Details

Time bar (total: 2.2m)

sample481.0ms

Algorithm
intervals
Results
233.0ms96×body1280valid
69.0ms60×body640valid
22.0ms67×body80valid
19.0ms26×body320valid
3.0ms7×body160valid

simplify316.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
315.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize67.0ms

Local error

Found 4 expressions with local error:

3.4b
(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)))))

rewrite84.0ms

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
35.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin ky) (sin ky))
10.0ms
(* (sin kx) (sin kx))

series393.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
153.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
33.0ms
(* (sin ky) (sin ky))
22.0ms
(* (sin kx) (sin kx))

simplify4.6s

Counts
115 → 128
Calls
115 calls:
Slowest
352.0ms
(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))))))
310.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
304.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
299.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
261.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.4b

localize50.0ms

Local error

Found 4 expressions with local error:

3.4b
(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)))

rewrite77.0ms

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
24.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
22.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
15.0ms
(* (sin ky) (sin ky))
11.0ms
(* (sin kx) (sin kx))

series333.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
122.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
34.0ms
(* (sin ky) (sin ky))
33.0ms
(* (sin kx) (sin kx))

simplify13.5s

Counts
230 → 198
Calls
230 calls:
Slowest
627.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
439.0ms
(/ (* (* 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))))
384.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
350.0ms
(/ (* (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)))))
305.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))

prune2.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.4b

localize50.0ms

Local error

Found 4 expressions with local error:

3.4b
(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)))

rewrite149.0ms

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
79.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
21.0ms
(* (sin kx) (sin kx))
14.0ms
(* (sin ky) (sin ky))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
97.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
30.0ms
(* (sin kx) (sin kx))
24.0ms
(* (sin ky) (sin ky))

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))))
670.0ms
(/ (/ 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)))))
651.0ms
(/ (/ 1 (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))) (sqrt (/ 1 (sin ky))))
642.0ms
(/ (/ (* (* 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))))
525.0ms
(/ (/ (* (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)))))

prune7.0s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.4b

localize58.0ms

Local error

Found 4 expressions with local error:

3.4b
(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)))))

rewrite84.0ms

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)))))
22.0ms
(* (sin kx) (sin kx))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
10.0ms
(* (sin ky) (sin ky))

series304.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
97.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
31.0ms
(* (sin kx) (sin kx))
20.0ms
(* (sin ky) (sin ky))

simplify4.7s

Counts
115 → 128
Calls
115 calls:
Slowest
378.0ms
(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))))))
323.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
300.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
290.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
268.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.4b

regimes1.0s

Accuracy

0% (1.4b remaining)

Error of 12.5b against oracle of 11.1b and baseline of 12.5b

bsearch5.0ms

end0.0ms

sample12.1s

Algorithm
intervals
Results
6.7s2750×body1280valid
3.4s1854×body640valid
841.0ms2308×body80valid
700.0ms742×body320valid
242.0ms346×body160valid