Details

sample563.0ms

Algorithm

intervals

Results

326.0ms	98×	body	1280	valid
77.0ms	61×	body	640	valid
18.0ms	24×	body	320	valid
18.0ms	64×	body	80	valid
4.0ms	9×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2046
7	2046
6	911
5	367
4	177
3	95
2	61
1	25
0	13

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite36.0ms

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))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
25.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series819.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(hypot (sin ky) (sin kx))
272.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
381.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify965.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2001
3	2001
2	1003
1	305
0	133

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite45.0ms

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))))

series807.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(hypot (sin ky) (sin kx))
251.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
382.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify977.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2001
3	2001
2	1003
1	305
0	133

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (log1p (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
0.2b	(log1p (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `pow-prod-down` `log1p-expm1` `associate-r/` `-commutative` `expm1-udef`

Counts

4 → 89

Calls

4 calls:

0.0ms	(expm1 (log1p (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))))
12.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
23.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
1.0ms	(log1p (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

329.0ms	(expm1 (log1p (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))))
267.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
373.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
328.0ms	(log1p (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx)))))

simplify1.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	2001
3	2001
2	917
1	311
0	143

prune2.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 6.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (sin ky) (sin kx)))
0.1b	(/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
0.2b	(* (sin th) (/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
0.5b	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
22×	`pow1`
21×	`sqrt-prod`
20×	`add-cbrt-cube` `add-exp-log`
18×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r`
9×	`sqrt-pow1` `pow1/2` `associate-l`
8×	`swap-sqr`
7×	`times-frac`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr` `associate-/l*`
2×	`*-commutative` `div-inv`
1×	`pow2` `rem-sqrt-square` `clear-num` `associate-/r` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/`

Counts

4 → 123

Calls

4 calls:

1.0ms	(sqrt (hypot (sin ky) (sin kx)))
13.0ms	(/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
54.0ms	(* (sin th) (/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
24.0ms	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

series927.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(sqrt (hypot (sin ky) (sin kx)))
231.0ms	(/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
339.0ms	(* (sin th) (/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
181.0ms	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

simplify1.2s

Counts

135 → 135

Iterations

Iter	Nodes
done	2004
3	2004
2	1274
1	417
0	171

prune1.8s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 6.9b

regimes960.0ms

Accuracy

0% (0.2b remaining)

Error of 9.1b against oracle of 8.9b and baseline of 9.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample12.0s

Algorithm

intervals

Results

7.1s	2761×	body	1280	valid
2.8s	1858×	body	640	valid
837.0ms	762×	body	320	valid
780.0ms	2289×	body	80	valid
189.0ms	330×	body	160	valid