Details

Time bar (total: 47.2s)

sample458.0ms

Algorithm
intervals
Results
152.0ms81×body1280valid
75.0ms56×body640valid
64.0ms84×body80valid
21.0ms23×body320valid
7.0ms12×body160valid

simplify360.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
359.0ms
(* (/ (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: 11.9b

localize31.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b
(* (sin kx) (sin kx))
0.2b
(* (sin ky) (sin ky))
0.1b
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
31×associate-*r*
27×*-un-lft-identity add-cube-cbrt
21×pow1
20×times-frac
13×add-cbrt-cube add-exp-log sqrt-prod
9×associate-*l*
6×sqrt-div swap-sqr sin-mult
5×unswap-sqr
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×pow-prod-down associate-/r/ *-commutative
2×pow2 flip3-+ pow-plus frac-add pow-sqr pow-prod-up flip-+ sqr-sin
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*r/ div-inv
Counts
4 → 119
Calls
4 calls:
Slowest
102.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
21.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
20.0ms
(* (sin ky) (sin ky))
11.0ms
(* (sin kx) (sin kx))

series405.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
135.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
25.0ms
(* (sin ky) (sin ky))
24.0ms
(* (sin kx) (sin kx))

simplify5.2s

Counts
105 → 131
Calls
105 calls:
Slowest
381.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
342.0ms
(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
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
322.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
313.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.3b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
35×sqrt-prod
27×*-un-lft-identity
25×add-cube-cbrt
23×associate-*r*
22×times-frac
20×pow1
13×add-cbrt-cube add-exp-log
9×associate-*l*
6×associate-/r/
5×pow-prod-down prod-exp cbrt-unprod sin-mult unswap-sqr
4×insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 sqrt-div swap-sqr associate-*r/ *-commutative
2×flip3-+ frac-add flip-+ div-inv
1×pow2 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin pow-flip inv-pow
Counts
4 → 119
Calls
4 calls:
Slowest
72.0ms
(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
70.0ms
(* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
39.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
11.0ms
(* (sin kx) (sin kx))

series578.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(* (sin ky) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
190.0ms
(* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
158.0ms
(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
38.0ms
(* (sin kx) (sin kx))

simplify6.7s

Counts
101 → 131
Calls
101 calls:
Slowest
598.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (* (sin th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
590.0ms
(* (* (* (sin ky) (sin ky)) (sin ky)) (* (* (* (sin th) (sin th)) (sin th)) (* (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))))
362.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
359.0ms
(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))))))
339.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.8s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.3b

localize69.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.6b
(cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-div sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sin-mult
7×pow1
6×cbrt-prod
4×flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square cbrt-div sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 69
Calls
4 calls:
Slowest
19.0ms
(cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
18.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
18.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(cbrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
133.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
116.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
102.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify6.6s

Counts
45 → 81
Calls
45 calls:
Slowest
663.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
358.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
341.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
339.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
335.0ms
(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))

prune1.6s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 11.3b

localize35.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
1.3b
(exp (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
1.3b
(log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b
(* (sin kx) (sin kx))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×pow1
14×*-un-lft-identity add-cube-cbrt
12×log-prod
9×sqrt-div sqrt-prod
7×add-exp-log sin-mult
6×log-div exp-prod add-cbrt-cube exp-sum log-pow
4×insert-posit16 add-log-exp
3×sqrt-pow1 flip3-+ pow1/2 exp-diff swap-sqr associate-*r* associate-*l* frac-add flip-+
1×pow2 rem-sqrt-square pow-plus rem-log-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin unswap-sqr rem-exp-log
Counts
4 → 90
Calls
4 calls:
Slowest
29.0ms
(log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
25.0ms
(exp (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
21.0ms
(* (sin kx) (sin kx))
19.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
118.0ms
(exp (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
116.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms
(* (sin kx) (sin kx))

simplify5.4s

Counts
70 → 102
Calls
70 calls:
Slowest
395.0ms
(exp (log (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))
366.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
348.0ms
(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
335.0ms
(log (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3))))
320.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune1.7s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.3b

regimes1.4s

Accuracy

0% (1.6b remaining)

Error of 12.9b against oracle of 11.2b and baseline of 12.9b

bsearch6.0ms

end0.0ms

sample11.6s

Algorithm
intervals
Results
7.0s2668×body1280valid
2.7s1848×body640valid
809.0ms758×body320valid
710.0ms2349×body80valid
248.0ms377×body160valid