Details

sample151.0ms

Algorithm

intervals

Results

113.0ms

256×

body

valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	22	29
1	52	29
2	132	28
3	344	28
4	1245	28
done	5000	28

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ (* 2.0 l) Om) 2.0)
0.3b	(pow (sin kx) 2.0)
2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-sqr-sqrt` `unpow-prod-down`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`associate-l`
7×	`pow1` `pow-exp` `prod-exp`
6×	`pow-unpow` `times-frac` `add-cbrt-cube`
5×	`associate-r`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `sqrt-prod` `unswap-sqr`
2×	`pow-pow` `flip3-+` `sqrt-div` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

12.0ms	(pow (/ (* 2.0 l) Om) 2.0)
4.0ms	(pow (sin kx) 2.0)
92.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

132.0ms	(pow (/ (* 2.0 l) Om) 2.0)
177.0ms	(pow (sin kx) 2.0)
624.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
557.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify2.2s

Counts

112 → 112

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	213	1892
1	610	1730
2	2564	1647
done	5000	1645

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.4b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
1.4b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`add-exp-log`
17×	`*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-cube-cbrt`
11×	`associate-l`
7×	`pow1`
6×	`pow-unpow` `prod-exp` `add-cbrt-cube`
5×	`associate-r` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `times-frac` `sqrt-prod` `unswap-sqr`
2×	`pow-pow` `flip3-+` `sqrt-div` `associate-*r/` `div-exp` `flip-+` `distribute-lft-out`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

4.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
102.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

137.0ms	(pow (sin ky) 2.0)
140.0ms	(pow (sin kx) 2.0)
606.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
498.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify2.1s

Counts

106 → 106

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	206	2129
1	571	1963
2	2513	1681
done	5000	1678

prune970.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

localize72.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
10.1b	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
10.1b	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
10.1b	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
3.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
3.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
3.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series2.3s

Counts

4 → 12

Calls

4 calls:

576.0ms	(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
576.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
591.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
542.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify1.0s

Counts

73 → 73

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	84	2273
1	163	2058
2	398	1835
3	1464	1692
done	5000	1536

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.4b

localize110.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
10.1b	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
14.1b	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
14.1b	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

2.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
2.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
1.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
1.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

508.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
584.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
492.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
437.0ms	(cbrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

simplify1.5s

Counts

68 → 68

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	84	1792
1	164	1664
2	388	1370
3	1427	1360
done	5001	1348

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.4b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.3b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	41
1	32	41
done	32	41

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.5s

8000×

body

valid