Details

Time bar (total: 30.6s)

sample564.0ms

Algorithm
intervals
Results
301.0ms98×body1280valid
117.0ms43×body640valid
27.0ms28×body320valid
24.0ms75×body80valid
8.0ms12×body160valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done2046
72046
6911
5367
4177
395
261
125
013

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.4b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (sin ky) (sin kx))
0.1b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 76
Calls
3 calls:
0.0ms
(hypot (sin ky) (sin kx))
17.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
38.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series805.0ms

Counts
3 → 9
Calls
3 calls:
161.0ms
(hypot (sin ky) (sin kx))
209.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
435.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.2s

Counts
85 → 85
Iterations
IterNodes
done2001
32001
21003
1305
0133

prune706.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.2b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (sin ky) (sin kx))
0.1b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b
(* (sin th) (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac prod-exp
8×pow1
5×cbrt-unprod
3×expm1-log1p-u associate-/r* div-exp associate-*l* pow-prod-down insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv 1-exp associate-*r/
1×hypot-udef clear-num frac-2neg associate-*r* *-commutative div-inv
Counts
3 → 67
Calls
3 calls:
0.0ms
(hypot (sin ky) (sin kx))
15.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
42.0ms
(* (sin th) (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))))

series769.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(hypot (sin ky) (sin kx))
243.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
346.0ms
(* (sin th) (* 1 (/ (sin ky) (hypot (sin ky) (sin kx)))))

simplify1.6s

Counts
76 → 76
Iterations
IterNodes
done2012
42012
31803
2740
1310
0140

prune531.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sin ky) (sin kx))
0.2b
(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
0.2b
(/ 1 (hypot (sin ky) (sin kx)))
0.3b
(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
28×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
20×times-frac add-cbrt-cube
14×associate-*r*
13×prod-exp
12×pow1
7×cbrt-unprod
6×div-exp associate-*l*
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp associate-/l* unswap-sqr
2×un-div-inv *-commutative div-inv
1×hypot-udef clear-num frac-2neg pow-flip inv-pow
Counts
4 → 111
Calls
4 calls:
0.0ms
(hypot (sin ky) (sin kx))
55.0ms
(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
8.0ms
(/ 1 (hypot (sin ky) (sin kx)))
25.0ms
(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

series1.0s

Counts
4 → 12
Calls
4 calls:
162.0ms
(hypot (sin ky) (sin kx))
416.0ms
(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
234.0ms
(/ 1 (hypot (sin ky) (sin kx)))
223.0ms
(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

simplify1.7s

Counts
123 → 123
Iterations
IterNodes
done2001
32001
21263
1393
0168

prune854.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin th) (* (sin ky) (/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))))
0.2b
(/ 1 (sqrt (hypot (sin ky) (sin kx))))
0.3b
(* (sin ky) (/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
0.3b
(/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
534×times-frac
318×add-sqr-sqrt
285×*-un-lft-identity
281×add-cube-cbrt
273×sqrt-prod
137×associate-*r*
54×add-exp-log
34×add-cbrt-cube
25×associate-/l*
20×pow1 div-exp
17×div-inv
16×prod-exp
12×associate-/r* unswap-sqr
10×cbrt-undiv cbrt-unprod
8×pow-flip
6×associate-*l* pow-div
5×sqrt-pow1 pow1/2
4×expm1-log1p-u rec-exp 1-exp pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/
2×clear-num frac-2neg *-commutative inv-pow
1×associate-/l/
Counts
4 → 434
Calls
4 calls:
49.0ms
(* (sin th) (* (sin ky) (/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))))
7.0ms
(/ 1 (sqrt (hypot (sin ky) (sin kx))))
44.0ms
(* (sin ky) (/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
19.0ms
(/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))

series1.0s

Counts
4 → 12
Calls
4 calls:
408.0ms
(* (sin th) (* (sin ky) (/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))))
197.0ms
(/ 1 (sqrt (hypot (sin ky) (sin kx))))
218.0ms
(* (sin ky) (/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
198.0ms
(/ (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))

simplify1.4s

Counts
446 → 446
Iterations
IterNodes
done2003
22003
11223
0452

prune2.0s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.1b

regimes1.2s

Accuracy

0% (0.3b remaining)

Error of 9.0b against oracle of 8.7b and baseline of 9.0b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done17
117
012

end0.0ms

sample13.0s

Algorithm
intervals
Results
6.6s2759×body1280valid
3.8s1835×body640valid
838.0ms2296×body80valid
800.0ms772×body320valid
637.0ms338×body160valid