Details

sample371.0ms

Algorithm

intervals

Results

136.0ms	94×	body	1280	valid
79.0ms	71×	body	80	valid
45.0ms	53×	body	640	valid
14.0ms	24×	body	320	valid
5.0ms	14×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	39	16
3	68	16
4	156	16
5	653	16
done	5000	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite142.0ms

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:

63.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
12.0ms	(pow (sin kx) 2.0)
7.0ms	(pow (sin ky) 2.0)
49.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series692.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
194.0ms	(pow (sin kx) 2.0)
143.0ms	(pow (sin ky) 2.0)
138.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.1s

Counts

129 → 129

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	178	1808
1	394	1625
2	1646	1559
done	5001	1558

prune819.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b

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

0.2b

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

0.2b

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

rewrite46.0ms

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)))

33.0ms

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

10.0ms

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

series1.5s

Counts

3 → 9

Calls

3 calls:

368.0ms

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

509.0ms

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

620.0ms

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

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	134	1912
1	311	1885
2	1346	1676
done	5000	1669

prune639.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
0.2b	(* (log1p (expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
0.2b	(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.3b	(expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
10.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
9.0ms	(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
1.0ms	(expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

506.0ms	(log1p (expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
526.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
519.0ms	(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
495.0ms	(expm1 (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify4.4s

Counts

83 → 83

Iterations

Useful iterations: 3 (992.0ms)

Iter	Nodes	Cost
0	122	1931
1	229	1838
2	755	1635
3	4938	1632
done	5001	1632

prune667.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.9b

localize24.0ms

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 th) (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)))))

rewrite42.0ms

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)))

9.0ms

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

30.0ms

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

series1.9s

Counts

3 → 9

Calls

3 calls:

410.0ms

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

501.0ms

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

1.0s

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

simplify1.4s

Counts

82 → 82

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	132	1911
1	309	1876
2	1506	1665
done	5001	1659

prune442.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 8.9b

regimes1.3s

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	19
1	15	19
done	15	19

end0.0ms

sample9.6s

Algorithm

intervals

Results

5.2s	2800×	body	1280	valid
2.4s	1814×	body	640	valid
823.0ms	750×	body	320	valid
463.0ms	2283×	body	80	valid
185.0ms	353×	body	160	valid