Details

sample110.0ms

Algorithm

intervals

Results

51.0ms	77×	body	1280	valid
30.0ms	68×	body	640	valid
6.0ms	25×	body	320	valid
6.0ms	77×	body	80	valid
2.0ms	9×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	39	10
2	67	10
3	153	10
4	439	10
5	1830	10
6	5001	10
done	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`add-exp-log` `associate-/r*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 117

Calls

4 calls:

36.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms	(pow (sin ky) 2.0)
6.0ms	(pow (sin kx) 2.0)
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
103.0ms	(pow (sin ky) 2.0)
103.0ms	(pow (sin kx) 2.0)
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify37.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	341	1065
1	1159	981
2	5001	976
done	5001	976

prune446.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.1b

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

0.1b

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

0.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

19.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

8.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series1.0s

Counts

3 → 9

Calls

3 calls:

269.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

366.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

393.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify36.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	295	1114
1	1091	988
2	5001	986
done	5001	986

prune352.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.3b

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

0.3b

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

0.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

18.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

8.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series1.0s

Counts

3 → 9

Calls

3 calls:

267.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

392.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

349.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify40.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	291	1109
1	1164	984
2	5002	983
done	5002	983

prune366.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
0.2b	(/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
0.4b	(* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
0.4b	(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite136.0ms

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-r` `prod-exp`
23×	`associate-l`
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-*l/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 206

Calls

4 calls:

68.0ms	(* (* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
7.0ms	(/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
43.0ms	(* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
10.0ms	(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

381.0ms	(* (* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
295.0ms	(/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
316.0ms	(* (/ 1 (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))) (/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
355.0ms	(/ (sin ky) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify97.0ms

Counts

218 → 218

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	734	4689
1	3565	4030
2	5002	3684
done	5002	3684

prune606.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 9.2b

regimes727.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	11
1	15	11
done	15	11

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	2778×	body	1280	valid
735.0ms	1823×	body	640	valid
203.0ms	761×	body	320	valid
197.0ms	2295×	body	80	valid
65.0ms	343×	body	160	valid