Details

Time bar (total: 29.5s)

sample192.0ms

Algorithm
intervals
Results
55.0ms80×body1280valid
55.0ms68×body640valid
29.0ms240×body80valid
15.0ms42×body320valid
7.0ms27×body160valid

simplify240.0ms

Counts
1 → 1
Iterations
IterNodes
done113
7113
6101
591
479
370
248
125
012

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.1b
(* (+ (* a1 a1) (* a2 a2)) (cos th))
0.4b
(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1 add-log-exp
4×associate-*l/
3×flip3-+ associate-*r* associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/
1×+-commutative frac-2neg pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 60
Calls
3 calls:
17.0ms
(+ (* a1 a1) (* a2 a2))
68.0ms
(* (+ (* a1 a1) (* a2 a2)) (cos th))
46.0ms
(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

series556.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ (* a1 a1) (* a2 a2))
184.0ms
(* (+ (* a1 a1) (* a2 a2)) (cos th))
309.0ms
(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

simplify2.3s

Counts
69 → 69
Iterations
IterNodes
done5000
2964
1282
0112

prune639.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.2b
(/ (sqrt 2.0) (cos th))
0.4b
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
93×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×sqrt-prod
25×associate-/r*
10×add-exp-log add-cbrt-cube
9×associate-/l*
6×div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1
2×frac-2neg flip3-+ clear-num flip-+ associate-/l/
1×+-commutative sum-log associate-/r/
Counts
3 → 158
Calls
3 calls:
17.0ms
(+ (* a1 a1) (* a2 a2))
15.0ms
(/ (sqrt 2.0) (cos th))
67.0ms
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series445.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ (* a1 a1) (* a2 a2))
78.0ms
(/ (sqrt 2.0) (cos th))
302.0ms
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify2.7s

Counts
167 → 167
Iterations
IterNodes
done5001
22051
1659
0250

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)) (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))))
0.4b
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
5.4b
(sqrt (+ (* a1 a1) (* a2 a2)))
5.4b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod
72×times-frac
61×add-sqr-sqrt
59×add-cube-cbrt *-un-lft-identity
40×associate-*l*
18×add-exp-log add-cbrt-cube
11×pow1
10×sqrt-div
6×associate-*r/ prod-exp associate-/r* cbrt-unprod associate-/l*
5×flip3-+ flip-+
4×add-log-exp
3×cbrt-undiv div-exp pow-prod-down
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-inv associate-/l/
1×sqrt-undiv frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 157
Calls
4 calls:
166.0ms
(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)) (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))))
39.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
25.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
17.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series626.0ms

Counts
4 → 12
Calls
4 calls:
301.0ms
(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)) (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))))
183.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
66.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
75.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify3.0s

Counts
169 → 169
Iterations
IterNodes
done5000
21309
1451
0179

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
0.3b
(* (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)) (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))))
5.4b
(sqrt (+ (* a1 a1) (* a2 a2)))
5.6b
(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
33×sqrt-prod
31×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*l*
13×pow1
12×sqrt-div
11×add-exp-log add-cbrt-cube
8×associate-*r/
7×associate-*r*
4×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ add-log-exp
3×rem-sqrt-square
2×frac-times sqrt-pow1 pow1/2 *-commutative div-inv unswap-sqr
1×associate-*l/
Counts
4 → 100
Calls
4 calls:
54.0ms
(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
140.0ms
(* (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)) (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))))
18.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
20.0ms
(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

series688.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
254.0ms
(* (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)) (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))))
105.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
130.0ms
(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

simplify4.9s

Counts
112 → 112
Iterations
IterNodes
done5030
33674
21147
1372
0165

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes642.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done16
116
013

end0.0ms

sample7.6s

Algorithm
intervals
Results
2.5s2452×body1280valid
1.9s2141×body640valid
1.9s8203×body80valid
442.0ms1047×body320valid
167.0ms487×body160valid