Details

Time bar (total: 13.4s)

sample46.0ms

Algorithm
intervals
Results
28.0ms256×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
15229
211529
326729
475129
5320729
done500029

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.4b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.7b
(* (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)))))

rewrite57.0ms

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:
2.0ms
(pow (sin ky) 2.0)
5.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
44.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
106.0ms
(pow (sin ky) 2.0)
381.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
378.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
372.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify627.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (178.0ms)

IterNodesCost
02223044
15062763
217092653
done50012653

prune496.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.9b

localize29.0ms

Local error

Found 4 expressions with local error:

6.1b
(cbrt (sqrt (+ 1.0 (* (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)))))
9.2b
(sqrt (+ 1.0 (* (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)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
2.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
290.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
319.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
328.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
315.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify822.0ms

Counts
73 → 73
Iterations

Useful iterations: 3 (151.0ms)

IterNodesCost
0662113
11311879
23691759
316491756
done50001756

prune393.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.9b

localize35.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (+ 1.0 (* (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)))))
9.2b
(sqrt (+ 1.0 (* (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)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
317.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
317.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
321.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
321.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify792.0ms

Counts
72 → 72
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0481960
11081704
23391608
315971608
done50001608

prune436.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ (* 2.0 l) Om) 2.0)
0.3b
(pow (sin ky) 2.0)
1.2b
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×unpow-prod-down
19×add-sqr-sqrt
18×*-un-lft-identity
14×add-cube-cbrt
11×associate-*l*
7×pow1 pow-exp prod-exp
6×pow-unpow times-frac add-cbrt-cube
5×log-prod associate-*r* add-log-exp
4×div-exp sqr-pow
3×pow-to-exp log-pow unswap-sqr
2×distribute-rgt-in pow-pow distribute-lft-in associate-*r/ exp-sum div-inv distribute-lft-out
1×exp-prod exp-to-pow flip3-+ rem-log-exp *-commutative cbrt-unprod flip-+
Counts
4 → 93
Calls
4 calls:
4.0ms
(pow (/ (* 2.0 l) Om) 2.0)
1.0ms
(pow (sin ky) 2.0)
4.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
41.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series973.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(pow (/ (* 2.0 l) Om) 2.0)
110.0ms
(pow (sin ky) 2.0)
388.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
387.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify569.0ms

Counts
105 → 105
Iterations

Useful iterations: 2 (172.0ms)

IterNodesCost
02001759
14731647
215671529
done50001529

prune485.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.9b

regimes533.0ms

Accuracy

0% (0.4b remaining)

Error of 1.9b against oracle of 1.4b and baseline of 1.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
028121
135121
done35121

end0.0ms

sample990.0ms

Algorithm
intervals
Results
766.0ms7999×body80valid
0.0ms1×body160valid