Details

Time bar (total: 32.7s)

sample580.0ms

Algorithm
intervals
Results
182.0ms91×body1280valid
149.0ms24×body320valid
115.0ms60×body640valid
58.0ms74×body80valid
3.0ms7×body160valid

simplify441.0ms

Calls
1 calls:
Slowest
440.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize35.0ms

Local error

Found 4 expressions with local error:

4.6b
(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))))

rewrite72.0ms

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
42.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
21.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.0ms
(pow (sin ky) 2)
2.0ms
(pow (sin kx) 2)

series381.0ms

Calls
4 calls:
Slowest
172.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
157.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
29.0ms
(pow (sin ky) 2)
23.0ms
(pow (sin kx) 2)

simplify2.7s

Calls
92 calls:
Slowest
253.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
247.0ms
(/ (* (* (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)))))
225.0ms
(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)))))
209.0ms
(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)))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.2b

localize8.0ms

Local error

Found 4 expressions with local error:

4.6b
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
0.3b
(pow (sin kx) 2)
0.2b
(pow (sin ky) 2)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt add-exp-log
9×add-cube-cbrt
8×pow1 unpow-prod-down
6×add-cbrt-cube associate-*r*
5×sqrt-prod
4×sqrt-div insert-posit16 add-log-exp
3×associate-*l*
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ flip-+ distribute-lft-out unpow2
1×rem-sqrt-square rec-exp pow1/2 pow-prod-down associate-*r/ un-div-inv *-commutative cbrt-unprod div-inv
Calls
4 calls:
Slowest
9.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
8.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
1.0ms
(pow (sin kx) 2)
1.0ms
(pow (sin ky) 2)

series292.0ms

Calls
4 calls:
Slowest
165.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
77.0ms
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
28.0ms
(pow (sin kx) 2)
22.0ms
(pow (sin ky) 2)

simplify2.1s

Calls
44 calls:
Slowest
422.0ms
(* (* (* (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))))))
254.0ms
(sqrt (- (* (pow (sin kx) 2) (pow (sin kx) 2)) (* (pow (sin ky) 2) (pow (sin ky) 2))))
230.0ms
(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)))))
204.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
124.0ms
(- (+ (pow kx 2) (* 2/45 (pow kx 6))) (* 1/3 (pow kx 4)))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.2b

localize25.0ms

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))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×sqrt-prod
13×associate-*r*
12×add-sqr-sqrt pow1
11×*-un-lft-identity add-cube-cbrt
9×add-exp-log associate-/r/
8×add-cbrt-cube
7×sin-mult
6×associate-*l*
4×insert-posit16 add-log-exp
3×associate-/r* flip3-+ frac-add flip-+ div-inv
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod
1×pow2 rem-sqrt-square rec-exp clear-num frac-2neg pow-plus pow1/2 associate-*r/ pow-prod-up sqr-sin pow-flip inv-pow
Calls
4 calls:
Slowest
12.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
10.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
7.0ms
(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.0ms
(* (sin kx) (sin kx))

series408.0ms

Calls
4 calls:
Slowest
156.0ms
(* (sin ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
133.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
100.0ms
(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
19.0ms
(* (sin kx) (sin kx))

simplify2.8s

Calls
57 calls:
Slowest
346.0ms
(* (* (* (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
(+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
285.0ms
(- (+ (* 7/360 (pow ky 3)) (* 1/6 ky)) (* 17/240 (* (pow kx 2) ky)))
275.0ms
(sqrt (/ 1 (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))))))
233.0ms
(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))))))

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.2b

localize10.0ms

Local error

Found 4 expressions with local error:

4.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.2b
(/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))

rewrite30.0ms

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
7×sin-mult
6×associate-/r* times-frac sqrt-div associate-*r* associate-*l*
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* associate-/l/
Calls
4 calls:
Slowest
14.0ms
(/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
7.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.0ms
(* (sin ky) (sin ky))
4.0ms
(* (sin kx) (sin kx))

series347.0ms

Calls
4 calls:
Slowest
185.0ms
(/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
112.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
30.0ms
(* (sin kx) (sin kx))
20.0ms
(* (sin ky) (sin ky))

simplify2.7s

Calls
72 calls:
Slowest
298.0ms
(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))))))
278.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
252.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
236.0ms
(sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))
201.0ms
(/ (* (* (* (sin th) (sin ky)) (* (sin th) (sin ky))) (* (sin th) (sin ky))) (* (* (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))))))

prune1.4s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 12.2b

regimes1.6s

Accuracy

0% (1.3b remaining)

Error of 12.0b against oracle of 10.6b and baseline of 12.0b

bsearch4.0ms

end0.0ms

sample12.2s

Algorithm
intervals
Results
6.6s2760×body1280valid
3.8s1853×body640valid
718.0ms783×body320valid
634.0ms2279×body80valid
241.0ms325×body160valid