Details

Time bar (total: 52.0s)

sample437.0ms

Algorithm
intervals
Results
188.0ms83×body1280valid
72.0ms60×body640valid
24.0ms28×body320valid
22.0ms76×body80valid
4.0ms9×body160valid

simplify370.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
369.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.5b

localize25.0ms

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))

rewrite33.0ms

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
17.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
13.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms
(hypot (sin kx) (sin ky))

series663.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
342.0ms
(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
183.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))
137.0ms
(hypot (sin kx) (sin ky))

simplify3.4s

Counts
59 → 85
Calls
59 calls:
Slowest
416.0ms
(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
398.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
342.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))))
275.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
273.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.4b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
104×add-sqr-sqrt
92×*-un-lft-identity
90×add-cube-cbrt
44×associate-*r*
36×add-exp-log
20×add-cbrt-cube
16×associate-/r*
15×div-exp
10×div-inv
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* cbrt-unprod
2×clear-num frac-2neg associate-/r/
1×hypot-udef pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 196
Calls
4 calls:
Slowest
24.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
15.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
5.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series969.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
270.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
241.0ms
(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
161.0ms
(hypot (sin kx) (sin ky))

simplify13.9s

Counts
207 → 208
Calls
207 calls:
Slowest
718.0ms
(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))))
603.0ms
(* (* (* (sin th) (sin th)) (sin th)) (/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky)))))
473.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
471.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
456.0ms
(/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))

prune2.6s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.4b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r*
10×add-cbrt-cube add-exp-log
6×div-inv associate-/l*
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef associate-/r/
Counts
3 → 114
Calls
3 calls:
Slowest
15.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
5.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms
(hypot (sin kx) (sin ky))

series719.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
270.0ms
(/ (hypot (sin kx) (sin ky)) (sin ky))
266.0ms
(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
183.0ms
(hypot (sin kx) (sin ky))

simplify8.0s

Counts
132 → 123
Calls
132 calls:
Slowest
639.0ms
(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
531.0ms
(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
484.0ms
(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
458.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
439.0ms
(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))

prune1.5s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.4b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*l*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*r* 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-*l/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
14.0ms
(* (/ (sin th) (hypot (sin kx) (sin ky))) (sin ky))
12.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
0.0ms
(hypot (sin kx) (sin ky))

series779.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
318.0ms
(* (/ (sin th) (hypot (sin kx) (sin ky))) (sin ky))
259.0ms
(/ (sin th) (hypot (sin kx) (sin ky)))
201.0ms
(hypot (sin kx) (sin ky))

simplify3.5s

Counts
59 → 85
Calls
59 calls:
Slowest
465.0ms
(/ (* (* (sin th) (sin th)) (sin th)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
384.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
373.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
314.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin th))
296.0ms
(* (* (* (/ (sin th) (hypot (sin kx) (sin ky))) (/ (sin th) (hypot (sin kx) (sin ky)))) (/ (sin th) (hypot (sin kx) (sin ky)))) (* (* (sin ky) (sin ky)) (sin ky)))

prune1.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.4b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 8.6b against oracle of 8.4b and baseline of 8.6b

bsearch1.0ms

end0.0ms

sample11.6s

Algorithm
intervals
Results
5.7s2756×body1280valid
3.4s1805×body640valid
1.1s2335×body80valid
922.0ms742×body320valid
235.0ms362×body160valid