Details

Time bar (total: 1.8m)

sample536.0ms

Algorithm
intervals
Results
510.0ms256×body80valid

simplify610.0ms

Calls
1 calls:
Slowest
609.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize77.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
3.4b
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
0.5b
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
0.5b
(/ 4 (/ Om l))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
155×times-frac
75×add-sqr-sqrt
74×*-un-lft-identity add-cube-cbrt
44×div-inv
35×associate-/r*
24×associate-/r/
9×add-cbrt-cube add-exp-log
6×sqrt-prod
4×pow1 sqrt-div insert-posit16 add-log-exp
3×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ associate-/l* associate-/l/
2×div-sub sqr-sin sin-mult
1×rem-sqrt-square associate-+r- pow1/2 frac-add associate-+l-
Calls
4 calls:
Slowest
28.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
24.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
4.0ms
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
0.0ms
(/ 4 (/ Om l))

series1.1s

Calls
4 calls:
Slowest
373.0ms
(/ 1/2 (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))))
356.0ms
(/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))
345.0ms
(sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))
29.0ms
(/ 4 (/ Om l))

simplify30.0s

Calls
217 calls:
Slowest
596.0ms
(/ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (/ (* (* (/ Om l) (/ Om l)) (/ Om l)) (* (* (/ 4 (/ Om l)) (/ 4 (/ Om l))) (/ 4 (/ Om l)))))
518.0ms
(- (log (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (- (log (/ Om l)) (log (/ 4 (/ Om l)))))
482.0ms
(/ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (/ (/ Om l) (/ 4 (/ Om l))) (/ (/ Om l) (/ 4 (/ Om l)))) (/ (/ Om l) (/ 4 (/ Om l)))))
445.0ms
(/ 1/2 (/ (/ Om l) (/ 4 (/ Om l))))
423.0ms
(sqrt (+ (* 1 1) (- (* (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))) (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))) (* 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l))))))))

prune3.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.2b

localize41.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
3.7b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
0.5b
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
0.4b
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
75×add-sqr-sqrt
74×*-un-lft-identity add-cube-cbrt
45×div-inv
20×associate-/l*
14×associate-/r*
11×add-cbrt-cube add-exp-log
9×associate-/r/
6×div-sub sqrt-prod
4×pow1 cbrt-undiv sqrt-div div-exp sqr-sin insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg flip3-+ flip-+
2×associate-+r- associate-+l- sin-mult
1×rem-sqrt-square pow1/2 frac-add
Calls
4 calls:
Slowest
26.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
25.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
2.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
1.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))

series1.3s

Calls
4 calls:
Slowest
399.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
305.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
301.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
284.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))

simplify19.2s

Calls
226 calls:
Slowest
816.0ms
(sqrt (* (cbrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))) (cbrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))))
375.0ms
(cbrt (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
374.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
370.0ms
(sqrt (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
362.0ms
(sqrt (cbrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize11.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
3.7b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
2.3b
(log (exp (/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))))
0.5b
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
12×times-frac
10×associate-/r*
7×log-pow div-inv
6×exp-prod add-cbrt-cube sqrt-div add-exp-log sqrt-prod
5×pow1 associate-/r/
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×log-prod associate-/l* associate-/l/
2×clear-num frac-2neg div-sub sqr-sin sin-mult
1×cbrt-undiv rem-sqrt-square associate-+r- pow1/2 div-exp rem-log-exp frac-add associate-+l-
Calls
4 calls:
Slowest
42.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
7.0ms
(log (exp (/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))))
2.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
1.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))

series1.2s

Calls
4 calls:
Slowest
352.0ms
(sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))
306.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
272.0ms
(log (exp (/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))))
233.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))

simplify9.4s

Calls
72 calls:
Slowest
502.0ms
(log (sqrt (exp (/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))))))
459.0ms
(log (* (cbrt (exp (/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))))) (cbrt (exp (/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))))))
448.0ms
(/ 1 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))
431.0ms
(cbrt (/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l)))))))
427.0ms
(/ 1/2 (sqrt (+ 1 (* 4 (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize19.0ms

Local error

Found 4 expressions with local error:

3.7b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
2.7b
(log (exp (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))
0.4b
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
0.3b
(* (sin ky) (sin ky))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
256×times-frac
124×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
78×div-inv
74×log-pow
73×exp-prod
20×associate-/l*
13×add-cbrt-cube add-exp-log
12×associate-/r/
10×pow1 div-sub
8×associate-/r*
7×sqr-sin
4×cbrt-undiv div-exp insert-posit16 add-log-exp associate-/l/
3×log-prod associate-+r- associate-*r* associate-*l* associate-+l- sin-mult
2×log-div clear-num frac-2neg exp-diff
1×pow2 flip3-+ pow-plus rem-log-exp pow-prod-down frac-add prod-exp *-commutative pow-prod-up cbrt-unprod flip-+
Calls
4 calls:
Slowest
31.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
24.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
18.0ms
(log (exp (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))
8.0ms
(* (sin ky) (sin ky))

series922.0ms

Calls
4 calls:
Slowest
318.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
314.0ms
(log (exp (/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))))
259.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))
32.0ms
(* (sin ky) (sin ky))

simplify24.4s

Calls
303 calls:
Slowest
557.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ Om l))
363.0ms
(/ (* (* (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))) (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l))) (* (* (/ Om l) (/ Om l)) (/ Om l)))
329.0ms
(/ (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (/ Om l)) (/ 1 l))
308.0ms
(/ (* (+ (pow (sin ky) 2) (pow (sin kx) 2)) (pow l 2)) (pow Om 2))
306.0ms
(- (- (log (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (log (/ Om l))) (log (/ Om l)))

prune5.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.2b

regimes739.0ms

Accuracy

0% (0.8b remaining)

Error of 1.6b against oracle of 0.8b and baseline of 1.6b

bsearch8.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.3s8000×body80valid