Details

Time bar (total: 36.0s)

sample683.0ms

Algorithm
intervals
Results
325.0ms95×body1280valid
92.0ms56×body640valid
51.0ms70×body80valid
27.0ms23×body320valid
10.0ms12×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
73496
61008
5394
4173
382
247
125
013

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.2b
(* (sin kx) (sin kx))
0.3b
(* (sin ky) (sin ky))
5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite120.0ms

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:
53.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
11.0ms
(* (sin kx) (sin kx))
22.0ms
(* (sin ky) (sin ky))
31.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
34.0ms
(* (sin kx) (sin kx))
34.0ms
(* (sin ky) (sin ky))
103.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.4s

Counts
131 → 131
Iterations
IterNodes
34848
21705
1550
0214

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
12×sqrt-div
8×sin-mult
7×pow1
4×flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 86
Calls
4 calls:
11.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
32.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series574.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
89.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
115.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
122.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.4s

Counts
98 → 98
Iterations
IterNodes
45321
31825
2690
1311
0172

prune2.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.4b

localize82.0ms

Local error

Found 4 expressions with local error:

5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
6.2b
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
6.2b
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
6.2b
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt cbrt-div
8×*-un-lft-identity add-cube-cbrt sin-mult
5×pow1
4×flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 add-log-exp
3×pow1/3 sqrt-div sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
18.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
18.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
26.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
124.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
127.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
141.0ms
(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.6s

Counts
74 → 74
Iterations
IterNodes
43365
31309
2525
1209
099

prune2.2s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 12.4b

localize125.0ms

Local error

Found 4 expressions with local error:

5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
5.6b
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-div sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt sin-mult
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 frac-add add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 68
Calls
4 calls:
12.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
19.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
130.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
113.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
111.0ms
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.3s

Counts
80 → 80
Iterations
IterNodes
42136
3889
2355
1147
068

prune1.8s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 12.4b

regimes1.2s

Accuracy

0% (1.5b remaining)

Error of 12.4b against oracle of 11.0b and baseline of 12.4b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
227
127
022

end0.0ms

sample12.1s

Algorithm
intervals
Results
6.2s2705×body1280valid
3.3s1861×body640valid
1.3s752×body320valid
838.0ms2349×body80valid
259.0ms333×body160valid