Details

sample81.0ms

Algorithm

intervals

Results

41.0ms

256×

body

valid

simplify63.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize95.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.1b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite140.0ms

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×	`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 → 86

Calls

4 calls:

4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
120.0ms	(* (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)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

154.0ms	(pow (sin kx) 2.0)
139.0ms	(pow (sin ky) 2.0)
591.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
668.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify52.0ms

Counts: 98 → 98

prune643.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.5b

localize38.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

11.0ms	(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
7.0ms	(cbrt (/ (* 2.0 l) Om))
8.0ms	(cbrt (/ (* 2.0 l) Om))
7.0ms	(cbrt (/ (* 2.0 l) Om))

series1.2s

Counts

4 → 12

Calls

4 calls:

736.0ms	(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
171.0ms	(cbrt (/ (* 2.0 l) Om))
138.0ms	(cbrt (/ (* 2.0 l) Om))
136.0ms	(cbrt (/ (* 2.0 l) Om))

simplify178.0ms

Counts: 75 → 75

prune732.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.5b

localize79.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
4×	`pow1` `add-exp-log` `cbrt-div` `pow1/3` `add-cbrt-cube` `div-inv` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

7.0ms	(cbrt (/ (* 2.0 l) Om))
7.0ms	(cbrt (/ (* 2.0 l) Om))
7.0ms	(cbrt (/ (* 2.0 l) Om))
9.0ms	(cbrt (/ (* 2.0 l) Om))

series544.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (/ (* 2.0 l) Om))
134.0ms	(cbrt (/ (* 2.0 l) Om))
143.0ms	(cbrt (/ (* 2.0 l) Om))
117.0ms	(cbrt (/ (* 2.0 l) Om))

simplify30.0ms

Counts: 76 → 76

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.5b

localize93.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))
14.7b	(cbrt (/ (* 2.0 l) Om))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
4×	`pow1` `add-exp-log` `cbrt-div` `pow1/3` `add-cbrt-cube` `div-inv` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

4.0ms	(cbrt (/ (* 2.0 l) Om))
4.0ms	(cbrt (/ (* 2.0 l) Om))
4.0ms	(cbrt (/ (* 2.0 l) Om))
4.0ms	(cbrt (/ (* 2.0 l) Om))

series573.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (/ (* 2.0 l) Om))
151.0ms	(cbrt (/ (* 2.0 l) Om))
150.0ms	(cbrt (/ (* 2.0 l) Om))
126.0ms	(cbrt (/ (* 2.0 l) Om))

simplify42.0ms

Counts: 76 → 76

prune955.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.5b

regimes675.0ms

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify184.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.5s

8000×

body

valid