Details

Time bar (total: 56.8s)

sample111.0ms

Algorithm
intervals
Results
38.0ms78×body1280valid
21.0ms68×body640valid
17.0ms242×body80valid
8.0ms39×body320valid
2.0ms12×body160valid

simplify154.0ms

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.3b
(/ (sqrt 2.0) (cos th))
0.3b
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite76.0ms

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:
6.0ms
(+ (* a1 a1) (* a2 a2))
7.0ms
(/ (sqrt 2.0) (cos th))
52.0ms
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series344.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (* a1 a1) (* a2 a2))
82.0ms
(/ (sqrt 2.0) (cos th))
212.0ms
(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify2.1s

Counts
167 → 167
Iterations
IterNodes
done5000
24529
1680
0250

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.1b
(/ (sqrt (sqrt 2.0)) (cos th))
0.2b
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (sqrt 2.0)) (cos th)))
0.3b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
2743×times-frac
1800×sqrt-prod
1264×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
67×div-inv
43×associate-/r* associate-/l*
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
6×add-log-exp
4×pow1
3×clear-num frac-2neg associate-/l/
2×flip3-+ flip-+
1×+-commutative sum-log associate-/r/
Counts
4 → 1158
Calls
4 calls:
12.0ms
(+ (* a1 a1) (* a2 a2))
14.0ms
(/ (sqrt (sqrt 2.0)) (cos th))
93.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (sqrt 2.0)) (cos th)))
32.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

series693.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ (* a1 a1) (* a2 a2))
128.0ms
(/ (sqrt (sqrt 2.0)) (cos th))
266.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (sqrt 2.0)) (cos th)))
254.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

simplify3.9s

Counts
1170 → 1170
Iterations
IterNodes
done5000
14653
01196

prune5.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×*-un-lft-identity add-cube-cbrt
22×associate-*l* sqrt-prod
10×add-cbrt-cube add-exp-log
6×associate-/r*
5×pow1 add-log-exp
3×associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative clear-num sum-log frac-2neg pow-prod-down associate-*l/ *-commutative
Counts
3 → 94
Calls
3 calls:
9.0ms
(+ (* a1 a1) (* a2 a2))
37.0ms
(* (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)) (cos th))
38.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series397.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ (* a1 a1) (* a2 a2))
239.0ms
(* (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)) (cos th))
114.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify1.3s

Counts
103 → 103
Iterations
IterNodes
done5002
21997
1365
0139

prune969.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (cbrt (sqrt 2.0))) (cos th))
0.2b
(* (/ 1 (fabs (cbrt (sqrt 2.0)))) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (cbrt (sqrt 2.0))) (cos th))))
0.3b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
0.3b
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (cbrt (sqrt 2.0))) (cos th)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
7202×times-frac
4632×sqrt-prod
3477×add-sqr-sqrt
3198×*-un-lft-identity
3177×add-cube-cbrt
1245×associate-*r*
1182×cbrt-prod
149×div-inv
97×add-exp-log
63×unswap-sqr
61×add-cbrt-cube
52×associate-/r* div-exp
46×associate-/l*
31×cbrt-undiv
20×prod-exp
13×associate-*l*
10×cbrt-unprod
6×pow1
5×rec-exp 1-exp
4×add-log-exp
3×clear-num frac-2neg associate-/l/
2×associate-/r/
1×frac-times flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
4 → 2810
Calls
4 calls:
15.0ms
(/ (sqrt (cbrt (sqrt 2.0))) (cos th))
657.0ms
(* (/ 1 (fabs (cbrt (sqrt 2.0)))) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (cbrt (sqrt 2.0))) (cos th))))
20.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
118.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (cbrt (sqrt 2.0))) (cos th)))

series2.4s

Counts
4 → 12
Calls
4 calls:
326.0ms
(/ (sqrt (cbrt (sqrt 2.0))) (cos th))
1.1s
(* (/ 1 (fabs (cbrt (sqrt 2.0)))) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (cbrt (sqrt 2.0))) (cos th))))
226.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
798.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (/ (sqrt (cbrt (sqrt 2.0))) (cos th)))

simplify6.5s

Counts
2822 → 2822
Iterations
IterNodes
done5000
02479

prune23.6s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes398.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
011

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.6s2508×body1280valid
1.5s2077×body640valid
1.2s7978×body80valid
936.0ms1041×body320valid
106.0ms518×body160valid