Details

Time bar (total: 3.5m)

sample6.1s

Algorithm
intervals
Results
5.8s1708×body10240exit
87.0ms82×body1280valid
52.0ms63×body640valid
14.0ms86×body80valid
11.0ms21×body320valid
1.0ms4×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (/ (* 2.0 l) Om) 2.0)
1.8b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.8b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite50.0ms

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×div-exp 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 → 92
Calls
4 calls:
1.0ms
(pow (sin ky) 2.0)
3.0ms
(pow (/ (* 2.0 l) Om) 2.0)
39.0ms
(* (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)))))

series893.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(pow (sin ky) 2.0)
82.0ms
(pow (/ (* 2.0 l) Om) 2.0)
389.0ms
(* (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)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0499897
11984856
25001856

prune430.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.4b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.7b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.8b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
124×add-exp-log
72×prod-exp
37×pow-exp
24×div-exp
22×associate-*l*
20×add-sqr-sqrt unpow-prod-down
18×*-un-lft-identity
14×add-cube-cbrt
13×pow-to-exp
11×add-cbrt-cube
6×pow1 times-frac associate-*r/ associate-*r*
5×distribute-rgt-in distribute-lft-in
4×cbrt-unprod add-log-exp sqr-pow
3×pow-unpow flip3-+ sqrt-prod flip-+ unswap-sqr
2×sqrt-div *-commutative div-inv distribute-lft-out
1×rem-sqrt-square pow-pow sqrt-pow1 pow1/2
Counts
4 → 127
Calls
4 calls:
1.0ms
(pow (sin ky) 2.0)
42.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
42.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (sin ky) 2.0)
382.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
390.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
325.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06061919
125451698
250011696

prune505.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
1.1b
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.2b
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
25×unpow-prod-down
19×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt
14×pow-pow
12×add-exp-log
11×exp-prod
9×pow-unpow
8×log-prod
7×pow1
6×times-frac pow-exp
5×sqr-pow
4×pow-to-exp add-cbrt-cube add-log-exp
3×rem-log-exp
2×unpow-prod-up div-exp div-inv distribute-lft-out
1×prod-exp log-pow
Counts
4 → 88
Calls
4 calls:
1.0ms
(pow (sin ky) 2.0)
4.0ms
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
8.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
22.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series628.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(pow (sin ky) 2.0)
84.0ms
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
222.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
210.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04621110
120961013
25001951

prune674.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.8b

regimes272.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03222
13222

end0.0ms

sample3.3m

Algorithm
intervals
Results
3.2m56042×body10240exit
2.9s2662×body1280valid
1.4s1842×body640valid
417.0ms793×body320valid
399.0ms2358×body80valid
119.0ms345×body160valid