Details

sample516.0ms

Algorithm

intervals

Results

221.0ms	82×	body	1280	valid
97.0ms	71×	body	640	valid
22.0ms	72×	body	80	valid
21.0ms	24×	body	320	valid
4.0ms	7×	body	160	valid

simplify355.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

354.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize22.0ms

Local error

Found 3 expressions with local error:

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

20.0ms	(* (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))

series798.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

398.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
223.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
176.0ms	(hypot (sin kx) (sin ky))

simplify3.5s

Counts

59 → 85

Calls

59 calls:

Slowest

443.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
309.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
283.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
281.0ms	(* (* (* (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)))))
273.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune991.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.8b

localize21.0ms

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

rewrite56.0ms

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

33.0ms	(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
9.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
8.0ms	(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series945.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

306.0ms	(* (sin th) (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))))
222.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
219.0ms	(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))
198.0ms	(hypot (sin kx) (sin ky))

simplify14.7s

Counts

207 → 208

Calls

207 calls:

Slowest

624.0ms	(* (* (* (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)))))
564.0ms	(* (* (* (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)))))
498.0ms	(sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2)))
496.0ms	(/ (* (* 1 1) 1) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
467.0ms	(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))

prune2.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.8b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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

17.0ms	(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
6.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms	(hypot (sin kx) (sin ky))

series695.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

269.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
261.0ms	(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
165.0ms	(hypot (sin kx) (sin ky))

simplify7.7s

Counts

132 → 123

Calls

132 calls:

Slowest

541.0ms	(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
482.0ms	(/ (* (* (sin th) (sin th)) (sin th)) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
443.0ms	(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
424.0ms	(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
348.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.8s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.8b

localize39.0ms

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))

rewrite35.0ms

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

19.0ms	(* (/ (sin th) (hypot (sin kx) (sin ky))) (sin ky))
14.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series727.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

307.0ms	(* (/ (sin th) (hypot (sin kx) (sin ky))) (sin ky))
295.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
125.0ms	(hypot (sin kx) (sin ky))

simplify3.5s

Counts

59 → 85

Calls

59 calls:

Slowest

463.0ms	(/ (* (* (sin th) (sin th)) (sin th)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
374.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
321.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
320.0ms	(* (* (* (/ (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)))
277.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin th))

prune1.1s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 7.8b

regimes1.4s

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample11.8s

Algorithm

intervals

Results

7.3s	2740×	body	1280	valid
2.3s	1744×	body	640	valid
901.0ms	2347×	body	80	valid
812.0ms	816×	body	320	valid
345.0ms	353×	body	160	valid