Details

Time bar (total: 11.5s)

sample70.0ms

Algorithm
intervals
Results
49.0ms256×body80valid

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: 1.6b

localize24.0ms

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))))))
1.6b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.4b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite58.0ms

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:
1.0ms
(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))))))
45.0ms
(* (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)
374.0ms
(/ 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)))
310.0ms
(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 (49.0ms)

IterNodesCost
05051609
120461504
250021501

prune501.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
1.6b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.3b
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-sqr-sqrt
17×*-un-lft-identity
16×unpow-prod-down
13×add-cube-cbrt
11×associate-*l*
7×pow1
6×pow-unpow prod-exp add-cbrt-cube
5×log-prod associate-*r* pow-exp add-log-exp
4×sqr-pow
3×pow-to-exp times-frac log-pow unswap-sqr
2×distribute-rgt-in pow-pow distribute-lft-in associate-*r/ div-exp exp-sum distribute-lft-out
1×exp-prod exp-to-pow flip3-+ rem-log-exp *-commutative cbrt-unprod flip-+ div-inv
Counts
4 → 87
Calls
4 calls:
1.0ms
(pow (sin ky) 2.0)
1.0ms
(pow (sin kx) 2.0)
44.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series958.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(pow (sin ky) 2.0)
105.0ms
(pow (sin kx) 2.0)
375.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
374.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify57.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0447832
11728766
25001766

prune442.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt Om)
2.2b
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.6b
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.4b
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
54×prod-exp
37×associate-*l*
36×add-sqr-sqrt
34×unpow-prod-down
28×*-un-lft-identity
27×pow-exp
24×add-cube-cbrt
23×times-frac
16×div-exp
13×cbrt-prod
11×pow-to-exp add-cbrt-cube
6×associate-*r/ associate-*r*
5×pow1 distribute-rgt-in distribute-lft-in unswap-sqr
4×cbrt-unprod add-log-exp
3×flip3-+ sqrt-prod flip-+ sqr-pow
2×sqrt-div *-commutative div-inv distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 132
Calls
4 calls:
1.0ms
(cbrt Om)
55.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
57.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt Om)
419.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
540.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
537.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify102.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08372066
135951961
250021959

prune862.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.2b

localize35.0ms

Local error

Found 4 expressions with local error:

2.8b
(exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.6b
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.4b
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
28.8b
(log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
18×add-sqr-sqrt
11×associate-*l*
10×add-cube-cbrt *-un-lft-identity prod-exp
9×unpow-prod-down
8×associate-*r/
7×pow1
6×log-div add-cbrt-cube
5×rem-log-exp pow-exp
4×exp-prod flip3-+ times-frac exp-diff associate-*r* flip-+ add-log-exp unswap-sqr
3×log-prod div-exp sqrt-prod
2×pow-to-exp sqrt-div exp-sum log-pow sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative cbrt-unprod div-inv rem-exp-log
Counts
4 → 81
Calls
4 calls:
55.0ms
(exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
190.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
16.0ms
(log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

series2.0s

Counts
4 → 12
Calls
4 calls:
410.0ms
(exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
546.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
541.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (exp (log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
453.0ms
(log (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

simplify68.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05201631
123081535
250021534

prune548.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes581.0ms

Accuracy

0% (0.8b remaining)

Error of 2.0b against oracle of 1.2b and baseline of 2.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03018
13018

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.6s8000×body80valid