Details

Time bar (total: 36.3s)

sample922.0ms

Algorithm
intervals
Results
399.0ms89×body1280valid
144.0ms24×body320valid
130.0ms59×body640valid
42.0ms15×body160valid
30.0ms69×body80valid

simplify40.0ms

Calls
1 calls:
Slowest
39.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune475.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize31.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(pow (sin ky) 2)
0.3b
(pow (sin kx) 2)
0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite58.0ms

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
24.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
12.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
1.0ms
(pow (sin ky) 2)
1.0ms
(pow (sin kx) 2)

series327.0ms

Calls
4 calls:
Slowest
165.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
120.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
25.0ms
(pow (sin kx) 2)
16.0ms
(pow (sin ky) 2)

simplify2.6s

Calls
92 calls:
Slowest
265.0ms
(/ (* (* (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)))))
220.0ms
(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)))))
196.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
196.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
108.0ms
(sqrt (+ (pow (pow (sin kx) 2) 3) (pow (pow (sin ky) 2) 3)))

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.8b

localize29.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.7b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.5b
(* (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
0.3b
(pow (sin ky) 2)

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
36×sqrt-prod
29×*-un-lft-identity
28×sqrt-div
15×add-sqr-sqrt
13×add-cube-cbrt
11×unpow-prod-down associate-*r* associate-*l*
10×pow1
8×flip3-+ flip-+ distribute-lft-out
7×add-exp-log
6×add-cbrt-cube pow1/2
4×frac-times insert-posit16 add-log-exp
2×rem-sqrt-square pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 pow-to-exp rem-square-sqrt pow-pow pow-plus sqrt-unprod pow-exp prod-exp *-commutative cbrt-unprod unpow2
Calls
4 calls:
Slowest
47.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
17.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
17.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
1.0ms
(pow (sin ky) 2)

series283.0ms

Calls
4 calls:
Slowest
95.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
91.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
83.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
15.0ms
(pow (sin ky) 2)

simplify4.7s

Calls
77 calls:
Slowest
313.0ms
(* (sqrt (sqrt (- (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (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)))))))
303.0ms
(* (sqrt (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 (sqrt (- (pow (sin kx) 2) (pow (sin ky) 2)))))
300.0ms
(* (sqrt (sqrt (+ (pow (pow (sin kx) 2) 3) (pow (pow (sin ky) 2) 3)))) (sqrt (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))))
287.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
271.0ms
(* (sqrt (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))) (sqrt (sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))))

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.8b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 associate-*r*
14×sqrt-prod
13×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
10×add-cbrt-cube add-exp-log
9×associate-*l*
6×associate-/r/ sin-mult
4×insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod
2×pow2 flip3-+ pow-plus sqrt-div frac-add pow-prod-up flip-+ sqr-sin div-inv
1×rem-sqrt-square pow1/2 associate-*r/
Calls
4 calls:
Slowest
18.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
9.0ms
(* (sin kx) (sin kx))
5.0ms
(* (sin ky) (sin ky))
5.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

series299.0ms

Calls
4 calls:
Slowest
142.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
118.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
24.0ms
(* (sin kx) (sin kx))
15.0ms
(* (sin ky) (sin ky))

simplify2.6s

Calls
63 calls:
Slowest
331.0ms
(* (* (* (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)))))))
278.0ms
(sqrt (/ 1 (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky)))))))
273.0ms
(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))))))
246.0ms
(sqrt (/ 1 (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))))))
244.0ms
(- (+ (* 7/360 (pow ky 3)) (* 1/6 ky)) (* 17/240 (* (pow kx 2) ky)))

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.8b

localize13.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))
0.2b
(/ (* (sin ky) (sqrt 1)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt pow1
13×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac sqrt-div associate-*r* associate-*l* sin-mult
4×insert-posit16 add-log-exp
3×prod-exp associate-/r/ cbrt-unprod
2×pow2 cbrt-undiv flip3-+ pow-plus div-exp pow-prod-down frac-add *-commutative pow-prod-up flip-+ sqr-sin
1×rem-sqrt-square clear-num frac-2neg pow1/2 div-inv associate-/l*
Calls
4 calls:
Slowest
28.0ms
(/ (* (sin ky) (sqrt 1)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
6.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.0ms
(* (sin kx) (sin kx))
4.0ms
(* (sin ky) (sin ky))

series260.0ms

Calls
4 calls:
Slowest
120.0ms
(/ (* (sin ky) (sqrt 1)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
99.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
22.0ms
(* (sin ky) (sin ky))
19.0ms
(* (sin kx) (sin kx))

simplify3.4s

Calls
71 calls:
Slowest
753.0ms
(/ (* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt 1) (sqrt 1)) (sqrt 1))) (* (* (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
376.0ms
(/ (* (* (* (sin ky) (sqrt 1)) (* (sin ky) (sqrt 1))) (* (sin ky) (sqrt 1))) (* (* (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
299.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
290.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
269.0ms
(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))))))

prune1.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.8b

regimes1.2s

Accuracy

0% (1.3b remaining)

Error of 12.5b against oracle of 11.2b and baseline of 12.5b

bsearch6.0ms

end0.0ms

sample12.3s

Algorithm
intervals
Results
6.4s2736×body1280valid
3.5s1816×body640valid
1.2s787×body320valid
783.0ms2296×body80valid
204.0ms365×body160valid