Details

Time bar (total: 58.8s)

sample479.0ms

Algorithm
intervals
Results
262.0ms83×body1280valid
74.0ms60×body640valid
25.0ms76×body80valid
22.0ms28×body320valid
6.0ms9×body160valid

simplify306.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
305.0ms
(* (/ (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: 9.4b

localize40.0ms

Local error

Found 4 expressions with local error:

1.9b
(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)))))

rewrite100.0ms

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
39.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
31.0ms
(* (sin kx) (sin kx))
13.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(* (sin ky) (sin ky))

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
156.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
30.0ms
(* (sin ky) (sin ky))
19.0ms
(* (sin kx) (sin kx))

simplify4.8s

Counts
115 → 128
Calls
115 calls:
Slowest
341.0ms
(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))))))
329.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
300.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
293.0ms
(/ (* (* (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))))))
289.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.6b

localize66.0ms

Local error

Found 4 expressions with local error:

1.9b
(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)))

rewrite97.0ms

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
26.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
21.0ms
(* (sin ky) (sin ky))
21.0ms
(* (sin kx) (sin kx))

series405.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
200.0ms
(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
136.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
38.0ms
(* (sin ky) (sin ky))
30.0ms
(* (sin kx) (sin kx))

simplify13.3s

Counts
230 → 198
Calls
230 calls:
Slowest
473.0ms
(/ (* (* 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))))
338.0ms
(/ (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)))))
331.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
329.0ms
(/ (* (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)))))
323.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune3.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.6b

localize54.0ms

Local error

Found 4 expressions with local error:

1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.9b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.5b
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b
(* (sin ky) (sin ky))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
56×add-sqr-sqrt
54×sqrt-div
36×pow1
34×sqrt-pow1
22×*-un-lft-identity add-cube-cbrt
21×sin-mult
18×pow1/2 swap-sqr
12×associate-*r* associate-*l*
10×flip3-+ frac-add pow-prod-up flip-+ unswap-sqr
9×frac-times
8×add-cbrt-cube add-exp-log
6×pow-prod-down pow-sqr
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×pow2 rem-sqrt-square pow-plus prod-exp *-commutative cbrt-unprod
1×rem-square-sqrt sqrt-unprod sqr-sin
Counts
4 → 153
Calls
4 calls:
Slowest
154.0ms
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
19.0ms
(* (sin ky) (sin ky))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
127.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
118.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
20.0ms
(* (sin ky) (sin ky))

simplify12.9s

Counts
181 → 165
Calls
181 calls:
Slowest
845.0ms
(* (sqrt (sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))) (sqrt (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))))
451.0ms
(* (sqrt (sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))) (sqrt (sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))))
378.0ms
(* (sqrt (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))))))) (sqrt (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))))))))
377.0ms
(* (sqrt (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))))))) (sqrt (sqrt (- (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
361.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune2.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.6b

localize73.0ms

Local error

Found 4 expressions with local error:

15.0b
(log (* (sin kx) (sin kx)))
1.9b
(sqrt (+ (exp (log (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))
1.6b
(exp (log (* (sin kx) (sin kx))))
0.3b
(* (sin ky) (sin ky))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
28×pow1
13×add-sqr-sqrt
12×log-pow
10×*-un-lft-identity add-cube-cbrt
9×exp-prod add-exp-log
6×add-cbrt-cube
5×sin-mult
4×insert-posit16 add-log-exp
3×pow2 log-div pow-plus sqrt-div swap-sqr associate-*r* associate-*l* pow-prod-down pow-sqr pow-prod-up sqrt-prod
2×log-prod exp-diff rem-log-exp prod-exp
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 exp-sum frac-add *-commutative cbrt-unprod flip-+ sqr-sin unswap-sqr rem-exp-log
Counts
4 → 83
Calls
4 calls:
Slowest
59.0ms
(sqrt (+ (exp (log (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))
17.0ms
(log (* (sin kx) (sin kx)))
16.0ms
(exp (log (* (sin kx) (sin kx))))
11.0ms
(* (sin ky) (sin ky))

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(sqrt (+ (exp (log (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))
98.0ms
(log (* (sin kx) (sin kx)))
26.0ms
(* (sin ky) (sin ky))
19.0ms
(exp (log (* (sin kx) (sin kx))))

simplify2.9s

Counts
62 → 95
Calls
62 calls:
Slowest
322.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
317.0ms
(sqrt (- (* (exp (log (* (sin kx) (sin kx)))) (exp (log (* (sin kx) (sin kx))))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
294.0ms
(- (+ (* 2/45 (pow ky 6)) (pow ky 2)) (* 1/3 (pow ky 4)))
287.0ms
(sqrt (+ (pow (exp (log (* (sin kx) (sin kx)))) 3) (pow (* (sin ky) (sin ky)) 3)))
229.0ms
(sqrt (+ (* (exp (log (- (cos (- kx kx)) (cos (+ kx kx))))) 2) (* (exp (log 2)) (- (cos (- ky ky)) (cos (+ ky ky))))))

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.6b

regimes1.0s

Accuracy

0% (1.5b remaining)

Error of 12.4b against oracle of 10.9b and baseline of 12.4b

bsearch3.0ms

end0.0ms

sample12.3s

Algorithm
intervals
Results
7.0s2756×body1280valid
3.2s1805×body640valid
871.0ms742×body320valid
714.0ms2335×body80valid
276.0ms362×body160valid