Details

Time bar (total: 21.7s)

sample62.0ms

Algorithm
intervals
Results
34.0ms256×body80valid

simplify5.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
02229
15229
213128
333028
4115228
5477228
done500028

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
1.2b
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
7.8b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log unpow-prod-down pow-unpow
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow-to-exp pow-pow pow-exp sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 63
Calls
4 calls:
7.0ms
(pow (sin ky) 2.0)
6.0ms
(pow (sin kx) 2.0)
0.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
4.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
142.0ms
(pow (sin ky) 2.0)
161.0ms
(pow (sin kx) 2.0)
372.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
521.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify1.5s

Counts
75 → 75
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01371098
12801019
2684899
32173895
done5001883

prune527.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin ky))
0.6b
(cbrt (sin ky))
1.2b
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))) 1.0)
7.8b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))) 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 51
Calls
4 calls:
3.0ms
(cbrt (sin ky))
3.0ms
(cbrt (sin ky))
1.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))) 1.0)
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))) 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
200.0ms
(cbrt (sin ky))
136.0ms
(cbrt (sin ky))
392.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))) 1.0)
502.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (* (pow (* (cbrt (sin ky)) (cbrt (sin ky))) 2.0) (pow (cbrt (sin ky)) 2.0))) 1.0))

simplify1.2s

Counts
63 → 63
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01021327
12081231
2503967
31607957
done5000943

prune593.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
0.5b
(expm1 (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
1.2b
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log unpow-prod-down pow-unpow
5×log1p-expm1-u
4×expm1-log1p-u add-cbrt-cube add-log-exp
2×pow-to-exp pow-pow pow-exp sqr-pow
1×expm1-log1p fma-udef expm1-udef
Counts
4 → 59
Calls
4 calls:
4.0ms
(pow (sin ky) 2.0)
4.0ms
(pow (sin kx) 2.0)
0.0ms
(expm1 (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
0.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
167.0ms
(pow (sin ky) 2.0)
172.0ms
(pow (sin kx) 2.0)
470.0ms
(expm1 (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
341.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)

simplify1.9s

Counts
71 → 71
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0136999
1292956
2703815
32176811
done5000799

prune529.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.9b

localize25.0ms

Local error

Found 1 expressions with local error:

1.0b
(expm1 1.0)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×log1p-expm1-u
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt expm1-log1p *-un-lft-identity add-cbrt-cube expm1-udef add-log-exp
Counts
1 → 11
Calls
1 calls:
1.0ms
(expm1 1.0)

series0.0ms

Counts
1 → 1
Calls
1 calls:
0.0ms
(expm1 1.0)

simplify2.4s

Counts
12 → 12
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01239
11337
21533
32033
42633
53633
65733
712933
841333
9185433
done500033

prune47.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.9b

regimes709.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02539
12939
done2939

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.5s7999×body80valid
1.0ms1×body160valid