Details

Time bar (total: 2.5m)

sample664.0ms

Algorithm
intervals
Results
196.0ms84×body1280valid
78.0ms66×body640valid
24.0ms26×body320valid
17.0ms69×body80valid
6.0ms11×body160valid

simplify393.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
392.0ms
(* (/ (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: 12.3b

localize57.0ms

Local error

Found 4 expressions with local error:

3.2b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))
0.2b
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite127.0ms

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
40.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
37.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms
(* (sin kx) (sin kx))
23.0ms
(* (sin ky) (sin ky))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
139.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
35.0ms
(* (sin kx) (sin kx))
34.0ms
(* (sin ky) (sin ky))

simplify5.1s

Counts
115 → 128
Calls
115 calls:
Slowest
373.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
372.0ms
(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))))))
358.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
337.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
327.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.7b

localize42.0ms

Local error

Found 4 expressions with local error:

3.2b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))
0.2b
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

rewrite54.0ms

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
13.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
13.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin ky) (sin ky))
11.0ms
(* (sin kx) (sin kx))

series286.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
80.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
34.0ms
(* (sin kx) (sin kx))
27.0ms
(* (sin ky) (sin ky))

simplify14.5s

Counts
230 → 198
Calls
230 calls:
Slowest
704.0ms
(sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))
523.0ms
(/ (* (* 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))))
393.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
374.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
359.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune2.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.7b

localize42.0ms

Local error

Found 4 expressions with local error:

3.2b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))
0.2b
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))

rewrite70.0ms

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
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms
(* (sin ky) (sin ky))
13.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
11.0ms
(* (sin kx) (sin kx))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
103.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
35.0ms
(* (sin ky) (sin ky))
29.0ms
(* (sin kx) (sin kx))

simplify14.0s

Counts
230 → 198
Calls
230 calls:
Slowest
458.0ms
(/ (* (* 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))))
405.0ms
(/ (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)))))
397.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
355.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
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)))))

prune2.8s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.7b

localize41.0ms

Local error

Found 4 expressions with local error:

3.2b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))
0.2b
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))

rewrite134.0ms

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)))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin kx) (sin kx))
11.0ms
(* (sin ky) (sin ky))

series395.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(/ (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ 1 (sin ky)))
142.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
34.0ms
(* (sin kx) (sin kx))
33.0ms
(* (sin ky) (sin ky))

simplify1.4m

Counts
773 → 481
Calls
773 calls:
Slowest
1.2s
(/ (* (* (/ 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))))
750.0ms
(/ (/ (* (* 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))))
733.0ms
(/ (* (cbrt (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (cbrt (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (/ (sqrt 1) (* (cbrt (sin ky)) (cbrt (sin ky)))))
659.0ms
(/ (/ 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)))))
645.0ms
(/ (/ 1 (sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))) 1)

prune7.0s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.7b

regimes994.0ms

Accuracy

0% (1.3b remaining)

Error of 12.7b against oracle of 11.4b and baseline of 12.7b

bsearch3.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
6.0s2766×body1280valid
3.3s1811×body640valid
1.0s2305×body80valid
845.0ms772×body320valid
227.0ms346×body160valid