Details

Time bar (total: 7.8s)

sample43.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify41.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216
done500216

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.3b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×add-exp-log
17×*-un-lft-identity
16×unpow-prod-down
13×add-cube-cbrt
11×associate-*l*
7×pow1
6×pow-unpow prod-exp add-cbrt-cube
5×associate-*r* pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp times-frac sqrt-prod unswap-sqr
2×pow-pow flip3-+ sqrt-div associate-*r/ div-exp flip-+ distribute-lft-out
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
74.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series952.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (sin kx) 2.0)
112.0ms
(pow (sin ky) 2.0)
384.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
351.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify56.0ms

Counts
106 → 106
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0489887
11950857
25002857
done5002857

prune431.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize28.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 71
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))
4.0ms
(cbrt (/ (* 2.0 l) Om))

series767.0ms

Counts
4 → 12
Calls
4 calls:
483.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
95.0ms
(cbrt (/ (* 2.0 l) Om))
95.0ms
(cbrt (/ (* 2.0 l) Om))
94.0ms
(cbrt (/ (* 2.0 l) Om))

simplify149.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0200867
1610819
23836811
35001811
done5001811

prune498.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (pow (log1p (expm1 (cbrt (/ (* 2.0 l) Om)))) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
18×add-sqr-sqrt
17×*-un-lft-identity
13×add-cube-cbrt
9×add-exp-log times-frac
7×associate-*l*
6×unpow-prod-down add-cbrt-cube
5×associate-*r*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 prod-exp div-inv unswap-sqr
2×associate-*r/ distribute-lft-out sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in flip3-+ pow-exp *-commutative cbrt-unprod flip-+
Counts
4 → 87
Calls
4 calls:
65.0ms
(* (pow (log1p (expm1 (cbrt (/ (* 2.0 l) Om)))) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))
7.0ms
(cbrt (/ (* 2.0 l) Om))

series759.0ms

Counts
4 → 12
Calls
4 calls:
478.0ms
(* (pow (log1p (expm1 (cbrt (/ (* 2.0 l) Om)))) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
93.0ms
(cbrt (/ (* 2.0 l) Om))
93.0ms
(cbrt (/ (* 2.0 l) Om))
95.0ms
(cbrt (/ (* 2.0 l) Om))

simplify50.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0341915
11350838
25002826
done5002826

prune656.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (pow (log1p (expm1 (cbrt (/ (* 2.0 l) Om)))) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
18×add-sqr-sqrt
17×*-un-lft-identity
13×add-cube-cbrt
9×add-exp-log times-frac
7×associate-*l*
6×unpow-prod-down add-cbrt-cube
5×associate-*r*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 prod-exp div-inv unswap-sqr
2×associate-*r/ distribute-lft-out sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in flip3-+ pow-exp *-commutative cbrt-unprod flip-+
Counts
4 → 87
Calls
4 calls:
69.0ms
(* (pow (log1p (expm1 (cbrt (/ (* 2.0 l) Om)))) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))

series914.0ms

Counts
4 → 12
Calls
4 calls:
635.0ms
(* (pow (log1p (expm1 (cbrt (/ (* 2.0 l) Om)))) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
94.0ms
(cbrt (/ (* 2.0 l) Om))
89.0ms
(cbrt (/ (* 2.0 l) Om))
96.0ms
(cbrt (/ (* 2.0 l) Om))

simplify47.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0341915
11350838
25002826
done5002826

prune662.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

regimes311.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03326
13326
done3326

end0.0ms

sample1.1s

Algorithm
intervals
Results
770.0ms8000×body80valid