Details

Time bar (total: 16.7s)

sample110.0ms

Algorithm
intervals
Results
41.0ms86×body1280valid
20.0ms268×body80valid
15.0ms49×body640valid
8.0ms32×body320valid
2.0ms13×body160valid

simplify131.0ms

Counts
1 → 1

prune53.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

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))

rewrite81.0ms

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))
56.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
13.0ms
(/ (cos th) (sqrt 2.0))

series431.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (* a1 a1) (* a2 a2))
308.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
76.0ms
(/ (cos th) (sqrt 2.0))

simplify795.0ms

Counts
107 → 107

prune368.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a1 2) (pow a2 2))
0.1b
(* (cos th) (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2.0)))
0.4b
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2.0))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
62×times-frac
48×add-sqr-sqrt
40×add-cube-cbrt
34×associate-*r* sqrt-prod
28×unpow-prod-down distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 associate-/l* add-log-exp
3×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 → 122
Calls
3 calls:
25.0ms
(+ (pow a1 2) (pow a2 2))
116.0ms
(* (cos th) (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2.0)))
49.0ms
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2.0))

series473.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ (pow a1 2) (pow a2 2))
314.0ms
(* (cos th) (/ (+ (pow a1 2) (pow a2 2)) (sqrt 2.0)))
115.0ms
(/ (+ (pow a1 2) (pow a2 2)) (sqrt 2.0))

simplify721.0ms

Counts
131 → 131

prune472.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a2 2) (pow a1 2))
0.1b
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.4b
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
62×times-frac
48×add-sqr-sqrt
40×add-cube-cbrt
34×associate-*r* sqrt-prod
28×unpow-prod-down distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 associate-/l* add-log-exp
3×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 → 122
Calls
3 calls:
16.0ms
(+ (pow a2 2) (pow a1 2))
91.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
84.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series557.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (pow a2 2) (pow a1 2))
340.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
169.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify728.0ms

Counts
131 → 131

prune464.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt (+ (pow a2 2) (pow a1 2))) (cos th)) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (sqrt 2.0)))
0.4b
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))
4.7b
(sqrt (+ (pow a2 2) (pow a1 2)))
4.7b
(sqrt (+ (pow a2 2) (pow a1 2)))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
127×*-un-lft-identity
126×sqrt-prod
96×times-frac
69×add-sqr-sqrt
67×add-cube-cbrt
52×associate-*r*
30×unpow-prod-down distribute-lft-out
18×add-exp-log add-cbrt-cube
11×pow1
10×sqrt-div
8×associate-/l*
6×associate-*l/ prod-exp associate-/r* cbrt-unprod
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 → 187
Calls
4 calls:
201.0ms
(* (* (sqrt (+ (pow a2 2) (pow a1 2))) (cos th)) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (sqrt 2.0)))
65.0ms
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))
26.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
47.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(* (* (sqrt (+ (pow a2 2) (pow a1 2))) (cos th)) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (sqrt 2.0)))
154.0ms
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))
46.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
49.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

simplify999.0ms

Counts
199 → 199

prune763.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes154.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.7s

end0.0ms

sample6.4s

Algorithm
intervals
Results
1.8s2498×body1280valid
1.7s8158×body80valid
1.3s2147×body640valid
803.0ms1031×body320valid
110.0ms522×body160valid