Details

Time bar (total: 9.9s)

sample73.0ms

Algorithm
intervals
Results
24.0ms198×body80valid
13.0ms16×body1280valid
8.0ms15×body640valid
8.0ms20×body320valid
2.0ms7×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.8b

Counts
2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.4b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
67×add-sqr-sqrt
62×times-frac
58×associate-*l*
48×add-cube-cbrt unpow-prod-down
25×sqrt-prod
19×add-exp-log
14×associate-*r*
12×distribute-lft-out
9×unswap-sqr
8×pow1 associate-/r* add-cbrt-cube
6×prod-exp
4×sqrt-div pow-exp *-commutative add-log-exp
3×pow-unpow flip3-+ div-exp flip-+ associate-/l* sqr-pow
2×+-commutative distribute-rgt-in pow-to-exp distribute-lft-in associate-*r/ associate-/r/ div-inv
1×cbrt-undiv rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num cbrt-unprod
Counts
4 → 158
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
33.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
31.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms
(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:
106.0ms
(pow (sin kx) 2.0)
377.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
378.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
319.0ms
(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
170 → 170
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
08472146
133642024
250022021

prune696.0ms

Filtered
170 candidates to 116 candidates (68.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1673170
Fresh000
Picked101
Done000
Total1683171

Merged error: 0.6b

Counts
171 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
2.3b
(* (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)))))
14.7b
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
133×*-un-lft-identity
113×times-frac
110×cbrt-prod
103×add-sqr-sqrt
85×unpow-prod-down
84×add-cube-cbrt
64×associate-*l*
55×sqrt-prod
40×cube-prod
25×associate-/r*
24×distribute-lft-out
18×add-exp-log
14×associate-*r*
9×add-cbrt-cube unswap-sqr
7×pow1 sqr-pow
6×sqrt-div prod-exp
5×cube-mult unpow3
4×cube-div cbrt-div flip3-+ *-commutative flip-+ add-log-exp
3×div-exp pow-exp associate-/l*
2×cbrt-undiv +-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-/r/ rem-cbrt-cube div-inv
1×pow-to-exp rem-sqrt-square pow-unpow frac-2neg sqrt-pow1 pow1/2 pow1/3 pow-prod-down clear-num cbrt-unprod
Counts
4 → 244
Calls
4 calls:
38.0ms
(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
31.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
38.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

series1.4s

Counts
4 → 12
Calls
4 calls:
381.0ms
(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
370.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
306.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
314.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify113.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
09474475
136293909
250013853

prune897.0ms

Filtered
256 candidates to 135 candidates (52.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2542256
Fresh202
Picked101
Done000
Total2572259

Merged error: 0.6b

Counts
259 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.8b
(log (exp (/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))))
10.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.7b
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
120×*-un-lft-identity
113×times-frac
98×add-sqr-sqrt
88×cbrt-prod
82×log-pow
81×exp-prod
79×add-cube-cbrt
77×unpow-prod-down
62×associate-*l*
45×sqrt-prod
32×cube-prod
20×distribute-lft-out
17×add-exp-log
14×associate-*r*
9×unswap-sqr
8×pow1
6×sqrt-div prod-exp add-cbrt-cube sqr-pow
4×cube-div cube-mult cbrt-div flip3-+ unpow3 *-commutative flip-+ add-log-exp
3×log-prod pow-exp
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ div-exp rem-log-exp associate-/r/ rem-cbrt-cube div-inv
1×pow-to-exp rem-sqrt-square pow-unpow sqrt-pow1 pow1/2 pow1/3 pow-prod-down cbrt-unprod
Counts
4 → 220
Calls
4 calls:
28.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
49.0ms
(log (exp (/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))))
36.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
34.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

series1.5s

Counts
4 → 12
Calls
4 calls:
403.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
406.0ms
(log (exp (/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))))
337.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
318.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify104.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
010033051
134772666
250012641

prune1.0s

Filtered
232 candidates to 137 candidates (59.1%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2320232
Fresh011
Picked011
Done000
Total2322234

Merged error: 0.6b

Counts
234 → 2

localize7.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify5.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022

Merged error: 0.6b

Counts
2 → 2

regimes371.0ms

Accuracy

0% (0.4b remaining)

Error of 1.2b against oracle of 0.8b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03320
13320

end0.0ms

sample2.0s

Algorithm
intervals
Results
774.0ms6239×body80valid
431.0ms524×body1280valid
356.0ms635×body640valid
155.0ms403×body320valid
51.0ms199×body160valid