Details

Time bar (total: 30.8s)

sample668.0ms

Algorithm
intervals
Results
239.0ms84×body1280valid
134.0ms65×body640valid
55.0ms25×body320valid
25.0ms68×body80valid
9.0ms14×body160valid

simplify1.6s

Counts
1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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
12.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
9.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series730.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
306.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
291.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
132.0ms
(hypot (sin kx) (sin ky))

simplify922.0ms

Counts
85 → 85

prune929.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize25.0ms

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)))

rewrite75.0ms

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))))
1.0ms
(sqrt (hypot (sin kx) (sin ky)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
320.0ms
(* (/ (sin th) (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
279.0ms
(/ (sin th) (sqrt (hypot (sin kx) (sin ky))))
249.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
162.0ms
(sqrt (hypot (sin kx) (sin ky)))

simplify1.2s

Counts
188 → 188

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
0.3b
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
0.3b
(/ 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))))))

rewrite112.0ms

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
61.0ms
(* (sin th) (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
25.0ms
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
17.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
5.0ms
(/ 1 (sqrt (hypot (sin kx) (sin ky))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
326.0ms
(* (sin th) (* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
273.0ms
(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
199.0ms
(* (/ 1 (sqrt (hypot (sin kx) (sin ky)))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
170.0ms
(/ 1 (sqrt (hypot (sin kx) (sin ky))))

simplify857.0ms

Counts
222 → 222

prune3.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.6b

localize39.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

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
33.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
16.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series820.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
362.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
270.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
187.0ms
(hypot (sin kx) (sin ky))

simplify915.0ms

Counts
85 → 85

prune1.1s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 9.6b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 8.8b against oracle of 8.7b and baseline of 8.8b

bsearch2.0ms

end0.0ms

sample12.2s

Algorithm
intervals
Results
6.3s2715×body1280valid
3.5s1942×body640valid
1.2s2219×body80valid
798.0ms756×body320valid
239.0ms368×body160valid