Details

Time bar (total: 20.1s)

sample292.0ms

Algorithm
intervals
Results
240.0ms256×body80valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done5000
41239
3345
2132
152
022

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt (fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))
0.4b
(/ 2.0 (/ Om l))
2.4b
(fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
9.9b
(sqrt (fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
93×times-frac
63×add-sqr-sqrt
62×*-un-lft-identity add-cube-cbrt
19×associate-/r*
15×sqrt-prod
11×add-cbrt-cube add-exp-log
6×div-inv associate-/l*
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ fma-udef
Counts
4 → 138
Calls
4 calls:
5.0ms
(/ 1.0 (sqrt (fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))
10.0ms
(/ 2.0 (/ Om l))
0.0ms
(fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
4.0ms
(sqrt (fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
708.0ms
(/ 1.0 (sqrt (fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))
28.0ms
(/ 2.0 (/ Om l))
338.0ms
(fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
517.0ms
(sqrt (fma (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify1.1s

Counts
150 → 150
Iterations
IterNodes
done5000
22366
1611
0272

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.1b

localize87.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
4.0ms
(sqrt (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)))
4.0ms
(sqrt (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)))
2.0ms
(sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0))
3.0ms
(sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
376.0ms
(sqrt (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)))
427.0ms
(sqrt (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)))
400.0ms
(sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0))
410.0ms
(sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0))

simplify626.0ms

Counts
84 → 84
Iterations
IterNodes
done5001
4840
3301
2152
182
053

prune914.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (cbrt (pow (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)) 3)))
2.4b
(fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)
9.9b
(sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0))
12.5b
(cbrt (pow (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)) 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
90×cbrt-prod
63×times-frac
57×add-sqr-sqrt
56×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
30×unpow-prod-down cube-prod
21×associate-/r*
6×add-exp-log
5×cube-mult pow1 add-cbrt-cube unpow3 sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l*
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow1/3 div-exp rem-cbrt-cube fma-udef div-inv
Counts
4 → 155
Calls
4 calls:
18.0ms
(/ 1.0 (cbrt (pow (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)) 3)))
0.0ms
(fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)
1.0ms
(sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0))
4.0ms
(cbrt (pow (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)) 3))

series1.5s

Counts
4 → 12
Calls
4 calls:
445.0ms
(/ 1.0 (cbrt (pow (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)) 3)))
168.0ms
(fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)
436.0ms
(sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0))
422.0ms
(cbrt (pow (sqrt (fma (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (* (/ 2.0 Om) l) 2.0) 1.0)) 3))

simplify1.3s

Counts
167 → 167
Iterations
IterNodes
done5000
21864
1308
0172

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.1b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 87
Calls
4 calls:
1.0ms
(sqrt (fma (pow (* (* (/ (cbrt 2.0) (cbrt (/ Om l))) (/ (cbrt 2.0) (cbrt (/ Om l)))) (/ (cbrt 2.0) (cbrt (/ Om l)))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
2.0ms
(cbrt (/ Om l))
2.0ms
(cbrt (/ Om l))
2.0ms
(cbrt (/ Om l))

series987.0ms

Counts
4 → 12
Calls
4 calls:
699.0ms
(sqrt (fma (pow (* (* (/ (cbrt 2.0) (cbrt (/ Om l))) (/ (cbrt 2.0) (cbrt (/ Om l)))) (/ (cbrt 2.0) (cbrt (/ Om l)))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
111.0ms
(cbrt (/ Om l))
87.0ms
(cbrt (/ Om l))
90.0ms
(cbrt (/ Om l))

simplify825.0ms

Counts
99 → 99
Iterations
IterNodes
done5000
31843
2531
1226
0132

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 2.1b

regimes655.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done27
127
023

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.4s7999×body80valid
1.0ms1×body160valid