Details

Time bar (total: 10.3s)

sample96.0ms

Algorithm
intervals
Results
29.0ms73×body1280valid
18.0ms63×body640valid
17.0ms258×body80valid
9.0ms42×body320valid
3.0ms19×body160valid

simplify8.0ms

Counts
1 → 1

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize41.0ms

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))

rewrite69.0ms

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:
14.0ms
(+ (* a1 a1) (* a2 a2))
38.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
14.0ms
(/ (cos th) (sqrt 2.0))

series336.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* a1 a1) (* a2 a2))
240.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
65.0ms
(/ (cos th) (sqrt 2.0))

simplify49.0ms

Counts
107 → 107

prune299.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite148.0ms

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))
71.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
55.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series651.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (pow a2 2) (pow a1 2))
512.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
109.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify45.0ms

Counts
131 → 131

prune297.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0)))
0.4b
(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0))))
5.6b
(sqrt (+ (pow a2 2) (pow a1 2)))
5.6b
(sqrt (+ (pow a2 2) (pow a1 2)))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
187×*-un-lft-identity
184×times-frac
183×sqrt-prod
161×add-sqr-sqrt
114×cbrt-prod
99×add-cube-cbrt
76×associate-*r*
44×unpow-prod-down distribute-lft-out
27×add-exp-log
21×unswap-sqr
19×add-cbrt-cube
12×associate-*l*
9×associate-/r*
8×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l*
6×sqrt-div
4×add-log-exp
3×flip3-+ flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 270
Calls
4 calls:
45.0ms
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0)))
170.0ms
(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0))))
24.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
28.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0)))
107.0ms
(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (sqrt 2.0))))
44.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
41.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

simplify99.0ms

Counts
282 → 282

prune710.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0)))))
0.4b
(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0))))))
5.6b
(sqrt (+ (pow a2 2) (pow a1 2)))
5.6b
(sqrt (+ (pow a2 2) (pow a1 2)))

rewrite547.0ms

Algorithm
rewrite-expression-head
Rules
277×add-exp-log
150×cbrt-prod
149×times-frac
140×prod-exp
139×add-sqr-sqrt
137×*-un-lft-identity
117×sqrt-prod
101×associate-*r*
91×add-cbrt-cube
90×div-exp
68×add-cube-cbrt
60×cbrt-unprod
42×cbrt-undiv
30×unpow-prod-down distribute-lft-out
27×unswap-sqr
19×associate-*l*
16×rec-exp 1-exp
13×pow1
6×frac-times associate-*r/
4×sqrt-div pow-prod-down associate-*l/ add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 *-commutative flip-+
Counts
4 → 296
Calls
4 calls:
153.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0)))))
322.0ms
(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0))))))
25.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
24.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0)))))
118.0ms
(* (/ (sqrt (+ (pow a2 2) (pow a1 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (sqrt (+ (pow a2 2) (pow a1 2))) (cbrt (cbrt (sqrt 2.0))))))
39.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
40.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

simplify71.0ms

Counts
308 → 308

prune852.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes237.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.6s2544×body1280valid
1.1s8022×body80valid
746.0ms2134×body640valid
297.0ms1074×body320valid
72.0ms520×body160valid