms

sample6.4s

Algorithm
intervals
Results
3.0s2519×body1280valid
1.1s2110×body640valid
999.0ms7835×body80valid
408.0ms1010×body320valid
109.0ms527×body160valid