Details

sample462.0ms

Algorithm

intervals

Results

268.0ms	101×	body	1280	valid
73.0ms	54×	body	640	valid
19.0ms	22×	body	320	valid
18.0ms	71×	body	80	valid
5.0ms	8×	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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.5b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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))
13.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series752.0ms

Counts

3 → 9

Calls

3 calls:

187.0ms	(hypot (sin ky) (sin kx))
336.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
228.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify1.8s

Counts

85 → 85

Iterations

Iter	Nodes
3	2640
2	996
1	302
0	133

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.2b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `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:

1.0ms	(expm1 (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx)))))
34.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
0.0ms	(log1p (expm1 (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))))
16.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series1.2s

Counts

4 → 12

Calls

4 calls:

320.0ms	(expm1 (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx)))))
325.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
298.0ms	(log1p (expm1 (* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))))
241.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify1.7s

Counts

101 → 101

Iterations

Iter	Nodes
3	2281
2	908
1	311
0	143

prune1.4s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.1b	(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
0.2b	(/ 1 (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac` `add-cbrt-cube`
14×	`associate-r`
13×	`prod-exp`
12×	`pow1`
7×	`cbrt-unprod`
6×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `associate-/l` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 111

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
30.0ms	(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
4.0ms	(/ 1 (hypot (sin ky) (sin kx)))
13.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

series947.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(hypot (sin ky) (sin kx))
384.0ms	(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
199.0ms	(/ 1 (hypot (sin ky) (sin kx)))
196.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

simplify2.9s

Counts

123 → 123

Iterations

Iter	Nodes
3	3277
2	1224
1	390
0	168

prune1.1s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 7.2b

localize38.0ms

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))))))
0.2b	(/ (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))))

rewrite53.0ms

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)))
28.0ms	(* (sin th) (/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
13.0ms	(/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
9.0ms	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

series929.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(sqrt (hypot (sin ky) (sin kx)))
325.0ms	(* (sin th) (/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))))
231.0ms	(/ (sin ky) (* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx)))))
195.0ms	(* (sqrt (hypot (sin ky) (sin kx))) (sqrt (hypot (sin ky) (sin kx))))

simplify3.6s

Counts

135 → 135

Iterations

Iter	Nodes
3	4643
2	1323
1	408
0	171

prune1.2s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 7.2b

regimes946.0ms

Accuracy

0% (0.2b remaining)

Error of 8.5b against oracle of 8.2b and baseline of 8.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.9s	2755×	body	1280	valid
2.7s	1787×	body	640	valid
1.2s	756×	body	320	valid
840.0ms	2351×	body	80	valid
619.0ms	351×	body	160	valid