Details

Time bar (total: 11.1s)

sample80.0ms

Algorithm
intervals
Results
26.0ms82×body1280valid
14.0ms68×body640valid
13.0ms272×body80valid
5.0ms37×body320valid
1.0ms13×body160valid

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01219
12513
24913
37613
49513
511113
612513
713913
done13913

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

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))

rewrite60.0ms

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:
8.0ms
(+ (* a1 a1) (* a2 a2))
39.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
10.0ms
(/ (cos th) (sqrt 2.0))

series296.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* a1 a1) (* a2 a2))
209.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
59.0ms
(/ (cos th) (sqrt 2.0))

simplify1.1s

Counts
107 → 107
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01581536
14801469
215991325
done50001322

prune280.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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-*r/
3×flip3-+ associate-*r* associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 62
Calls
3 calls:
8.0ms
(+ (* a1 a1) (* a2 a2))
23.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
21.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series349.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* a1 a1) (* a2 a2))
112.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
210.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify999.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (153.0ms)

IterNodesCost
01151083
13031038
21190886
done5000886

prune184.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 94
Calls
3 calls:
8.0ms
(+ (* a1 a1) (* a2 a2))
31.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
27.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series331.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* a1 a1) (* a2 a2))
213.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
91.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify1.8s

Counts
103 → 103
Iterations

Useful iterations: 3 (840.0ms)

IterNodesCost
01411776
13361685
211431547
336841541
done50001541

prune253.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×add-exp-log cbrt-prod add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
23×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×pow1 associate-/l* add-log-exp
4×associate-*r/
3×flip3-+ associate-*r* associate-*l* flip-+ associate-/l/
2×frac-2neg clear-num
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down sum-log *-commutative unswap-sqr
Counts
4 → 136
Calls
4 calls:
10.0ms
(+ (* a1 a1) (* a2 a2))
23.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
23.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
31.0ms
(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* a1 a1) (* a2 a2))
114.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
652.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
218.0ms
(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify874.0ms

Counts
148 → 148
Iterations

Useful iterations: done (863.0ms)

IterNodesCost
02254059
15743723
222023211
done50003201

prune401.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes236.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01834
12432
done2432

end0.0ms

sample2.5s

Algorithm
intervals
Results
811.0ms2546×body1280valid
547.0ms8036×body80valid
448.0ms2117×body640valid
157.0ms1047×body320valid
57.0ms561×body160valid