Details

Time bar (total: 3.6m)

sample463.0ms

Algorithm
intervals
Results
183.0ms75×body1280valid
84.0ms71×body640valid
21.0ms73×body80valid
20.0ms25×body320valid
12.0ms12×body160valid

simplify374.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
374.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize46.0ms

Local error

Found 4 expressions with local error:

1.8b
(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 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite101.0ms

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
38.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
25.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
21.0ms
(* (sin kx) (sin kx))
13.0ms
(* (sin ky) (sin ky))

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
127.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
40.0ms
(* (sin kx) (sin kx))
24.0ms
(* (sin ky) (sin ky))

simplify4.7s

Counts
115 → 128
Calls
115 calls:
Slowest
404.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
370.0ms
(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))))))
333.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
279.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
274.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.8b

localize47.0ms

Local error

Found 4 expressions with local error:

1.8b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))
0.2b
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

rewrite52.0ms

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
15.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
12.0ms
(* (sin kx) (sin kx))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin ky) (sin ky))

series368.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
132.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
30.0ms
(* (sin kx) (sin kx))
20.0ms
(* (sin ky) (sin ky))

simplify13.1s

Counts
230 → 198
Calls
230 calls:
Slowest
589.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
480.0ms
(/ (* (* 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))))
325.0ms
(/ (* (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 (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
311.0ms
(/ (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)))))

prune3.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.8b

localize67.0ms

Local error

Found 4 expressions with local error:

1.8b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))
0.2b
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))

rewrite116.0ms

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
51.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
18.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
14.0ms
(* (sin kx) (sin kx))
11.0ms
(* (sin ky) (sin ky))

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
101.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
33.0ms
(* (sin ky) (sin ky))
29.0ms
(* (sin kx) (sin kx))

simplify1.4m

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))))
640.0ms
(/ (/ (* (* 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))))
638.0ms
(/ (/ 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)))))
544.0ms
(/ (/ (* (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)))))
516.0ms
(/ (sqrt (- (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (/ 1 (sin ky)))

prune7.0s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.8b

localize37.0ms

Local error

Found 4 expressions with local error:

1.8b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.3b
(* (sin kx) (sin kx))
0.3b
(/ (/ 1 (sin ky)) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite139.0ms

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-/r*
20×add-cbrt-cube
19×pow1
15×flip3-+ frac-add flip-+
13×associate-/l*
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
58.0ms
(/ (/ 1 (sin ky)) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
27.0ms
(* (sin ky) (sin ky))
21.0ms
(* (sin kx) (sin kx))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series329.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(/ (/ 1 (sin ky)) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
114.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
39.0ms
(* (sin ky) (sin ky))
22.0ms
(* (sin kx) (sin kx))

simplify1.4m

Counts
773 → 481
Calls
773 calls:
Slowest
1.3s
(/ (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))) (* (* (/ 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)))))))
676.0ms
(/ (* (* (/ 1 (sin ky)) (/ 1 (sin ky))) (/ 1 (sin ky))) (/ (* (* 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)))))))
593.0ms
(/ (/ (* (* 1 1) 1) (* (* (sin ky) (sin ky)) (sin ky))) (/ (* (* 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)))))))
590.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin ky)) (cbrt (sin ky)))) (/ 1 (* (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
482.0ms
(/ 1 (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))

prune7.6s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.2b

regimes1.4s

Accuracy

0% (1.9b remaining)

Error of 12.3b against oracle of 10.4b and baseline of 12.3b

bsearch3.0ms

end0.0ms

sample12.4s

Algorithm
intervals
Results
6.7s2704×body1280valid
2.9s1869×body640valid
1.2s810×body320valid
716.0ms2246×body80valid
706.0ms371×body160valid