Details

Time bar (total: 53.5s)

sample543.0ms

Algorithm
intervals
Results
251.0ms91×body1280valid
88.0ms60×body640valid
75.0ms24×body320valid
22.0ms74×body80valid
4.0ms7×body160valid

simplify367.0ms

Calls
1 calls:
Slowest
366.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize56.0ms

Local error

Found 4 expressions with local error:

4.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity add-cube-cbrt
19×pow1
18×times-frac
15×sqrt-prod
10×add-cbrt-cube add-exp-log
6×associate-/r* sqrt-div swap-sqr associate-*r* associate-*l* sin-mult
4×insert-posit16 add-log-exp
3×associate-/r/ associate-/l*
2×pow2 flip3-+ pow-plus pow-prod-down frac-add prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ sqr-sin unswap-sqr
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
24.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
19.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms
(* (sin ky) (sin ky))
12.0ms
(* (sin kx) (sin kx))

series303.0ms

Calls
4 calls:
Slowest
159.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
102.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
21.0ms
(* (sin ky) (sin ky))
20.0ms
(* (sin kx) (sin kx))

simplify4.3s

Calls
115 calls:
Slowest
317.0ms
(sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
309.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
296.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
265.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
258.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.2b

localize30.0ms

Local error

Found 4 expressions with local error:

4.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
0.2b
(* (sin ky) (sin ky))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
93×add-sqr-sqrt
88×*-un-lft-identity add-cube-cbrt
39×sqrt-prod
22×associate-/r*
20×pow1
19×add-exp-log
13×add-cbrt-cube
7×div-exp
6×swap-sqr associate-*r* associate-*l*
5×div-inv
4×insert-posit16 sin-mult add-log-exp
3×cbrt-undiv sqrt-div associate-/l*
2×pow2 rec-exp pow-plus 1-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 frac-add associate-/r/ flip-+ pow-flip inv-pow
Calls
4 calls:
Slowest
14.0ms
(* (sin kx) (sin kx))
14.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
14.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin ky) (sin ky))

series314.0ms

Calls
4 calls:
Slowest
155.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
89.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
36.0ms
(* (sin ky) (sin ky))
33.0ms
(* (sin kx) (sin kx))

simplify12.9s

Calls
230 calls:
Slowest
481.0ms
(/ (* (* 1 1) 1) (* (* (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))))
359.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
325.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
314.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
275.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune3.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.2b

localize56.0ms

Local error

Found 4 expressions with local error:

4.6b
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity add-cube-cbrt
19×pow1
18×times-frac
15×sqrt-prod
10×add-cbrt-cube add-exp-log
6×associate-/r* sqrt-div swap-sqr associate-*r* associate-*l* sin-mult
4×insert-posit16 add-log-exp
3×associate-/r/ associate-/l*
2×pow2 flip3-+ pow-plus pow-prod-down frac-add prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ sqr-sin unswap-sqr
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
33.0ms
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
20.0ms
(/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
14.0ms
(* (sin kx) (sin kx))
11.0ms
(* (sin ky) (sin ky))

series336.0ms

Calls
4 calls:
Slowest
170.0ms
(/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
96.0ms
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
35.0ms
(* (sin kx) (sin kx))
34.0ms
(* (sin ky) (sin ky))

simplify4.7s

Calls
115 calls:
Slowest
376.0ms
(sqrt (+ (pow (* (sin ky) (sin ky)) 3) (pow (* (sin kx) (sin kx)) 3)))
331.0ms
(sqrt (+ (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
305.0ms
(sqrt (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))))
296.0ms
(- (+ (* 1/12 (* kx (pow ky 2))) kx) (* 1/6 (pow kx 3)))
257.0ms
(- (+ (pow kx 2) (* 2/45 (pow kx 6))) (* 1/3 (pow kx 4)))

prune1.8s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 10.7b

localize39.0ms

Local error

Found 4 expressions with local error:

4.6b
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b
(* (sin kx) (sin kx))
0.2b
(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
35×sqrt-prod
34×*-un-lft-identity
32×add-cube-cbrt
31×times-frac
22×associate-*r*
16×pow1
12×add-exp-log
10×add-cbrt-cube
9×associate-/r/
7×sin-mult
6×associate-*l*
5×unswap-sqr
4×insert-posit16 add-log-exp
3×rem-sqrt-square associate-/r* sqrt-pow1 flip3-+ swap-sqr frac-add flip-+ div-inv associate-/l*
2×sqrt-div div-exp pow-prod-down prod-exp *-commutative cbrt-unprod pow-flip inv-pow
1×pow2 cbrt-undiv rec-exp clear-num frac-2neg pow-plus pow1/2 1-exp associate-*r/ pow-sqr pow-prod-up sqr-sin
Calls
4 calls:
Slowest
63.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
29.0ms
(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
26.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
12.0ms
(* (sin kx) (sin kx))

series518.0ms

Calls
4 calls:
Slowest
180.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
159.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
138.0ms
(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
40.0ms
(* (sin kx) (sin kx))

simplify7.0s

Calls
121 calls:
Slowest
582.0ms
(/ (* (* 1 1) 1) (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
378.0ms
(sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
371.0ms
(+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
368.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
300.0ms
(sqrt (/ 1 (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3))))

prune1.9s

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 10.7b

regimes1.1s

Accuracy

0% (2.1b remaining)

Error of 12.0b against oracle of 9.9b and baseline of 12.0b

bsearch3.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
7.0s2760×body1280valid
2.9s1853×body640valid
701.0ms783×body320valid
646.0ms2279×body80valid
174.0ms325×body160valid