Details

Time bar (total: 32.1s)

sample430.0ms

Algorithm
intervals
Results
194.0ms85×body1280valid
85.0ms68×body640valid
20.0ms23×body320valid
18.0ms70×body80valid
9.0ms10×body160valid

simplify475.0ms

Calls
1 calls:
Slowest
474.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize49.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin kx) 2)
0.2b
(pow (sin ky) 2)
0.2b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
30×associate-*l*
24×add-sqr-sqrt times-frac
23×add-cube-cbrt
20×sqrt-prod
14×unpow-prod-down
11×add-exp-log
9×add-cbrt-cube
8×pow1 distribute-lft-out
4×sqrt-div insert-posit16 add-log-exp
3×associate-*r*
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+ unpow2
1×cbrt-undiv rem-sqrt-square pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Calls
4 calls:
Slowest
23.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
19.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.0ms
(pow (sin ky) 2)
2.0ms
(pow (sin kx) 2)

series408.0ms

Calls
4 calls:
Slowest
207.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
140.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
34.0ms
(pow (sin kx) 2)
27.0ms
(pow (sin ky) 2)

simplify2.7s

Calls
68 calls:
Slowest
264.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
243.0ms
(* (* (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (sin th) (sin th)) (sin th)))
237.0ms
(/ (sin ky) (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2)))))
219.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
124.0ms
(/ (sin ky) (sqrt (+ (pow (pow (sin kx) 2) 3) (pow (pow (sin ky) 2) 3))))

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.0b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.4b
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.3b
(pow (sin kx) 2)
0.3b
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
13×*-un-lft-identity
12×pow1
11×add-cbrt-cube
10×add-sqr-sqrt
9×associate-*l* add-cube-cbrt
7×prod-exp
5×unpow-prod-down sqrt-prod
4×sqrt-div associate-*r* pow-prod-down cbrt-unprod insert-posit16 add-log-exp
2×rec-exp flip3-+ associate-*l/ associate-/r/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow pow1/2 pow-exp associate-*r/ div-inv unpow2
Calls
4 calls:
Slowest
29.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
17.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
12.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
3.0ms
(pow (sin kx) 2)

series575.0ms

Calls
4 calls:
Slowest
226.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
209.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))
107.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
32.0ms
(pow (sin kx) 2)

simplify3.3s

Calls
48 calls:
Slowest
632.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (sin th) (sin th)) (sin th))))
488.0ms
(* (* (* (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (* (sin th) (sin th)) (sin th)))
244.0ms
(/ 1 (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2)))))
188.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
177.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune1.5s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 12.0b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.5b
(cbrt (sin ky))
0.5b
(cbrt (sin ky))
0.5b
(cbrt (sin ky))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt
5×sqrt-prod
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×unpow-prod-down sqrt-div distribute-lft-out
1×rem-sqrt-square flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
8.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))
1.0ms
(cbrt (sin ky))

series510.0ms

Calls
4 calls:
Slowest
167.0ms
(cbrt (sin ky))
138.0ms
(cbrt (sin ky))
118.0ms
(cbrt (sin ky))
87.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify1.1s

Calls
29 calls:
Slowest
267.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
213.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
174.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))
123.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))
112.0ms
(- (pow ky 1/3) (+ (* 1/3240 (pow (pow ky 13) 1/3)) (* 1/18 (pow (pow ky 7) 1/3))))

prune1.4s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 12.0b

localize11.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.6b
(cbrt (sin th))
0.6b
(cbrt (sin th))
0.6b
(cbrt (sin th))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt
5×sqrt-prod
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×unpow-prod-down sqrt-div distribute-lft-out
1×rem-sqrt-square flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
8.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
1.0ms
(cbrt (sin th))
1.0ms
(cbrt (sin th))
1.0ms
(cbrt (sin th))

series526.0ms

Calls
4 calls:
Slowest
144.0ms
(cbrt (sin th))
137.0ms
(cbrt (sin th))
125.0ms
(cbrt (sin th))
120.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify1.1s

Calls
29 calls:
Slowest
256.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
237.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
128.0ms
(- (pow th 1/3) (+ (* 1/18 (pow (pow th 7) 1/3)) (* 1/3240 (pow (pow th 13) 1/3))))
111.0ms
(- (pow th 1/3) (+ (* 1/18 (pow (pow th 7) 1/3)) (* 1/3240 (pow (pow th 13) 1/3))))
109.0ms
(- (pow th 1/3) (+ (* 1/18 (pow (pow th 7) 1/3)) (* 1/3240 (pow (pow th 13) 1/3))))

prune1.1s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 12.0b

regimes2.9s

Accuracy

64.1% (0.5b remaining)

Error of 11.9b against oracle of 11.4b and baseline of 12.7b

bsearch23.0ms

end0.0ms

sample12.3s

Algorithm
intervals
Results
6.3s2708×body1280valid
3.2s1869×body640valid
1.2s770×body320valid
1.2s2290×body80valid
196.0ms363×body160valid