Details

Time bar (total: 2.2m)

sample980.0ms

Algorithm
intervals
Results
554.0ms66×body640valid
208.0ms81×body1280valid
43.0ms13×body320valid
20.0ms87×body80valid
4.0ms9×body160valid

simplify224.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
223.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize33.0ms

Local error

Found 4 expressions with local error:

4.8b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.1b
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite65.0ms

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
Counts
4 → 116
Calls
4 calls:
Slowest
19.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
18.0ms
(* (sin ky) (sin ky))
13.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms
(* (sin kx) (sin kx))

series270.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
97.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
20.0ms
(* (sin ky) (sin ky))
20.0ms
(* (sin kx) (sin kx))

simplify4.5s

Counts
115 → 128
Calls
115 calls:
Slowest
334.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
327.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
294.0ms
(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))))))
292.0ms
(- (+ (pow kx 2) (* 2/45 (pow kx 6))) (* 1/3 (pow kx 4)))
287.0ms
(/ (* (* (sin ky) (sin ky)) (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))))))

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize64.0ms

Local error

Found 4 expressions with local error:

4.8b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

rewrite73.0ms

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
Counts
4 → 186
Calls
4 calls:
Slowest
25.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
20.0ms
(* (sin ky) (sin ky))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin kx) (sin kx))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
99.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
34.0ms
(* (sin kx) (sin kx))
20.0ms
(* (sin ky) (sin ky))

simplify12.8s

Counts
230 → 198
Calls
230 calls:
Slowest
498.0ms
(/ (* (* 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))))
343.0ms
(/ (* (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)))))
314.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
304.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
297.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune2.9s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.0b

localize51.0ms

Local error

Found 4 expressions with local error:

4.8b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.2b
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
811×times-frac
382×add-sqr-sqrt
377×*-un-lft-identity add-cube-cbrt
129×sqrt-prod
48×add-exp-log
45×sqrt-div
43×associate-/r/
41×div-inv
32×div-exp sin-mult
25×associate-/l*
20×add-cbrt-cube
19×pow1
15×flip3-+ frac-add flip-+
13×associate-/r*
8×cbrt-undiv rec-exp 1-exp
6×swap-sqr associate-*r* associate-*l*
4×insert-posit16 add-log-exp
2×pow2 pow-plus 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 pow1/2 associate-/l/
Counts
4 → 469
Calls
4 calls:
Slowest
78.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
22.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
22.0ms
(* (sin kx) (sin kx))
22.0ms
(* (sin ky) (sin ky))

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
108.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
34.0ms
(* (sin kx) (sin kx))
30.0ms
(* (sin ky) (sin ky))

simplify1.3m

Counts
773 → 481
Calls
773 calls:
Slowest
1.1s
(/ (* (* (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))))
711.0ms
(/ (/ (* (* 1 1) 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)))))) (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))))
651.0ms
(/ (/ 1 (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
591.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (/ 1 (* (cbrt (sin ky)) (cbrt (sin ky)))))
573.0ms
(/ (/ 1 (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))) (sqrt (/ 1 (sin ky))))

prune7.3s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 12.0b

localize88.0ms

Local error

Found 4 expressions with local error:

16.7b
(cbrt (* (sin kx) (sin kx)))
16.7b
(cbrt (* (sin kx) (sin kx)))
16.7b
(cbrt (* (sin kx) (sin kx)))
4.8b
(sqrt (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
22×sin-mult
15×cbrt-div
9×sqrt-div
7×frac-add
6×add-sqr-sqrt
5×frac-times pow1 *-un-lft-identity associate-*l/ add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod pow1/3 associate-*r/ sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 56
Calls
4 calls:
Slowest
94.0ms
(sqrt (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))
10.0ms
(cbrt (* (sin kx) (sin kx)))
6.0ms
(cbrt (* (sin kx) (sin kx)))
5.0ms
(cbrt (* (sin kx) (sin kx)))

series559.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(cbrt (* (sin kx) (sin kx)))
155.0ms
(cbrt (* (sin kx) (sin kx)))
151.0ms
(cbrt (* (sin kx) (sin kx)))
90.0ms
(sqrt (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))

simplify3.8s

Counts
32 → 68
Calls
32 calls:
Slowest
396.0ms
(sqrt (+ (* (* (* (cbrt (- (cos (- kx kx)) (cos (+ kx kx)))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) 2) (* (* (* (cbrt 2) (cbrt 2)) (cbrt 2)) (- (cos (- ky ky)) (cos (+ ky ky))))))
319.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
273.0ms
(sqrt (- (* (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx))))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
235.0ms
(sqrt (+ (* (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) 2) (* (* (cbrt 2) (cbrt 2)) (- (cos (- ky ky)) (cos (+ ky ky))))))
223.0ms
(sqrt (+ (* (* (* (cbrt (- (cos (- kx kx)) (cos (+ kx kx)))) (cbrt (- (cos (- kx kx)) (cos (+ kx kx))))) (cbrt (* (sin kx) (sin kx)))) 2) (* (* (cbrt 2) (cbrt 2)) (- (cos (- ky ky)) (cos (+ ky ky))))))

prune1.1s

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 12.0b

regimes1.4s

Accuracy

0% (1.3b remaining)

Error of 12.8b against oracle of 11.4b and baseline of 12.8b

bsearch5.0ms

end0.0ms

sample11.4s

Algorithm
intervals
Results
6.2s2685×body1280valid
2.9s1834×body640valid
1.0s2370×body80valid
747.0ms720×body320valid
209.0ms391×body160valid