Details

Time bar (total: 9.9s)

sample43.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify38.0ms

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: 2.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.5b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.6b
(* (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)))))

rewrite101.0ms

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×sqrt-div pow-exp 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 → 110
Calls
4 calls:
4.0ms
(pow (sin ky) 2.0)
10.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
78.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(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:
99.0ms
(pow (sin ky) 2.0)
376.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
352.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
303.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05051608
120471504
250011501

prune508.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 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)))
2.6b
(* (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)))))
14.5b
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

rewrite120.0ms

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 cbrt-div flip3-+ flip-+ 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 → 182
Calls
4 calls:
21.0ms
(/ 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)))
76.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(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))

series1.5s

Counts
4 → 12
Calls
4 calls:
367.0ms
(/ 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)))
478.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
303.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
309.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify88.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05963726
123233237
250023165

prune645.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.0b

localize33.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b
(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)))))
10.3b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.5b
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

rewrite152.0ms

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 cube-mult cbrt-div flip3-+ unpow3 flip-+ 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 → 162
Calls
4 calls:
76.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
53.0ms
(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)))))
5.0ms
(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))

series1.3s

Counts
4 → 12
Calls
4 calls:
349.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
371.0ms
(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)))))
301.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
300.0ms
(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify75.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06592509
122322170
250012145

prune720.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.5b
(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
2.6b
(* (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)))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
17×add-exp-log
14×add-cube-cbrt
13×unpow-prod-down
11×associate-*l*
7×pow1 log-pow
6×exp-prod prod-exp sqrt-prod add-cbrt-cube
5×associate-*r*
4×pow-exp add-log-exp
3×pow-unpow log-prod times-frac unswap-sqr sqr-pow
2×pow-to-exp flip3-+ sqrt-div associate-*r/ div-exp flip-+ distribute-lft-out
1×distribute-rgt-in rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow1/2 rem-log-exp *-commutative cbrt-unprod div-inv
Counts
4 → 87
Calls
4 calls:
4.0ms
(pow (sin ky) 2.0)
14.0ms
(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
76.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(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:
104.0ms
(pow (sin ky) 2.0)
304.0ms
(log (exp (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
350.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
303.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify55.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
04511021
11747968
25002968

prune544.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.0b

regimes484.0ms

Accuracy

0% (0.4b remaining)

Error of 1.7b against oracle of 1.3b and baseline of 1.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03320
13320

end0.0ms

sample1.1s

Algorithm
intervals
Results
789.0ms8000×body80valid