Details

Time bar (total: 6.5s)

sample43.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
1.5b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite52.0ms

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×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 → 86
Calls
4 calls:
1.0ms
(pow (sin ky) 2.0)
1.0ms
(pow (sin kx) 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)))))

series911.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (sin ky) 2.0)
111.0ms
(pow (sin kx) 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)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0473829
11858802
25002802

prune419.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.5b
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×*-un-lft-identity
21×sqrt-prod
16×add-exp-log
15×unpow-prod-down
12×add-cube-cbrt
11×associate-*l*
8×sqrt-div associate-*r*
7×pow1
6×prod-exp add-cbrt-cube distribute-lft-out unswap-sqr
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 pow-exp sqr-pow
2×associate-*r/ div-exp
1×pow-to-exp *-commutative cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
49.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

series951.0ms

Counts
4 → 12
Calls
4 calls:
476.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
315.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
03631506
111591433
250021433

prune498.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.5b
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×*-un-lft-identity
21×sqrt-prod
16×add-exp-log
15×unpow-prod-down
12×add-cube-cbrt
11×associate-*l*
8×sqrt-div associate-*r*
7×pow1
6×prod-exp add-cbrt-cube distribute-lft-out unswap-sqr
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 pow-exp sqr-pow
2×associate-*r/ div-exp
1×pow-to-exp *-commutative cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
45.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

series947.0ms

Counts
4 → 12
Calls
4 calls:
482.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
311.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03631506
111591433
250021433

prune549.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.0b

localize11.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 1.0b

regimes443.0ms

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.3b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03230
13230

end0.0ms

sample1.2s

Algorithm
intervals
Results
956.0ms8000×body80valid