Details

Time bar (total: 31.2s)

sample163.0ms

Algorithm
intervals
Results
115.0ms256×body80valid

simplify5.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
02229
15229
213128
333028
4115228
5477228
done500028

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ (* 2.0 l) Om) 2.0)
0.3b
(/ 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)))
8.9b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
24×add-exp-log times-frac
17×unpow-prod-down
15×sqrt-prod
11×associate-*l*
8×add-cbrt-cube
7×prod-exp
6×pow1 pow-exp associate-/r*
5×div-exp associate-*r*
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×pow-unpow flip3-+ flip-+ div-inv associate-/l* unswap-sqr sqr-pow
2×pow-to-exp associate-*r/ associate-/r/ 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 → 124
Calls
4 calls:
17.0ms
(pow (/ (* 2.0 l) Om) 2.0)
11.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
127.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
112.0ms
(pow (/ (* 2.0 l) Om) 2.0)
661.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
567.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
598.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.2s

Counts
136 → 136
Iterations

Useful iterations: 2 (334.0ms)

IterNodesCost
02363337
15333048
217292849
done50012849

prune894.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))
2.4b
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
3.6b
(log (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))))
8.9b
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
24×sqrt-prod
23×log-pow
22×exp-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod associate-/l*
2×div-inv
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num fma-udef
Counts
4 → 102
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))
1.0ms
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
20.0ms
(log (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))))
2.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
620.0ms
(/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))
254.0ms
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
668.0ms
(log (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)))))
465.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

simplify2.6s

Counts
114 → 114
Iterations

Useful iterations: 2 (144.0ms)

IterNodesCost
01493106
12062792
23642612
38212612
432432612
done50002612

prune949.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.4b

localize57.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
3.6b
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
8.9b
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
8.9b
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
50×log-pow
48×sqrt-pow1
44×exp-prod
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
30×sqrt-prod
12×log-prod
10×pow1
6×add-exp-log
4×expm1-log1p-u pow1/2 add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square rem-log-exp div-inv
Counts
4 → 112
Calls
4 calls:
18.0ms
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
19.0ms
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
2.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
2.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
890.0ms
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
812.0ms
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
404.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
385.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

simplify2.4s

Counts
124 → 124
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
01243228
11682836
22542660
34152660
48742660
526222660
done50002660

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

localize68.0ms

Local error

Found 4 expressions with local error:

2.4b
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
3.6b
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
8.9b
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
8.9b
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
25×sqrt-pow1 log-pow
23×add-sqr-sqrt
22×exp-prod
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×pow1
6×log-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square
1×rem-log-exp fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
1.0ms
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
23.0ms
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
2.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
2.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

series2.1s

Counts
4 → 12
Calls
4 calls:
235.0ms
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
986.0ms
(log (sqrt (exp (/ 1.0 (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))))))
444.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
477.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))

simplify2.5s

Counts
93 → 93
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
01312232
11761992
22961851
37141851
428861851
done50011851

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

regimes682.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02556
12956
done2956

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.6s8000×body80valid