Details

Time bar (total: 8.7s)

sample43.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify41.0ms

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: 2.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (* 2.0 l) Om) 2.0)
0.3b
(pow (sin kx) 2.0)
2.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite54.0ms

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:
4.0ms
(pow (/ (* 2.0 l) Om) 2.0)
1.0ms
(pow (sin kx) 2.0)
43.0ms
(* (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)))))

series913.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(pow (/ (* 2.0 l) Om) 2.0)
108.0ms
(pow (sin kx) 2.0)
391.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
327.0ms
(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

prune491.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.5b

localize33.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 69
Calls
4 calls:
2.0ms
(cbrt (sqrt (+ 1.0 (* (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)))))
3.0ms
(sqrt (+ 1.0 (* (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)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
289.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
321.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
317.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
326.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify87.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01351217
14321159
223571157
350011157

prune476.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.5b

localize38.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 (* (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)))))
3.0ms
(sqrt (+ 1.0 (* (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)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
318.0ms
(sqrt (+ 1.0 (* (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)))))
316.0ms
(sqrt (+ 1.0 (* (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)))))

simplify91.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01111092
14021048
223061048
350011048

prune535.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (* 2.0 l) Om) 2.0)
0.3b
(pow (sin kx) 2.0)
2.5b
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×unpow-prod-down
19×add-sqr-sqrt
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×log-prod associate-*r* add-log-exp
4×expm1-log1p-u div-exp log1p-expm1-u sqr-pow
3×pow-to-exp log-pow unswap-sqr
2×distribute-rgt-in pow-pow distribute-lft-in associate-*r/ exp-sum div-inv distribute-lft-out
1×exp-prod exp-to-pow flip3-+ rem-log-exp *-commutative cbrt-unprod flip-+
Counts
4 → 101
Calls
4 calls:
4.0ms
(pow (/ (* 2.0 l) Om) 2.0)
1.0ms
(pow (sin kx) 2.0)
4.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
46.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series964.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(pow (/ (* 2.0 l) Om) 2.0)
108.0ms
(pow (sin kx) 2.0)
387.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
383.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify60.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0485956
11914875
25003875

prune656.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.5b

regimes465.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.2b and baseline of 1.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03672
13672

end0.0ms

sample1.0s

Algorithm
intervals
Results
784.0ms8000×body80valid