Details

sample144.0ms

Algorithm

intervals

Results

108.0ms

256×

body

valid

simplify336.0ms

Calls

1 calls:

Slowest

335.0ms

(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize77.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
2.3b	(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
0.3b	(pow (sin kx) 2)
0.2b	(pow (sin ky) 2)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`unpow-prod-down`
11×	`add-exp-log`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`associate-l`
6×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-r`
4×	`add-log-exp`
3×	`unpow2`
3×	`sqrt-prod`
3×	`prod-exp`
3×	`pow-exp`
3×	`pow-to-exp`
2×	`distribute-lft-out`
2×	`flip-+`
2×	`associate-*r/`
2×	`sqrt-div`
2×	`flip3-+`
2×	`pow-pow`
1×	`div-inv`
1×	`cbrt-unprod`
1×	`*-commutative`
1×	`pow1/2`
1×	`distribute-lft-in`
1×	`rem-sqrt-square`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

12.0ms	(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
2.0ms	(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
1.0ms	(pow (sin kx) 2)
1.0ms	(pow (sin ky) 2)

series402.0ms

Calls

4 calls:

Slowest

216.0ms	(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
153.0ms	(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
17.0ms	(pow (sin ky) 2)
15.0ms	(pow (sin kx) 2)

simplify4.0s

Calls

48 calls:

Slowest

524.0ms	(* (pow (sin ky) 2) (pow (/ (* 2 l) Om) 2))
472.0ms	(* (pow (/ (* 2 l) Om) 2) (pow (sin ky) 2))
287.0ms	(+ (log (pow (/ (* 2 l) Om) 2)) (log (+ (pow (sin kx) 2) (pow (sin ky) 2))))
262.0ms	(+ (* 4 (/ (* (pow kx 2) (pow l 2)) (pow Om 2))) (* 4 (/ (* (pow ky 2) (pow l 2)) (pow Om 2))))
253.0ms	(sqrt (* (cbrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (cbrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))

prune1.6s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize54.0ms

Local error

Found 4 expressions with local error:

12.8b	(cbrt (* (/ 2 Om) l))
12.8b	(cbrt (/ (* 2 l) Om))
9.4b	(sqrt (+ 1 (* (* (* (/ 2 Om) l) (cbrt (* (/ 2 Om) l))) (* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
0.9b	(* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
11×	`associate-l`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`add-exp-log`
9×	`unpow-prod-down`
9×	`cbrt-prod`
6×	`add-cbrt-cube`
5×	`associate-r`
4×	`add-log-exp`
4×	`pow1`
3×	`sqrt-prod`
3×	`prod-exp`
2×	`distribute-lft-out`
2×	`div-inv`
2×	`flip-+`
2×	`associate-*r/`
2×	`sqrt-div`
2×	`pow1/3`
2×	`flip3-+`
2×	`cbrt-div`
1×	`unpow2`
1×	`cbrt-unprod`
1×	`*-commutative`
1×	`pow-exp`
1×	`associate-*l/`
1×	`pow1/2`
1×	`distribute-lft-in`
1×	`rem-sqrt-square`
1×	`pow-to-exp`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

19.0ms	(* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
1.0ms	(cbrt (* (/ 2 Om) l))
1.0ms	(sqrt (+ 1 (* (* (* (/ 2 Om) l) (cbrt (* (/ 2 Om) l))) (* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
0.0ms	(cbrt (/ (* 2 l) Om))

series872.0ms

Calls

4 calls:

Slowest

379.0ms	(sqrt (+ 1 (* (* (* (/ 2 Om) l) (cbrt (* (/ 2 Om) l))) (* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
260.0ms	(* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
123.0ms	(cbrt (* (/ 2 Om) l))
110.0ms	(cbrt (/ (* 2 l) Om))

simplify2.5s

Calls

48 calls:

Slowest

283.0ms	(sqrt (- (* 1 1) (* (* (* (* (/ 2 Om) l) (cbrt (* (/ 2 Om) l))) (* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (* (* (/ 2 Om) l) (cbrt (* (/ 2 Om) l))) (* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
241.0ms	(sqrt (+ (pow 1 3) (pow (* (* (* (/ 2 Om) l) (cbrt (* (/ 2 Om) l))) (* (pow (cbrt (/ (* 2 l) Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) 3)))
184.0ms	(* (* (* (pow (cbrt (/ (* 2 l) Om)) 2) (pow (cbrt (/ (* 2 l) Om)) 2)) (pow (cbrt (/ (* 2 l) Om)) 2)) (* (* (+ (pow (sin kx) 2) (pow (sin ky) 2)) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))
167.0ms	(* (cbrt 2) (exp (* 1/3 (- (log (/ 1 Om)) (log (/ 1 l))))))
148.0ms	(* (+ (pow (sin ky) 2) (pow (sin kx) 2)) (* (exp (* 1/3 (- (* 2 (log (/ 1 Om))) (* 2 (log (/ 1 l)))))) (pow (cbrt 2) 2)))

prune1.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

14.8b	(sqrt (+ 1 (* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om))))))
14.2b	(* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om))))
0.3b	(* (/ ky Om) (/ ky Om))
0.2b	(* (/ kx Om) (/ kx Om))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-*r/`
16×	`pow1`
11×	`associate-r`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
10×	`add-exp-log`
10×	`add-cbrt-cube`
10×	`*-un-lft-identity`
9×	`frac-add`
9×	`associate-l`
8×	`associate-*l/`
8×	`frac-times`
4×	`add-log-exp`
4×	`div-inv`
3×	`cbrt-unprod`
3×	`sqrt-prod`
3×	`*-commutative`
3×	`prod-exp`
3×	`pow-prod-down`
2×	`flip-+`
2×	`pow-prod-up`
2×	`sqrt-div`
2×	`pow-plus`
2×	`flip3-+`
2×	`pow2`
1×	`pow1/2`
1×	`distribute-lft-in`
1×	`rem-sqrt-square`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

32.0ms	(* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om))))
8.0ms	(* (/ ky Om) (/ ky Om))
6.0ms	(* (/ kx Om) (/ kx Om))
1.0ms	(sqrt (+ 1 (* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om))))))

series245.0ms

Calls

4 calls:

Slowest

110.0ms	(* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om))))
108.0ms	(sqrt (+ 1 (* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om))))))
13.0ms	(* (/ kx Om) (/ kx Om))
13.0ms	(* (/ ky Om) (/ ky Om))

simplify5.7s

Calls

68 calls:

Slowest

843.0ms	(* (* (* (/ ky Om) (/ ky Om)) (/ ky Om)) (* (* (/ ky Om) (/ ky Om)) (/ ky Om)))
816.0ms	(* (* (* (/ kx Om) (/ kx Om)) (/ kx Om)) (* (* (/ kx Om) (/ kx Om)) (/ kx Om)))
425.0ms	(sqrt (sqrt (+ 1 (* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om)))))))
417.0ms	(* (* (/ kx Om) (/ kx Om)) (* (* l l) 4))
337.0ms	(sqrt (* (cbrt (+ 1 (* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om)))))) (cbrt (+ 1 (* (* (* l l) 4) (+ (* (/ ky Om) (/ ky Om)) (* (/ kx Om) (/ kx Om))))))))

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.7b

regimes476.0ms

Accuracy

0% (0.6b remaining)

Error of 1.3b against oracle of 0.7b and baseline of 1.3b

bsearch9.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.4s

8000×

body

valid