Details

Time bar (total: 20.6s)

sample148.0ms

Algorithm
intervals
Results
64.0ms65×body1280valid
24.0ms254×body80valid
24.0ms58×body640valid
10.0ms33×body320valid
4.0ms18×body160valid

simplify131.0ms

Counts
1 → 1
Iterations
IterNodes
done142
7142
6126
5111
495
376
249
125
012

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

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)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
93×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×sqrt-prod
25×associate-/r*
10×add-cbrt-cube add-exp-log
9×associate-/l*
6×div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1
2×clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×+-commutative sum-log associate-/r/
Counts
3 → 158
Calls
3 calls:
12.0ms
(+ (* a1 a1) (* a2 a2))
11.0ms
(/ (sqrt 2.0) (cos th))
51.0ms
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series336.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (* a1 a1) (* a2 a2))
62.0ms
(/ (sqrt 2.0) (cos th))
227.0ms
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify1.7s

Counts
167 → 167
Iterations
IterNodes
done5000
24529
1680
0250

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize38.0ms

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)) (* 1 (/ (sqrt 2.0) (cos th))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
21×times-frac
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×add-exp-log
14×add-cbrt-cube
12×sqrt-prod
9×associate-/l*
8×div-exp
5×cbrt-undiv add-log-exp
4×associate-/r* prod-exp
3×pow1
2×clear-num frac-2neg flip3-+ 1-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative sum-log associate-*r/ associate-/r/
Counts
3 → 78
Calls
3 calls:
6.0ms
(+ (* a1 a1) (* a2 a2))
6.0ms
(/ (sqrt 2.0) (cos th))
52.0ms
(/ (+ (* a1 a1) (* a2 a2)) (* 1 (/ (sqrt 2.0) (cos th))))

series353.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(+ (* a1 a1) (* a2 a2))
54.0ms
(/ (sqrt 2.0) (cos th))
247.0ms
(/ (+ (* a1 a1) (* a2 a2)) (* 1 (/ (sqrt 2.0) (cos th))))

simplify1.6s

Counts
87 → 87
Iterations
IterNodes
done5001
22573
1427
0161

prune494.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (* (sqrt (+ (pow a1 2) (pow a2 2))) (cos th))))
0.5b
(/ (sqrt 2.0) (* (sqrt (+ (pow a1 2) (pow a2 2))) (cos th)))
6.4b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.4b
(sqrt (+ (pow a1 2) (pow a2 2)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
74×sqrt-prod
61×*-un-lft-identity
59×add-sqr-sqrt
57×add-cube-cbrt
22×sqrt-div
18×add-cbrt-cube add-exp-log
17×associate-/r/
16×associate-*l/
13×associate-/r*
12×associate-/l*
11×flip3-+ flip-+
9×div-inv
7×cbrt-undiv div-exp
6×pow1
4×add-log-exp
2×rem-sqrt-square clear-num unpow-prod-down frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod distribute-lft-out associate-/l/
Counts
4 → 170
Calls
4 calls:
50.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (* (sqrt (+ (pow a1 2) (pow a2 2))) (cos th))))
47.0ms
(/ (sqrt 2.0) (* (sqrt (+ (pow a1 2) (pow a2 2))) (cos th)))
9.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
20.0ms
(sqrt (+ (pow a1 2) (pow a2 2)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (* (sqrt (+ (pow a1 2) (pow a2 2))) (cos th))))
220.0ms
(/ (sqrt 2.0) (* (sqrt (+ (pow a1 2) (pow a2 2))) (cos th)))
45.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
55.0ms
(sqrt (+ (pow a1 2) (pow a2 2)))

simplify1.6s

Counts
182 → 182
Iterations
IterNodes
done5001
23214
1630
0260

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0)))
0.3b
(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0))))
6.4b
(sqrt (+ (* a1 a1) (pow a2 2)))
6.4b
(sqrt (+ (* a1 a1) (pow a2 2)))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
31×add-cbrt-cube
27×add-sqr-sqrt
26×times-frac
19×*-un-lft-identity add-cube-cbrt sqrt-prod
18×cbrt-prod
16×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
13×associate-*r*
10×associate-*l*
9×associate-/r*
8×pow1
6×sqrt-div
4×add-log-exp
3×flip3-+ associate-*l/ flip-+ div-inv unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*r/ *-commutative associate-/l*
Counts
4 → 121
Calls
4 calls:
40.0ms
(/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0)))
142.0ms
(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0))))
12.0ms
(sqrt (+ (* a1 a1) (pow a2 2)))
21.0ms
(sqrt (+ (* a1 a1) (pow a2 2)))

series918.0ms

Counts
4 → 12
Calls
4 calls:
524.0ms
(/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0)))
279.0ms
(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0))))
46.0ms
(sqrt (+ (* a1 a1) (pow a2 2)))
68.0ms
(sqrt (+ (* a1 a1) (pow a2 2)))

simplify1.8s

Counts
133 → 133
Iterations
IterNodes
done5000
23670
1564
0194

prune906.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes523.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done18
218
117
013

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.6s2548×body1280valid
1.6s2177×body640valid
999.0ms7942×body80valid
328.0ms997×body320valid
194.0ms534×body160valid