Details

sample495.0ms

Algorithm

intervals

Results

159.0ms	83×	body	1280	valid
70.0ms	23×	body	320	valid
61.0ms	66×	body	640	valid
15.0ms	73×	body	80	valid
5.0ms	11×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
7	3537
6	1018
5	404
4	185
3	94
2	59
1	25
0	13

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.0b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite46.0ms

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:

0.0ms	(hypot (sin ky) (sin kx))
16.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
27.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series805.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(hypot (sin ky) (sin kx))
231.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
406.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.6s

Counts

85 → 85

Iterations

Iter	Nodes
3	2773
2	977
1	301
0	133

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.9b

localize32.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

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:

0.0ms	(hypot (sin kx) (sin ky))
11.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
13.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))

series768.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(hypot (sin kx) (sin ky))
253.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
380.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))

simplify1.7s

Counts

85 → 85

Iterations

Iter	Nodes
3	2496
2	958
1	300
0	133

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))))
0.3b	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
0.3b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))
0.3b	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))

rewrite109.0ms

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:

48.0ms	(* (sin th) (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))))
5.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
12.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))
38.0ms	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

302.0ms	(* (sin th) (* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))))
187.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
264.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))
262.0ms	(* (/ 1 (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))

simplify23.7s

Counts

222 → 222

Iterations

Iter	Nodes
3	6366
2	1956
1	718
0	266

prune3.1s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.9b

localize48.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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:

0.0ms	(hypot (sin ky) (sin kx))
7.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
13.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series773.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(hypot (sin ky) (sin kx))
233.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
360.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.4s

Counts

85 → 85

Iterations

Iter	Nodes
3	2773
2	977
1	301
0	133

prune1.1s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 7.9b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.8b and baseline of 8.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	13
1	13
0	11

end0.0ms

sample12.4s

Algorithm

intervals

Results

7.3s	2745×	body	1280	valid
2.7s	1875×	body	640	valid
1.2s	733×	body	320	valid
659.0ms	2312×	body	80	valid
190.0ms	335×	body	160	valid