Details

sample108.0ms

Algorithm

intervals

Results

59.0ms

256×

body

valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4017
4	920
3	263
2	121
1	52
0	22

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.9b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.2b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

5.0ms	(pow (sin kx) 2.0)
16.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
79.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (sin kx) 2.0)
632.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
622.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
535.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1828
1	584
0	222

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.5b

localize193.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (* (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 66

Calls

4 calls:

15.0ms	(sqrt (* (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
2.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

411.0ms	(sqrt (* (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
460.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
392.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
469.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify2.3s

Counts

78 → 78

Iterations

Iter	Nodes
done	5007
3	2039
2	443
1	168
0	92

prune982.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.5b

localize156.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-exp-log`
15×	`*-un-lft-identity`
11×	`associate-l` `add-cube-cbrt`
10×	`unpow-prod-down`
9×	`cbrt-prod`
6×	`cbrt-div` `add-cbrt-cube` `prod-exp`
5×	`associate-r`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`times-frac` `pow1/3` `pow-exp` `unswap-sqr`
2×	`div-exp` `associate-*r/` `distribute-lft-out` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

93.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

540.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
423.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
474.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
451.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify3.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5016
3	4573
2	1198
1	367
0	136

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.5b

localize201.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.9b	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-exp-log`
15×	`*-un-lft-identity`
11×	`associate-l` `add-cube-cbrt`
10×	`unpow-prod-down`
9×	`cbrt-prod`
6×	`cbrt-div` `add-cbrt-cube` `prod-exp`
5×	`associate-r`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`times-frac` `pow1/3` `pow-exp` `unswap-sqr`
2×	`div-exp` `associate-*r/` `distribute-lft-out` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

84.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

527.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
529.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
468.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
537.0ms	(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify3.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5016
3	4573
2	1198
1	367
0	136

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.5b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 1.6b against oracle of 1.2b and baseline of 1.6b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.6s

8000×

body

valid