Details

Time bar (total: 36.2s)

sample748.0ms

Algorithm
intervals
Results
258.0ms76×body1280valid
200.0ms62×body640valid
88.0ms73×body80valid
35.0ms31×body320valid
15.0ms14×body160valid

simplify103.0ms

Calls
1 calls:
Slowest
102.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize64.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin kx) 2)
0.3b
(pow (sin ky) 2)
0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
25×add-sqr-sqrt sqrt-prod
24×times-frac add-cube-cbrt
16×unpow-prod-down
10×distribute-lft-out
8×associate-/r* add-exp-log
6×pow1 add-cbrt-cube
4×sqrt-div insert-posit16 add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+ unpow2
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
22.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
18.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.0ms
(pow (sin ky) 2)
2.0ms
(pow (sin kx) 2)

series320.0ms

Calls
4 calls:
Slowest
161.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
122.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
19.0ms
(pow (sin kx) 2)
17.0ms
(pow (sin ky) 2)

simplify2.7s

Calls
92 calls:
Slowest
274.0ms
(sqrt (+ (* (pow (sin kx) 2) (pow (sin kx) 2)) (- (* (pow (sin ky) 2) (pow (sin ky) 2)) (* (pow (sin kx) 2) (pow (sin ky) 2)))))
242.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
237.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
236.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
123.0ms
(- (+ (* 2/45 (pow ky 6)) (pow ky 2)) (* 1/3 (pow ky 4)))

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.4b

localize18.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin kx) 2)
0.3b
(pow (sin ky) 2)
0.2b
(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
28×associate-/r*
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt
20×sqrt-prod
14×unpow-prod-down
9×add-exp-log
8×distribute-lft-out
7×pow1
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-to-exp rec-exp pow-pow sqrt-div pow-exp div-inv unpow2
1×rem-sqrt-square clear-num frac-2neg flip3-+ pow1/2 div-exp associate-/r/ flip-+ pow-flip inv-pow
Calls
4 calls:
Slowest
17.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
11.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
2.0ms
(pow (sin kx) 2)
2.0ms
(pow (sin ky) 2)

series280.0ms

Calls
4 calls:
Slowest
143.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
106.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
15.0ms
(pow (sin ky) 2)
15.0ms
(pow (sin kx) 2)

simplify1.3s

Calls
60 calls:
Slowest
233.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
210.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
92.0ms
(- (+ (* 2/45 (pow ky 6)) (pow ky 2)) (* 1/3 (pow ky 4)))
83.0ms
(- (+ (pow kx 2) (* 2/45 (pow kx 6))) (* 1/3 (pow kx 4)))
74.0ms
(sqrt (+ (pow (pow (sin kx) 2) 3) (pow (pow (sin ky) 2) 3)))

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.4b

localize17.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin kx) 2)
0.3b
(pow (sin ky) 2)
0.3b
(/ (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sin ky)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×*-un-lft-identity
20×add-sqr-sqrt
19×add-cube-cbrt
14×add-exp-log
13×div-inv
12×sqrt-div
11×associate-/r/
8×unpow-prod-down
6×pow1 flip3-+ add-cbrt-cube flip-+ associate-/l*
5×sqrt-prod
4×rec-exp associate-/r* div-exp insert-posit16 add-log-exp
2×pow-to-exp pow-pow pow-exp distribute-lft-out unpow2
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg pow1/2 associate-/l/
Calls
4 calls:
Slowest
17.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
9.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sin ky)))
1.0ms
(pow (sin kx) 2)
1.0ms
(pow (sin ky) 2)

series263.0ms

Calls
4 calls:
Slowest
134.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (sin ky)))
87.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
25.0ms
(pow (sin ky) 2)
17.0ms
(pow (sin kx) 2)

simplify7.8s

Calls
92 calls:
Slowest
1.6s
(/ (* (* (/ 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))))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))))
298.0ms
(/ (sqrt (+ (* (pow (sin kx) 2) (pow (sin kx) 2)) (- (* (pow (sin ky) 2) (pow (sin ky) 2)) (* (pow (sin kx) 2) (pow (sin ky) 2))))) (/ 1 (sin ky)))
297.0ms
(/ (sqrt (+ (* (pow (sin kx) 2) (pow (sin kx) 2)) (- (* (pow (sin ky) 2) (pow (sin ky) 2)) (* (pow (sin kx) 2) (pow (sin ky) 2))))) (/ 1 (sin ky)))
264.0ms
(/ (/ 1 (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))) 1)
263.0ms
(/ (sqrt (+ (* (pow (sin kx) 2) (pow (sin kx) 2)) (- (* (pow (sin ky) 2) (pow (sin ky) 2)) (* (pow (sin kx) 2) (pow (sin ky) 2))))) (sqrt (/ 1 (sin ky))))

prune1.7s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 10.4b

localize38.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.5b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin kx) 2)
0.3b
(pow (sin kx) 2)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
10×add-sqr-sqrt unpow-prod-down sqrt-prod
8×add-cube-cbrt
6×pow1 add-exp-log
4×add-cbrt-cube sqrt-div insert-posit16 distribute-lft-out add-log-exp
2×pow-to-exp rem-sqrt-square pow-pow flip3-+ pow1/2 pow-exp flip-+ unpow2
Calls
4 calls:
Slowest
18.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
8.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
1.0ms
(pow (sin kx) 2)
1.0ms
(pow (sin kx) 2)

series169.0ms

Calls
4 calls:
Slowest
70.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
66.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
19.0ms
(pow (sin kx) 2)
14.0ms
(pow (sin kx) 2)

simplify1.6s

Calls
38 calls:
Slowest
257.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
257.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
222.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
204.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
124.0ms
(- (+ (pow kx 2) (* 2/45 (pow kx 6))) (* 1/3 (pow kx 4)))

prune1.3s

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 10.4b

regimes2.0s

Accuracy

68.5% (0.4b remaining)

Error of 11.6b against oracle of 11.1b and baseline of 12.5b

bsearch20.0ms

end0.0ms

sample12.2s

Algorithm
intervals
Results
6.5s2669×body1280valid
3.6s1856×body640valid
919.0ms744×body320valid
751.0ms2385×body80valid
279.0ms346×body160valid