Details

Time bar (total: 53.9s)

sample507.0ms

Algorithm
intervals
Results
256.0ms72×body1280valid
105.0ms66×body640valid
31.0ms81×body80valid
21.0ms21×body320valid
11.0ms16×body160valid

simplify336.0ms

Calls
1 calls:
Slowest
335.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize32.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
31×associate-*r*
27×*-un-lft-identity add-cube-cbrt
21×pow1
20×times-frac
13×add-cbrt-cube add-exp-log sqrt-prod
9×associate-*l*
6×sqrt-div swap-sqr sin-mult
5×unswap-sqr
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×pow-prod-down associate-/r/ *-commutative
2×pow2 flip3-+ pow-plus frac-add pow-sqr pow-prod-up flip-+ sqr-sin
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*r/ div-inv
Calls
4 calls:
Slowest
67.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
20.0ms
(* (sin ky) (sin ky))
13.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin kx) (sin kx))

series370.0ms

Calls
4 calls:
Slowest
228.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
99.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms
(* (sin ky) (sin ky))
20.0ms
(* (sin kx) (sin kx))

simplify5.0s

Calls
105 calls:
Slowest
350.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
348.0ms
(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))))))
330.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
307.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
303.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune2.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.1b

localize42.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.5b
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b
(* (sin kx) (sin kx))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
56×add-sqr-sqrt
54×sqrt-div
36×pow1
34×sqrt-pow1
22×*-un-lft-identity add-cube-cbrt
21×sin-mult
18×pow1/2 swap-sqr
12×associate-*r* associate-*l*
10×flip3-+ frac-add pow-prod-up flip-+ unswap-sqr
9×frac-times
8×add-cbrt-cube add-exp-log
6×pow-prod-down pow-sqr
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×pow2 rem-sqrt-square pow-plus prod-exp *-commutative cbrt-unprod
1×rem-square-sqrt sqrt-unprod sqr-sin
Calls
4 calls:
Slowest
87.0ms
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
22.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
10.0ms
(* (sin kx) (sin kx))

series367.0ms

Calls
4 calls:
Slowest
126.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
112.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
96.0ms
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
33.0ms
(* (sin kx) (sin kx))

simplify12.0s

Calls
181 calls:
Slowest
425.0ms
(* (sqrt (sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))) (sqrt (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))))
417.0ms
(* (sqrt (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))) (sqrt (sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))))
372.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
359.0ms
(* (sqrt (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))))))) (sqrt (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))))))))
359.0ms
(* (sqrt (sqrt (* 2 2))) (sqrt (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))))))))

prune2.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.1b

localize74.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.4b
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
12×sqrt-div
8×sin-mult
7×pow1
4×flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-div pow1/3 div-inv
Calls
4 calls:
Slowest
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
10.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

series524.0ms

Calls
4 calls:
Slowest
223.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
116.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
95.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
90.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify6.2s

Calls
62 calls:
Slowest
343.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))
330.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
306.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
303.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
298.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune1.8s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.1b

localize80.0ms

Local error

Found 4 expressions with local error:

5.2b
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.2b
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.2b
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt cbrt-div
8×*-un-lft-identity add-cube-cbrt sin-mult
5×pow1
4×flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 add-log-exp
3×pow1/3 sqrt-div sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
15.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
13.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
9.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series619.0ms

Calls
4 calls:
Slowest
169.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
166.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
144.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
139.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify6.2s

Calls
38 calls:
Slowest
655.0ms
(pow (+ (pow (sin ky) 2) (pow (sin kx) 2)) 1/3)
322.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
304.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
299.0ms
(cbrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
282.0ms
(- (+ (pow ky 2/3) (* 1/3 (* (pow kx 2) (pow (/ 1 (pow ky 4)) 1/3)))) (* 1/9 (pow (pow ky 8) 1/3)))

prune1.7s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 12.1b

regimes931.0ms

Accuracy

0% (1.5b remaining)

Error of 12.8b against oracle of 11.3b and baseline of 12.8b

bsearch5.0ms

end0.0ms

sample11.8s

Algorithm
intervals
Results
6.1s2680×body1280valid
3.7s1863×body640valid
849.0ms777×body320valid
777.0ms2321×body80valid
200.0ms359×body160valid