Details

Time bar (total: 25.4s)

sample593.0ms

Algorithm
intervals
Results
171.0ms60×body640valid
151.0ms74×body1280valid
69.0ms11×body160valid
49.0ms78×body80valid
28.0ms33×body320valid

simplify1.1s

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
4.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
27×add-sqr-sqrt
26×add-cube-cbrt
25×sqrt-prod
24×times-frac
16×unpow-prod-down
10×distribute-lft-out
8×add-exp-log associate-/r*
7×pow1
6×pow-unpow add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
73.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms
(pow (sin ky) 2.0)
4.0ms
(pow (sin kx) 2.0)
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series659.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
154.0ms
(pow (sin ky) 2.0)
170.0ms
(pow (sin kx) 2.0)
133.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.7s

Counts
112 → 112

prune696.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
0.3b
(pow (sin kx) 2)
4.8b
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
49×add-sqr-sqrt times-frac
45×sqrt-prod
36×add-cube-cbrt
24×associate-*l*
23×unpow-prod-down
20×distribute-lft-out
11×add-exp-log
10×pow1
8×add-cbrt-cube
6×associate-/r/
5×associate-/r*
4×add-log-exp unswap-sqr
3×rem-sqrt-square pow-unpow sqrt-pow1 flip3-+ associate-*r* flip-+ div-inv associate-/l*
2×pow-flip sqrt-div div-exp inv-pow
1×cbrt-undiv pow-to-exp rec-exp pow-pow frac-2neg pow1/2 1-exp pow-prod-down associate-*l/ pow-exp prod-exp clear-num *-commutative cbrt-unprod unpow2 sqr-pow
Counts
4 → 138
Calls
4 calls:
58.0ms
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
113.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
6.0ms
(pow (sin kx) 2)
38.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
181.0ms
(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
27.0ms
(pow (sin kx) 2)
125.0ms
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify733.0ms

Counts
150 → 150

prune790.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
4.8b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
53.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series575.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(cbrt (sin kx))
147.0ms
(cbrt (sin kx))
167.0ms
(cbrt (sin kx))
104.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify1.3s

Counts
60 → 60

prune534.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 12.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.4b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
185×sqrt-prod
163×add-sqr-sqrt
144×times-frac
132×*-un-lft-identity
72×add-cube-cbrt
39×associate-*r* associate-*l*
28×add-exp-log unswap-sqr
24×unpow-prod-down distribute-lft-out
18×add-cbrt-cube
16×sqrt-div
11×associate-/r*
9×div-exp
8×pow1 prod-exp
6×associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 225
Calls
4 calls:
322.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
47.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
30.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
42.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series693.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
231.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
142.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
118.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.4s

Counts
237 → 237

prune1.4s

Pruning

26 alts after pruning (24 fresh and 2 done)

Merged error: 12.7b

regimes2.0s

Accuracy

63.7% (0.6b remaining)

Error of 11.9b against oracle of 11.3b and baseline of 12.9b

bsearch4.0ms

simplify565.0ms

end0.0ms

sample9.3s

Algorithm
intervals
Results
4.8s2705×body1280valid
2.4s1903×body640valid
900.0ms2277×body80valid
563.0ms749×body320valid
156.0ms366×body160valid