Details

Time bar (total: 25.8s)

sample311.0ms

Algorithm
intervals
Results
81.0ms59×body640valid
75.0ms78×body1280valid
14.0ms32×body320valid
9.0ms74×body80valid
3.0ms13×body160valid

simplify986.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite114.0ms

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:
45.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
9.0ms
(pow (sin ky) 2.0)
5.0ms
(pow (sin kx) 2.0)
51.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series643.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
162.0ms
(pow (sin ky) 2.0)
163.0ms
(pow (sin kx) 2.0)
125.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.6s

Counts
112 → 112

prune591.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
0.3b
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
38×add-sqr-sqrt
30×associate-*r*
28×times-frac
25×add-cube-cbrt
22×sqrt-prod
15×add-exp-log
14×unpow-prod-down
9×pow1 add-cbrt-cube
8×distribute-lft-out
6×pow-unpow
5×unswap-sqr
4×sqrt-div prod-exp add-log-exp
3×associate-*l*
2×pow-to-exp pow-pow flip3-+ div-exp pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 106
Calls
4 calls:
7.0ms
(pow (sin ky) 2.0)
7.0ms
(pow (sin kx) 2.0)
134.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
38.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series673.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(pow (sin ky) 2.0)
197.0ms
(pow (sin kx) 2.0)
187.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
107.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.0s

Counts
118 → 118

prune703.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (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))))) (/ (cbrt 1) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite449.0ms

Algorithm
rewrite-expression-head
Rules
245×sqrt-prod
228×add-sqr-sqrt
198×times-frac
164×*-un-lft-identity
92×add-cube-cbrt
72×associate-*r*
57×cbrt-prod
40×unswap-sqr
39×associate-*l*
30×unpow-prod-down distribute-lft-out
18×add-exp-log
16×sqrt-div add-cbrt-cube
11×associate-/r*
8×pow1
6×associate-/r/
5×cbrt-undiv flip3-+ div-exp flip-+
4×prod-exp cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 266
Calls
4 calls:
51.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
291.0ms
(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (cbrt 1) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
36.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
42.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series715.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(/ (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))))) (/ (cbrt 1) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
124.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
113.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.6s

Counts
278 → 278

prune1.7s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 10.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
30×cbrt-prod sqrt-prod
25×add-sqr-sqrt
24×times-frac
22×add-cube-cbrt
12×unpow-prod-down distribute-lft-out
8×sqrt-div
7×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 90
Calls
4 calls:
18.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
56.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
30.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
28.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
148.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
147.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
126.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts
102 → 102

prune663.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 10.7b

regimes1.6s

Accuracy

73.9% (0.3b remaining)

Error of 11.7b against oracle of 11.3b and baseline of 12.7b

bsearch9.0ms

simplify821.0ms

end0.0ms

sample9.1s

Algorithm
intervals
Results
4.6s2744×body1280valid
2.4s1818×body640valid
909.0ms2339×body80valid
519.0ms751×body320valid
179.0ms348×body160valid