Details

sample501.0ms

Algorithm

intervals

Results

145.0ms	94×	body	1280	valid
110.0ms	53×	body	640	valid
59.0ms	76×	body	80	valid
11.0ms	18×	body	320	valid
9.0ms	15×	body	160	valid

simplify1.7s

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: 8.5b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

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` `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 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
7.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
20.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series785.0ms

Counts

3 → 9

Calls

3 calls:

184.0ms	(hypot (sin ky) (sin kx))
237.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
363.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.7s

Counts

82 → 82

Iterations

Iter	Nodes
3	2706
2	976
1	297
0	130

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (sin ky) (sin kx)))
0.1b	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
0.3b	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
0.4b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
306×	`add-sqr-sqrt`
281×	`*-un-lft-identity` `add-cube-cbrt`
272×	`sqrt-prod`
136×	`associate-r`
25×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
16×	`div-inv`
12×	`associate-/r*`
7×	`pow1` `cbrt-undiv` `div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 397

Calls

4 calls:

2.0ms	(sqrt (hypot (sin ky) (sin kx)))
29.0ms	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
14.0ms	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
7.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series1.0s

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt (hypot (sin ky) (sin kx)))
329.0ms	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
258.0ms	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
286.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify1.5s

Counts

409 → 409

Iterations

Iter	Nodes
2	3431
1	1147
0	427

prune6.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
0.3b	(* (* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx))))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
0.3b	(* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx)))))
0.4b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
73×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
54×	`add-exp-log`
44×	`associate-r` `sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-l` `pow-prod-down` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`un-div-inv` `pow-flip`
2×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 193

Calls

4 calls:

4.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
60.0ms	(* (* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx))))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
18.0ms	(* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx)))))
7.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series1.5s

Counts

4 → 12

Calls

4 calls:

596.0ms	(/ 1 (sqrt (hypot (sin ky) (sin kx))))
397.0ms	(* (* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx))))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
280.0ms	(* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx)))))
256.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify2.3s

Counts

205 → 205

Iterations

Iter	Nodes
2	2215
1	646
0	251

prune3.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (sin ky) (sin kx)))
0.1b	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
0.3b	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
0.4b	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
306×	`add-sqr-sqrt`
281×	`*-un-lft-identity` `add-cube-cbrt`
272×	`sqrt-prod`
136×	`associate-r`
25×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
16×	`div-inv`
12×	`associate-/r*`
7×	`pow1` `cbrt-undiv` `div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 397

Calls

4 calls:

1.0ms	(sqrt (hypot (sin ky) (sin kx)))
23.0ms	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
16.0ms	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
15.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series1.1s

Counts

4 → 12

Calls

4 calls:

212.0ms	(sqrt (hypot (sin ky) (sin kx)))
367.0ms	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))))
240.0ms	(/ (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))
266.0ms	(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify1.4s

Counts

409 → 409

Iterations

Iter	Nodes
2	3431
1	1147
0	427

prune5.7s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 8.4b

regimes1.2s

Accuracy

0% (0.5b remaining)

Error of 9.0b against oracle of 8.5b and baseline of 9.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample12.4s

Algorithm

intervals

Results

6.6s	2817×	body	1280	valid
3.1s	1844×	body	640	valid
1.1s	2282×	body	80	valid
1.1s	722×	body	320	valid
179.0ms	335×	body	160	valid