Details

Time bar (total: 17.8s)

sample110.0ms

Algorithm
intervals
Results
62.0ms256×body80valid

simplify982.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
41239
3345
2132
152
022

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize69.0ms

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))))))
2.2b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite132.0ms

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 associate-/r* prod-exp
5×associate-*r*
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u 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×distribute-rgt-in cbrt-undiv rem-sqrt-square clear-num pow-pow frac-2neg distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod
Counts
4 → 118
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
14.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
103.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(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:
153.0ms
(pow (sin ky) 2.0)
688.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
495.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
558.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.8s

Counts
130 → 130
Iterations
IterNodes
done5002
22471
1607
0230

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize65.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (/ 1.0 (sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
6.7b
(sqrt (/ 1.0 (sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
9.6b
(sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
9.6b
(sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
70×sqrt-prod
44×add-sqr-sqrt
40×times-frac
32×*-un-lft-identity add-cube-cbrt
8×pow1 rem-sqrt-square
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u add-log-exp
2×sqrt-div div-inv
Counts
4 → 104
Calls
4 calls:
8.0ms
(sqrt (/ 1.0 (sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
5.0ms
(sqrt (/ 1.0 (sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
1.0ms
(sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
1.0ms
(sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
642.0ms
(sqrt (/ 1.0 (sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
743.0ms
(sqrt (/ 1.0 (sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
538.0ms
(sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
554.0ms
(sqrt (fma (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify899.0ms

Counts
116 → 116
Iterations
IterNodes
done5000
31905
2578
1238
0142

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
1.0b
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
1.4b
(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×unpow-prod-down
13×add-sqr-sqrt add-cube-cbrt
11×pow-unpow
8×log-prod pow-pow
7×pow1 add-exp-log
5×exp-prod sqr-pow
4×expm1-log1p-u pow-to-exp add-cbrt-cube pow-exp log1p-expm1-u add-log-exp
3×rem-log-exp
2×unpow-prod-up distribute-lft-out
1×log-pow
Counts
4 → 86
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
24.0ms
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
24.0ms
(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
178.0ms
(pow (sin kx) 2.0)
168.0ms
(pow (sin ky) 2.0)
348.0ms
(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
317.0ms
(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))))

simplify1.3s

Counts
98 → 98
Iterations
IterNodes
done5002
21710
1463
0168

prune1.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.8b

regimes560.0ms

Accuracy

0% (0.4b remaining)

Error of 1.7b against oracle of 1.3b and baseline of 1.7b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done27
127
023

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.4s8000×body80valid