Details

Time bar (total: 15.1s)

sample43.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
15229
211529
326729
475129
5320629
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:

0.2b
(pow (sin kx) 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))))))
2.9b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.2b
(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 kx) 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 kx) 2.0)
379.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
379.0ms
(* (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)))))

simplify566.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
02223044
15062763
215542653
done50002653

prune511.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
2.9b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.2b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.1b
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
90×cbrt-prod
66×add-sqr-sqrt times-frac
64×*-un-lft-identity
60×add-cube-cbrt
40×unpow-prod-down
33×sqrt-prod
30×cube-prod
21×associate-/r*
18×add-exp-log
11×associate-*l*
7×add-cbrt-cube sqr-pow
6×sqrt-div prod-exp
5×pow1 cube-mult unpow3 associate-*r*
4×cube-div cbrt-div flip3-+ flip-+ add-log-exp
3×div-exp pow-exp associate-/l* unswap-sqr
2×associate-*r/ associate-/r/ div-inv distribute-lft-out
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow1/3 clear-num *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 182
Calls
4 calls:
12.0ms
(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
45.0ms
(* (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)))))
4.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

series1.4s

Counts
4 → 12
Calls
4 calls:
395.0ms
(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
388.0ms
(* (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)))))
320.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify627.0ms

Counts
194 → 194
Iterations

Useful iterations: done (619.0ms)

IterNodesCost
02727311
15965581
217305509
done50015507

prune666.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.5b

localize31.0ms

Local error

Found 4 expressions with local error:

7.9b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
10.2b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.1b
(cbrt (pow (* (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))) 3))
16.2b
(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
17×cbrt-prod
10×add-sqr-sqrt sqrt-div
9×add-cube-cbrt *-un-lft-identity flip3-+ flip-+
8×cube-div
6×sqrt-prod
5×pow1
4×add-exp-log frac-times add-cbrt-cube add-log-exp
3×pow1/3
2×associate-*r/ associate-*l/
1×cube-mult unpow-prod-down rem-sqrt-square sqrt-pow1 pow1/2 unpow3 cube-prod rem-cbrt-cube sqr-pow
Counts
4 → 69
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)))))
4.0ms
(cbrt (pow (* (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))) 3))
2.0ms
(cbrt (+ 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:
290.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
318.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
316.0ms
(cbrt (pow (* (cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))) 3))
287.0ms
(cbrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.5s

Counts
81 → 81
Iterations

Useful iterations: 3 (425.0ms)

IterNodesCost
01453830
13383280
210882804
343862669
done50002669

prune497.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.6b
(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
2.9b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.2b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
42×*-un-lft-identity
39×times-frac
38×add-cube-cbrt
25×log-pow
24×exp-prod sqrt-prod
18×add-exp-log
11×associate-*l*
10×unpow-prod-down
8×add-cbrt-cube
6×pow1 sqrt-div prod-exp associate-/r*
5×associate-*r*
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×log-prod div-exp pow-exp div-inv associate-/l* unswap-sqr
2×associate-*r/ distribute-lft-out sqr-pow
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 rem-log-exp clear-num *-commutative cbrt-unprod
Counts
4 → 129
Calls
4 calls:
5.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
12.0ms
(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
42.0ms
(* (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)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
391.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
393.0ms
(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
388.0ms
(* (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)))))

simplify551.0ms

Counts
141 → 141
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
02463979
15033555
214763378
done50013378

prune645.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.5b

regimes774.0ms

Accuracy

88.9% (0.0b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 1.6b

bsearch2.0ms

Steps
ItersRangePoint
0
0.999039350659352
1.0
0.999519675329676

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03696
14696
done4696

end0.0ms

sample1.0s

Algorithm
intervals
Results
794.0ms7999×body80valid
0.0ms1×body160valid