Details

Time bar (total: 7.1s)

sample82.0ms

Algorithm
intervals
Results
23.0ms196×body80valid
18.0ms17×body1280valid
13.0ms23×body640valid
7.0ms15×body320valid
1.0ms5×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.2b
(pow (/ (* 2.0 l) Om) 2.0)
1.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-sqr-sqrt unpow-prod-down
18×*-un-lft-identity
14×add-cube-cbrt
11×associate-*l*
7×pow1 pow-exp prod-exp
6×pow-unpow times-frac add-cbrt-cube
5×associate-*r*
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp sqrt-prod unswap-sqr
2×pow-pow flip3-+ sqrt-div associate-*r/ flip-+ div-inv distribute-lft-out
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod
Counts
4 → 100
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
5.0ms
(pow (/ (* 2.0 l) Om) 2.0)
19.0ms
(* (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)))))

series926.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(pow (sin kx) 2.0)
86.0ms
(pow (/ (* 2.0 l) Om) 2.0)
405.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
328.0ms
(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
112 → 112
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0514957
12069914
25001914

prune488.0ms

Filtered
112 candidates to 79 candidates (70.5%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0)))
1.7b
(* (expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b
(sqrt (+ 1.0 (* (expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.5b
(log1p (pow (/ (* 2.0 l) Om) 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-sqr-sqrt
7×pow1 add-cube-cbrt
6×add-exp-log add-cbrt-cube
5×expm1-log1p-u associate-*r*
4×log1p-expm1-u add-log-exp
3×associate-*l* sqrt-prod
2×unpow-prod-down flip3-+ sqrt-div associate-*r/ flip-+ distribute-lft-out
1×distribute-rgt-in rem-sqrt-square log1p-udef expm1-log1p distribute-lft-in sqrt-pow1 pow1/2 log1p-expm1 pow-prod-down prod-exp *-commutative cbrt-unprod expm1-udef unswap-sqr
Counts
4 → 65
Calls
4 calls:
1.0ms
(expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0)))
11.0ms
(* (expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.0ms
(log1p (pow (/ (* 2.0 l) Om) 2.0))

series988.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0)))
203.0ms
(* (expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
550.0ms
(sqrt (+ 1.0 (* (expm1 (log1p (pow (/ (* 2.0 l) Om) 2.0))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
114.0ms
(log1p (pow (/ (* 2.0 l) Om) 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0337919
11236842
25001838

prune404.0ms

Filtered
77 candidates to 62 candidates (80.5%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.2b
(pow (/ (* 2.0 l) Om) 2.0)
1.0b
(pow (exp (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (pow (/ (* 2.0 l) Om) 2.0))
1.8b
(log (pow (exp (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (pow (/ (* 2.0 l) Om) 2.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
27×unpow-prod-down
20×*-un-lft-identity
17×pow-unpow
16×add-sqr-sqrt add-cube-cbrt
12×add-exp-log
8×log-prod pow-pow
7×pow1
6×times-frac pow-exp
5×exp-prod sqr-pow
4×expm1-log1p-u pow-to-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-log-exp
2×div-exp exp-sum div-inv distribute-lft-out
1×prod-exp log-pow
Counts
4 → 98
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
6.0ms
(pow (/ (* 2.0 l) Om) 2.0)
13.0ms
(pow (exp (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (pow (/ (* 2.0 l) Om) 2.0))
10.0ms
(log (pow (exp (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (pow (/ (* 2.0 l) Om) 2.0)))

series764.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(pow (sin kx) 2.0)
87.0ms
(pow (/ (* 2.0 l) Om) 2.0)
252.0ms
(pow (exp (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (pow (/ (* 2.0 l) Om) 2.0))
315.0ms
(log (pow (exp (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (pow (/ (* 2.0 l) Om) 2.0)))

simplify45.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04141016
11491940
25001928

prune545.0ms

Filtered
110 candidates to 81 candidates (73.6%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 1.0b

regimes297.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03018
13018

end0.0ms

sample2.2s

Algorithm
intervals
Results
902.0ms6145×body80valid
444.0ms543×body1280valid
371.0ms681×body640valid
160.0ms416×body320valid
61.0ms215×body160valid