Details

Time bar (total: 6.9s)

sample77.0ms

Algorithm
intervals
Results
23.0ms194×body80valid
17.0ms33×body640valid
10.0ms13×body1280valid
4.0ms10×body320valid
2.0ms6×body160valid

simplify41.0ms

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: 1.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.7b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.9b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.3b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite35.0ms

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)
5.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
20.0ms
(* (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:
108.0ms
(pow (sin kx) 2.0)
388.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
385.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
322.0ms
(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

prune551.0ms

Filtered
130 candidates to 91 candidates (70.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.9b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.3b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.9b
(cbrt (pow (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) 3))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt times-frac
55×*-un-lft-identity
54×cbrt-prod
51×add-cube-cbrt
34×unpow-prod-down
33×sqrt-prod
24×cube-prod
18×add-exp-log
11×associate-*l*
8×sqrt-div add-cbrt-cube
6×prod-exp associate-/r* associate-/r/
5×pow1 flip3-+ associate-*r* flip-+
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×div-exp pow-exp associate-/l* unswap-sqr sqr-pow
2×associate-*r/ distribute-lft-out
1×cbrt-undiv cube-div distribute-rgt-in cube-mult pow-to-exp rem-sqrt-square cbrt-div frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow1/3 unpow3 clear-num *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 165
Calls
4 calls:
5.0ms
(/ 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)))))
8.0ms
(cbrt (pow (/ 1.0 (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:
386.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
389.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
323.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
385.0ms
(cbrt (pow (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) 3))

simplify99.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07593214
133273087
250012861

prune678.0ms

Filtered
177 candidates to 103 candidates (58.2%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize7.0ms

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)

Merged error: 0.8b

regimes397.0ms

Accuracy

0% (0.3b remaining)

Error of 0.9b against oracle of 0.6b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03118
13118

end0.0ms

sample2.2s

Algorithm
intervals
Results
883.0ms6174×body80valid
419.0ms527×body1280valid
381.0ms664×body640valid
162.0ms417×body320valid
55.0ms218×body160valid