Details

sample415.0ms

Algorithm

intervals

Results

138.0ms	75×	body	1280	valid
125.0ms	69×	body	640	valid
23.0ms	81×	body	80	valid
19.0ms	22×	body	320	valid
5.0ms	9×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	3061
6	850
5	327
4	155
3	80
2	49
1	25
0	13

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.2b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
3.3b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 107

Calls

4 calls:

68.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
6.0ms	(pow (sin kx) 2)
6.0ms	(pow (sin ky) 2)
36.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
34.0ms	(pow (sin kx) 2)
34.0ms	(pow (sin ky) 2)
107.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify2.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5036
3	3826
2	1251
1	448
0	182

prune822.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.7b

localize52.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
15.1b	(cbrt (pow (sin kx) 2))
15.1b	(cbrt (pow (sin kx) 2))
15.1b	(cbrt (pow (sin kx) 2))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `unpow2` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 67

Calls

4 calls:

98.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
2.0ms	(cbrt (pow (sin kx) 2))
2.0ms	(cbrt (pow (sin kx) 2))
2.0ms	(cbrt (pow (sin kx) 2))

series542.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
122.0ms	(cbrt (pow (sin kx) 2))
156.0ms	(cbrt (pow (sin kx) 2))
182.0ms	(cbrt (pow (sin kx) 2))

simplify2.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	1603
2	505
1	204
0	93

prune777.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 9.7b

localize75.0ms

Local error

Found 4 expressions with local error:

15.1b	(cbrt (pow (sin kx) 2))
15.1b	(cbrt (pow (sin kx) 2))
15.1b	(cbrt (pow (sin kx) 2))
15.1b	(cbrt (pow (sin kx) 2))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
12×	`add-sqr-sqrt` `unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt (pow (sin kx) 2))
2.0ms	(cbrt (pow (sin kx) 2))
2.0ms	(cbrt (pow (sin kx) 2))
2.0ms	(cbrt (pow (sin kx) 2))

series635.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (pow (sin kx) 2))
165.0ms	(cbrt (pow (sin kx) 2))
154.0ms	(cbrt (pow (sin kx) 2))
160.0ms	(cbrt (pow (sin kx) 2))

simplify2.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5002
5	4104
4	1292
3	544
2	223
1	98
0	48

prune912.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 9.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
0.4b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (sin th)))
3.3b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.3b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
87×	`*-un-lft-identity`
66×	`times-frac`
53×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
45×	`add-exp-log`
39×	`associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp`
18×	`unpow-prod-down` `distribute-lft-out`
12×	`sqrt-div`
11×	`pow1` `associate-/r*` `div-exp`
10×	`cbrt-unprod`
6×	`cbrt-undiv`
4×	`flip3-+` `associate-/r/` `flip-+` `insert-posit16` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-prod-down` `associate-l/` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-times` `clear-num` `frac-2neg` `associate-r` `associate-r/` `-commutative`

Counts

4 → 170

Calls

4 calls:

47.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
123.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (sin th)))
18.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
23.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
254.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (sin th)))
97.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
124.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify2.4s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
2	1879
1	572
0	244

prune1.1s

Pruning

19 alts after pruning (15 fresh and 4 done)

Merged error: 9.7b

regimes1.8s

Accuracy

0% (1.2b remaining)

Error of 12.5b against oracle of 11.3b and baseline of 12.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample11.5s

Algorithm

intervals

Results

6.0s	2645×	body	1280	valid
3.5s	1839×	body	640	valid
765.0ms	775×	body	320	valid
764.0ms	2387×	body	80	valid
217.0ms	354×	body	160	valid