Details

sample839.0ms

Algorithm

intervals

Results

419.0ms	12×	body	160	valid
160.0ms	81×	body	1280	valid
86.0ms	69×	body	640	valid
21.0ms	25×	body	320	valid
19.0ms	69×	body	80	valid

simplify326.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

325.0ms

(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize53.0ms

Local error

Found 4 expressions with local error:

4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (sin kx) (sin kx))
0.2b	(* (sin ky) (sin ky))
0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite163.0ms

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:

Slowest

77.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
39.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
22.0ms	(* (sin kx) (sin kx))
22.0ms	(* (sin ky) (sin ky))

series392.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

251.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
97.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms	(* (sin kx) (sin kx))
20.0ms	(* (sin ky) (sin ky))

simplify4.9s

Counts

105 → 131

Calls

105 calls:

Slowest

331.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
325.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
323.0ms	(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
296.0ms	(sqrt (+ (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
289.0ms	(sqrt (+ (* (- (cos (- kx kx)) (cos (+ kx kx))) 2) (* 2 (- (cos (- ky ky)) (cos (+ ky ky))))))

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.3b

localize49.0ms

Local error

Found 4 expressions with local error:

4.1b	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

Slowest

363.0ms	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))
2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))

series521.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(cbrt (sin kx))
137.0ms	(cbrt (sin kx))
127.0ms	(cbrt (sin kx))
94.0ms	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))

simplify2.8s

Counts

28 → 64

Calls

28 calls:

Slowest

429.0ms	(sqrt (+ (pow (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) 3) (pow (* (sin ky) (sin ky)) 3)))
323.0ms	(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
250.0ms	(- (pow kx 1/3) (+ (* 1/18 (pow (pow kx 7) 1/3)) (* 1/3240 (pow (pow kx 13) 1/3))))
235.0ms	(- (pow kx 1/3) (+ (* 1/18 (pow (pow kx 7) 1/3)) (* 1/3240 (pow (pow kx 13) 1/3))))
233.0ms	(- (pow kx 1/3) (+ (* 1/18 (pow (pow kx 7) 1/3)) (* 1/3240 (pow (pow kx 13) 1/3))))

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.3b

localize64.0ms

Local error

Found 4 expressions with local error:

4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.4b	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite95.0ms

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:

Slowest

24.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
22.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
22.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

251.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
116.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
110.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
110.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify6.2s

Counts

62 → 98

Calls

62 calls:

Slowest

341.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))))
332.0ms	(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
327.0ms	(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))
295.0ms	(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
294.0ms	(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.3b

localize136.0ms

Local error

Found 4 expressions with local error:

4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite76.0ms

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:

Slowest

24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
22.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
17.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

114.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
114.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
108.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
93.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify5.5s

Counts

44 → 80

Calls

44 calls:

Slowest

336.0ms	(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
334.0ms	(sqrt (- (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx))) (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky)))))
321.0ms	(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
320.0ms	(sqrt (+ (pow (* (sin kx) (sin kx)) 3) (pow (* (sin ky) (sin ky)) 3)))
312.0ms	(- (+ (* 1/12 (* (pow kx 2) ky)) ky) (* 1/6 (pow ky 3)))

prune1.8s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 10.3b

regimes936.0ms

Accuracy

0% (1.5b remaining)

Error of 13.0b against oracle of 11.5b and baseline of 13.0b

bsearch3.0ms

end0.0ms

sample11.8s

Algorithm

intervals

Results

6.8s	2645×	body	1280	valid
3.1s	1864×	body	640	valid
859.0ms	791×	body	320	valid
668.0ms	2346×	body	80	valid
182.0ms	354×	body	160	valid