Details

sample163.0ms

Algorithm

intervals

Results

117.0ms

256×

body

valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	22	29
1	52	29
2	123	29
3	285	29
4	1041	29
5	4464	29
done	5000	29

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (* 2.0 l) Om) 2.0)
0.3b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.9b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
24×	`add-exp-log` `times-frac`
17×	`unpow-prod-down`
15×	`sqrt-prod`
11×	`associate-l`
8×	`add-cbrt-cube`
7×	`prod-exp`
6×	`pow1` `pow-exp` `associate-/r*`
5×	`div-exp` `associate-r`
4×	`sqrt-div` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `div-inv` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `associate-/r/` `distribute-lft-out`
1×	`cbrt-undiv` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

8.0ms	(pow (/ (* 2.0 l) Om) 2.0)
11.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
109.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

120.0ms	(pow (/ (* 2.0 l) Om) 2.0)
629.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
619.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
587.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.7s

Counts

128 → 128

Iterations

Useful iterations: 2 (770.0ms)

Iter	Nodes	Cost
0	228	3197
1	518	2909
2	1653	2783
done	5000	2783

prune776.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
8.9b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
39×	`times-frac`
38×	`add-cube-cbrt`
25×	`log-pow`
24×	`exp-prod` `sqrt-prod`
18×	`add-exp-log`
11×	`associate-l`
10×	`unpow-prod-down`
8×	`add-cbrt-cube`
6×	`pow1` `sqrt-div` `prod-exp` `associate-/r*`
5×	`associate-r`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`log-prod` `div-exp` `pow-exp` `div-inv` `associate-/l*` `unswap-sqr`
2×	`associate-*r/` `distribute-lft-out` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `rem-log-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 129

Calls

4 calls:

22.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
95.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
47.0ms	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
11.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

651.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
577.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
620.0ms	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
581.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.2s

Counts

141 → 141

Iterations

Useful iterations: 2 (329.0ms)

Iter	Nodes	Cost
0	246	3979
1	497	3555
2	1527	3378
done	5000	3378

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.4b

localize58.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
3.6b	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
8.9b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.9b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

54×	`log-pow`
52×	`sqrt-pow1`
48×	`exp-prod`
38×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
30×	`sqrt-prod`
12×	`log-prod`
10×	`pow1`
8×	`sqrt-div`
6×	`add-exp-log`
4×	`flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `div-inv`

Counts

4 → 112

Calls

4 calls:

47.0ms	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
56.0ms	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
6.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
6.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.9s

Counts

4 → 12

Calls

4 calls:

950.0ms	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
956.0ms	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
483.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
474.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.9s

Counts

124 → 124

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	142	3604
1	228	3156
2	552	2948
3	2304	2948
done	5000	2948

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

localize114.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
8.9b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.9b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`sqrt-pow1` `log-pow`
25×	`add-cube-cbrt`
24×	`exp-prod`
21×	`times-frac`
18×	`sqrt-prod`
17×	`add-exp-log`
11×	`associate-l`
10×	`unpow-prod-down`
8×	`pow1`
6×	`log-prod` `sqrt-div` `prod-exp` `add-cbrt-cube`
5×	`associate-r`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow1/2` `pow-exp` `unswap-sqr`
2×	`rem-sqrt-square` `associate-*r/` `div-exp` `associate-/r/` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `rem-log-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

122.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
24.0ms	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
6.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
6.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

562.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.0s	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
454.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
546.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.3s

Counts

120 → 120

Iterations

Useful iterations: 2 (285.0ms)

Iter	Nodes	Cost
0	231	3145
1	472	2777
2	1457	2639
done	5000	2639

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

regimes922.0ms

Accuracy

0% (0.4b remaining)

Error of 1.6b against oracle of 1.3b and baseline of 1.6b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	58
1	32	58
done	32	58

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.3s

8000×

body

valid