Details

Time bar (total: 31.5s)

sample456.0ms

Algorithm
intervals
Results
211.0ms99×body1280valid
64.0ms56×body640valid
27.0ms31×body320valid
16.0ms54×body80valid
8.0ms16×body160valid

simplify1.6s

Counts
1 → 1

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.5b

localize44.0ms

Local error

Found 3 expressions with local error:

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

rewrite48.0ms

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:
Slowest
28.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
15.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series836.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
410.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
232.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
194.0ms
(hypot (sin kx) (sin ky))

simplify992.0ms

Counts
85 → 85

prune1.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.4b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

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:
Slowest
26.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
10.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series743.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
327.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
233.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
183.0ms
(hypot (sin kx) (sin ky))

simplify841.0ms

Counts
85 → 85

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
0.4b
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
0.2b
(/ 1 (sqrt (hypot (sin kx) (sin ky))))
0.2b
(* (sin th) (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
94×times-frac
67×*-un-lft-identity
64×add-exp-log
61×add-cube-cbrt
53×sqrt-prod
38×add-cbrt-cube
25×associate-*l* prod-exp
23×associate-*r*
19×div-exp
15×unswap-sqr
13×pow1 cbrt-unprod
12×associate-/r*
10×cbrt-undiv
6×associate-/l*
5×rec-exp 1-exp associate-*r/
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-flip
2×frac-times clear-num frac-2neg associate-*l/ *-commutative
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 210
Calls
4 calls:
Slowest
48.0ms
(* (sin th) (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
24.0ms
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
10.0ms
(/ 1 (sqrt (hypot (sin kx) (sin ky))))
8.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))

series931.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
295.0ms
(* (sin th) (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
249.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
217.0ms
(/ 1 (sqrt (hypot (sin kx) (sin ky))))
169.0ms
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))

simplify895.0ms

Counts
222 → 222

prune3.8s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
0.3b
(* (/ (sin th) (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
0.3b
(/ (sin th) (sqrt (hypot (sin kx) (sin ky))))
0.1b
(sqrt (hypot (sin kx) (sin ky)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
84×times-frac
61×*-un-lft-identity add-cube-cbrt
51×sqrt-prod
22×associate-*r* associate-*l*
20×add-cbrt-cube add-exp-log
12×associate-/r*
9×unswap-sqr
7×pow1
6×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 176
Calls
4 calls:
Slowest
38.0ms
(* (/ (sin th) (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
17.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
16.0ms
(/ (sin th) (sqrt (hypot (sin kx) (sin ky))))
2.0ms
(sqrt (hypot (sin kx) (sin ky)))

series957.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(* (/ (sin th) (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
265.0ms
(/ (sin th) (sqrt (hypot (sin kx) (sin ky))))
254.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
147.0ms
(sqrt (hypot (sin kx) (sin ky)))

simplify849.0ms

Counts
188 → 188

prune2.6s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.4b

regimes1.3s

Accuracy

0% (0.5b remaining)

Error of 9.3b against oracle of 8.8b and baseline of 9.3b

bsearch4.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
6.5s2738×body1280valid
2.5s1791×body640valid
1.3s751×body320valid
735.0ms2370×body80valid
276.0ms350×body160valid