Details

sample147.0ms

Algorithm

intervals

Results

106.0ms

256×

body

valid

simplify941.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	29
1	52	29
2	124	29
3	298	29
4	1125	29
done	5001	29

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 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))))))
1.4b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite124.0ms

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` `prod-exp` `associate-/r*`
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×	`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 → 110

Calls

4 calls:

4.0ms	(pow (sin kx) 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))))))
96.0ms	(* (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)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

165.0ms	(pow (sin kx) 2.0)
640.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
585.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
470.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.8s

Counts

122 → 122

Iterations

Useful iterations: 2 (477.0ms)

Iter	Nodes	Cost
0	222	3044
1	590	2779
2	2398	2653
done	5000	2653

prune804.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
0.3b	(pow (sin kx) 2.0)
1.4b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

23.0ms	(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
7.0ms	(pow (sin kx) 2.0)
101.0ms	(* (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)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

524.0ms	(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
167.0ms	(pow (sin kx) 2.0)
541.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
467.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.7s

Counts

99 → 99

Iterations

Useful iterations: 2 (473.0ms)

Iter	Nodes	Cost
0	195	2028
1	529	1811
2	2110	1716
done	5000	1716

prune740.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.5b

regimes769.0ms

Accuracy

0% (0.0b remaining)

Error of 1.5b against oracle of 1.5b and baseline of 1.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	29
1	28	29
done	28	29

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.4s

8000×

body

valid