Details

Time bar (total: 8.9s)

sample72.0ms

Algorithm
intervals
Results
24.0ms198×body80valid
12.0ms16×body1280valid
8.0ms15×body640valid
8.0ms20×body320valid
2.0ms7×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune9.0ms

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

localize23.0ms

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)))))

rewrite29.0ms

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:
3.0ms
(pow (sin kx) 2.0)
6.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
14.0ms
(* (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)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
98.0ms
(pow (sin kx) 2.0)
367.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
369.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
311.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05201686
121361580
250011576

prune531.0ms

Filtered
130 candidates to 91 candidates (70.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1273130
Fresh000
Picked101
Done000
Total1283131

Merged error: 0.6b

Counts
131 → 3

localize25.0ms

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))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
90×cbrt-prod
66×add-sqr-sqrt times-frac
64×*-un-lft-identity
60×add-cube-cbrt
40×unpow-prod-down
33×sqrt-prod
30×cube-prod
21×associate-/r*
18×add-exp-log
11×associate-*l*
7×add-cbrt-cube sqr-pow
6×sqrt-div prod-exp
5×pow1 cube-mult unpow3 associate-*r*
4×cube-div expm1-log1p-u cbrt-div flip3-+ flip-+ log1p-expm1-u add-log-exp
3×div-exp pow-exp associate-/l* unswap-sqr
2×associate-*r/ associate-/r/ div-inv distribute-lft-out
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow1/3 clear-num *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 190
Calls
4 calls:
9.0ms
(/ 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)))
14.0ms
(* (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)))))
5.0ms
(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:
377.0ms
(/ 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)))
366.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
302.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
306.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify85.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06113836
124033346
250013276

prune717.0ms

Filtered
202 candidates to 109 candidates (54.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2011202
Fresh112
Picked101
Done000
Total2032205

Merged error: 0.6b

Counts
205 → 2

localize29.0ms

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))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
72×cbrt-prod
70×log-pow
69×exp-prod
66×times-frac
61×add-sqr-sqrt
59×*-un-lft-identity
55×add-cube-cbrt
34×unpow-prod-down
27×sqrt-prod
24×cube-prod
16×add-exp-log
11×associate-*l*
6×pow1 sqrt-div prod-exp add-cbrt-cube sqr-pow
5×associate-*r*
4×cube-div expm1-log1p-u cube-mult cbrt-div flip3-+ unpow3 flip-+ log1p-expm1-u add-log-exp
3×log-prod pow-exp unswap-sqr
2×associate-*r/ div-exp associate-/r/ div-inv distribute-lft-out
1×distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow1/3 rem-log-exp *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 170
Calls
4 calls:
15.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(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)))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms
(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:
372.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
373.0ms
(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)))))
311.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
310.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify81.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06742613
123122272
250022247

prune812.0ms

Filtered
182 candidates to 110 candidates (60.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1811182
Fresh101
Picked011
Done000
Total1822184

Merged error: 0.6b

Counts
184 → 2

localize13.0ms

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

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022

Merged error: 0.6b

Counts
2 → 2

regimes391.0ms

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
734.0ms6239×body80valid
425.0ms524×body1280valid
362.0ms635×body640valid
156.0ms403×body320valid
51.0ms199×body160valid