Details

Time bar (total: 20.9s)

sample120.0ms

Algorithm
intervals
Results
81.0ms256×body80valid

simplify731.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
41131
3299
2124
152
022

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0)))
0.4b
(/ 2.0 (/ Om l))
3.1b
(* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0))
9.9b
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

rewrite343.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
112×add-sqr-sqrt
103×*-un-lft-identity
99×add-cube-cbrt
49×unpow-prod-down
48×associate-*r*
23×add-exp-log
19×associate-/r*
15×sqrt-prod
13×add-cbrt-cube
10×div-inv
7×div-exp
6×associate-/l*
5×pow1 associate-*l* prod-exp unswap-sqr
4×cbrt-undiv sqrt-div associate-/r/ add-log-exp
3×flip3-+ pow-exp flip-+
2×clear-num frac-2neg associate-*l/ distribute-lft-out sqr-pow
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 *-commutative cbrt-unprod
Counts
4 → 200
Calls
4 calls:
66.0ms
(/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0)))
15.0ms
(/ 2.0 (/ Om l))
169.0ms
(* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0))
75.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
695.0ms
(/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0)))
21.0ms
(/ 2.0 (/ Om l))
499.0ms
(* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0))
578.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

simplify718.0ms

Counts
212 → 212
Iterations
IterNodes
done5000
11081
0388

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.1b

localize104.0ms

Local error

Found 4 expressions with local error:

9.9b
(sqrt (+ (* (* (pow (/ (* (/ (cbrt 2.0) (cbrt (/ Om l))) (cbrt 2.0)) (cbrt (/ Om l))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) (pow (/ (cbrt 2.0) (cbrt (/ Om l))) 2.0)) 1.0))
16.2b
(cbrt (/ Om l))
16.2b
(cbrt (/ Om l))
16.2b
(cbrt (/ Om l))

rewrite353.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 81
Calls
4 calls:
337.0ms
(sqrt (+ (* (* (pow (/ (* (/ (cbrt 2.0) (cbrt (/ Om l))) (cbrt 2.0)) (cbrt (/ Om l))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) (pow (/ (cbrt 2.0) (cbrt (/ Om l))) 2.0)) 1.0))
4.0ms
(cbrt (/ Om l))
4.0ms
(cbrt (/ Om l))
4.0ms
(cbrt (/ Om l))

series915.0ms

Counts
4 → 12
Calls
4 calls:
654.0ms
(sqrt (+ (* (* (pow (/ (* (/ (cbrt 2.0) (cbrt (/ Om l))) (cbrt 2.0)) (cbrt (/ Om l))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) (pow (/ (cbrt 2.0) (cbrt (/ Om l))) 2.0)) 1.0))
105.0ms
(cbrt (/ Om l))
77.0ms
(cbrt (/ Om l))
78.0ms
(cbrt (/ Om l))

simplify634.0ms

Counts
93 → 93
Iterations
IterNodes
done5000
21091
1311
0147

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.1b

localize76.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
6.9b
(sqrt (sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
9.9b
(sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))
9.9b
(sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp
Counts
4 → 72
Calls
4 calls:
42.0ms
(sqrt (sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
64.0ms
(sqrt (sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
60.0ms
(sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))
44.0ms
(sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
479.0ms
(sqrt (sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
464.0ms
(sqrt (sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
485.0ms
(sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))
490.0ms
(sqrt (+ (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))

simplify613.0ms

Counts
84 → 84
Iterations
IterNodes
done5001
21192
1280
0108

prune980.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.1b

localize66.0ms

Local error

Found 4 expressions with local error:

12.5b
(cbrt (pow (sqrt (+ 1.0 (* (* (pow (/ (/ (cbrt 2.0) (cbrt (/ Om l))) (/ (cbrt (/ Om l)) (cbrt 2.0))) 2.0) (pow (/ (cbrt 2.0) (cbrt (/ Om l))) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))
16.2b
(cbrt (/ Om l))
16.2b
(cbrt (/ Om l))
16.2b
(cbrt (/ Om l))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
57×cbrt-prod
30×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
6×unpow-prod-down cube-prod sqrt-prod
5×cbrt-div
4×pow1 add-cbrt-cube pow1/3 add-exp-log add-log-exp
3×div-inv
2×cube-div sqrt-div
1×cube-mult flip3-+ unpow3 rem-cbrt-cube flip-+ sqr-pow
Counts
4 → 95
Calls
4 calls:
7.0ms
(cbrt (pow (sqrt (+ 1.0 (* (* (pow (/ (/ (cbrt 2.0) (cbrt (/ Om l))) (/ (cbrt (/ Om l)) (cbrt 2.0))) 2.0) (pow (/ (cbrt 2.0) (cbrt (/ Om l))) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))
2.0ms
(cbrt (/ Om l))
2.0ms
(cbrt (/ Om l))
2.0ms
(cbrt (/ Om l))

series949.0ms

Counts
4 → 12
Calls
4 calls:
711.0ms
(cbrt (pow (sqrt (+ 1.0 (* (* (pow (/ (/ (cbrt 2.0) (cbrt (/ Om l))) (/ (cbrt (/ Om l)) (cbrt 2.0))) 2.0) (pow (/ (cbrt 2.0) (cbrt (/ Om l))) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))
74.0ms
(cbrt (/ Om l))
83.0ms
(cbrt (/ Om l))
80.0ms
(cbrt (/ Om l))

simplify1.4s

Counts
107 → 107
Iterations
IterNodes
done5001
21959
1426
0181

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.1b

regimes1.0s

Accuracy

0% (0.4b remaining)

Error of 1.8b against oracle of 1.3b and baseline of 1.8b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done30
130
024

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.6s7999×body80valid
1.0ms1×body160valid