Details

sample358.0ms

Algorithm

intervals

Results

124.0ms	81×	body	1280	valid
108.0ms	67×	body	640	valid
16.0ms	75×	body	80	valid
13.0ms	19×	body	320	valid
7.0ms	14×	body	160	valid

simplify301.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize35.0ms

Local error

Found 4 expressions with local error:

3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite165.0ms

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

100.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
20.0ms	(* (sin kx) (sin kx))
20.0ms	(* (sin ky) (sin ky))
20.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
124.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
31.0ms	(* (sin kx) (sin kx))
31.0ms	(* (sin ky) (sin ky))

simplify640.0ms

Counts: 141 → 131

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.1b

localize47.0ms

Local error

Found 4 expressions with local error:

3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b	(/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

78×	`sqrt-prod`
54×	`times-frac`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*` `sqrt-div`
8×	`add-cbrt-cube` `add-exp-log` `sin-mult`
6×	`pow1` `associate-/r/` `associate-/l*`
4×	`flip3-+` `frac-add` `flip-+` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 144

Calls

4 calls:

Slowest

38.0ms	(/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
22.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
17.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

220.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
184.0ms	(/ (sin th) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
118.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
104.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify679.0ms

Counts: 220 → 156

prune2.7s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.1b

localize85.0ms

Local error

Found 4 expressions with local error:

3.5b	(pow (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) 1/4)
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (sin th) (pow (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) 1/4))
0.3b	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
45×	`*-un-lft-identity`
44×	`add-cube-cbrt`
39×	`sqrt-prod`
35×	`unpow-prod-down`
23×	`add-exp-log`
20×	`associate-r`
9×	`associate-/r*` `sqrt-div` `associate-/r/`
8×	`add-cbrt-cube` `pow-exp` `sin-mult`
7×	`pow1`
6×	`prod-exp`
5×	`div-exp` `unswap-sqr`
4×	`flip3-+` `frac-add` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-l` `div-inv` `associate-/l*` `sqr-pow`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 152

Calls

4 calls:

Slowest

144.0ms	(* (sin th) (pow (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) 1/4))
23.0ms	(pow (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) 1/4)
22.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
19.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

206.0ms	(* (sin th) (pow (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) 1/4))
199.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
149.0ms	(pow (/ 1 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) 1/4)
112.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify555.0ms

Counts: 217 → 164

prune2.8s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 11.1b

localize35.0ms

Local error

Found 4 expressions with local error:

3.9b	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (fabs (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b	(* (sin kx) (sin kx))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1`
12×	`associate-r`
10×	`cbrt-prod`
9×	`cbrt-div`
8×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
7×	`sin-mult`
6×	`associate-l`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `sqrt-div` `swap-sqr` `frac-add` `associate-*r/` `flip-+`
2×	`pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 88

Calls

4 calls:

Slowest

55.0ms	(* (fabs (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
19.0ms	(* (sin kx) (sin kx))
13.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
9.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(* (fabs (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
141.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
113.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms	(* (sin kx) (sin kx))

simplify709.0ms

Counts: 114 → 100

prune1.8s

Pruning

16 alts after pruning (12 fresh and 4 done)

Merged error: 11.1b

regimes1.1s

Accuracy

0% (1.2b remaining)

Error of 12.3b against oracle of 11.1b and baseline of 12.3b

bsearch7.0ms

end0.0ms

sample12.4s

Algorithm

intervals

Results

7.3s	2781×	body	1280	valid
3.1s	1839×	body	640	valid
745.0ms	2301×	body	80	valid
724.0ms	725×	body	320	valid
226.0ms	354×	body	160	valid