Details

Time bar (total: 8.4s)

sample44.0ms

Algorithm
intervals
Results
26.0ms256×body80valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.6b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.8b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite56.0ms

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×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×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 → 118
Calls
4 calls:
1.0ms
(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))))))
40.0ms
(* (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:
101.0ms
(pow (sin kx) 2.0)
383.0ms
(/ 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)))
314.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05201686
121361580
250011576

prune548.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.3b

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(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
50×add-sqr-sqrt
27×unpow-prod-down
24×*-un-lft-identity
21×sqrt-prod
19×hypot-def
16×add-exp-log
15×sqr-pow
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×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 pow-exp
2×associate-*r/ div-exp
1×pow-to-exp *-commutative cbrt-unprod div-inv
Counts
4 → 117
Calls
4 calls:
43.0ms
(* (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)))
6.0ms
(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)))))))

series937.0ms

Counts
4 → 12
Calls
4 calls:
472.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
314.0ms
(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)))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03781613
112321509
250011507

prune680.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize30.0ms

Local error

Found 4 expressions with local error:

3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(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)))))))
12.8b
(cbrt (pow (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))))))) 3))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
22×unpow-prod-down
20×*-un-lft-identity
19×sqrt-prod hypot-def
18×cbrt-prod
13×sqr-pow
12×add-cube-cbrt
8×sqrt-div
7×pow1
6×cube-prod
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube
Counts
4 → 105
Calls
4 calls:
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms
(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)))))))
4.0ms
(cbrt (pow (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))))))) 3))

series777.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms
(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)))))))
313.0ms
(cbrt (pow (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))))))) 3))

simplify52.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03102136
110262077
250012075

prune637.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.3b

localize39.0ms

Local error

Found 4 expressions with local error:

1.5b
(log (exp (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)))))))))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(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)))))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
19×hypot-def
18×*-un-lft-identity
16×unpow-prod-down sqrt-prod
12×sqr-pow
10×add-cube-cbrt
8×pow1
7×log-pow
6×exp-prod sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out add-log-exp
3×rem-sqrt-square log-prod sqrt-pow1 flip3-+ pow1/2 flip-+
1×rem-log-exp
Counts
4 → 94
Calls
4 calls:
6.0ms
(log (exp (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)))))))))
17.0ms
(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)))))))

series911.0ms

Counts
4 → 12
Calls
4 calls:
445.0ms
(log (exp (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)))))))))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
71.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
317.0ms
(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)))))))

simplify135.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
02421582
17271461
238161459
350011459

prune657.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.3b

regimes301.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03532
13532

end0.0ms

sample1.1s

Algorithm
intervals
Results
826.0ms8000×body80valid