Details

sample369.0ms

Algorithm

intervals

Results

173.0ms	90×	body	1280	valid
39.0ms	53×	body	640	valid
14.0ms	22×	body	320	valid
12.0ms	79×	body	80	valid
4.0ms	12×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
7	3442
6	908
5	294
4	128
3	62
2	35
1	23
0	13

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite141.0ms

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` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

69.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
61.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
163.0ms	(pow (sin kx) 2.0)
134.0ms	(pow (sin ky) 2.0)
106.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.0s

Counts

113 → 113

Iterations

Iter	Nodes
done	5006
3	4095
2	1252
1	442
0	181

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin ky) 2.0)
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

96.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.0ms	(pow (sin ky) 2.0)
53.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
137.0ms	(pow (sin ky) 2.0)
169.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
108.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.0s

Counts

145 → 145

Iterations

Iter	Nodes
done	5007
3	4424
2	1250
1	463
0	195

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th)))
0.3b	(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
0.3b	(* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th))
3.2b	(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
35×	`sqrt-prod`
31×	`*-un-lft-identity` `times-frac`
29×	`add-cube-cbrt`
22×	`associate-l`
15×	`add-exp-log`
14×	`pow1`
13×	`add-cbrt-cube`
9×	`associate-/r/`
6×	`sin-mult`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `associate-/r` `sqrt-pow1` `flip3-+` `sqrt-div` `frac-add` `flip-+` `div-inv` `associate-/l`
2×	`div-exp` `associate-l/` `-commutative` `pow-flip` `inv-pow`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `pow1/2` `1-exp` `associate-*r/`

Counts

4 → 122

Calls

4 calls:

106.0ms	(* (sin ky) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th)))
21.0ms	(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
58.0ms	(* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th))
17.0ms	(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

series721.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (sin ky) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th)))
133.0ms	(/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
218.0ms	(* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th))
146.0ms	(sqrt (/ 1 (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

simplify2.6s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
3	3163
2	1172
1	427
0	202

prune975.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.2b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
38.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (sin kx))
131.0ms	(cbrt (sin kx))
131.0ms	(cbrt (sin kx))
104.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify2.0s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	1677
2	503
1	191
0	81

prune573.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.1b

regimes2.7s

Accuracy

58.7% (0.6b remaining)

Error of 11.7b against oracle of 11.0b and baseline of 12.6b

bsearch5.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	50
1	50
0	38

end0.0ms

sample9.5s

Algorithm

intervals

Results

5.2s	2744×	body	1280	valid
2.1s	1836×	body	640	valid
957.0ms	805×	body	320	valid
489.0ms	2241×	body	80	valid
354.0ms	374×	body	160	valid