Details

sample41.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	22	29
1	52	29
2	123	28
3	308	28
4	848	28
5	3422	28
done	5000	28

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.5b	(/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
1.3b	(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
8.7b	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
7×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/l*`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-exp` `clear-num` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
3.0ms	(/ 1.0 (sqrt (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)
1.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

101.0ms	(pow (sin ky) 2.0)
419.0ms	(/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
225.0ms	(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
341.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify789.0ms

Counts

97 → 97

Iterations

Useful iterations: 3 (308.0ms)

Iter	Nodes	Cost
0	168	2499
1	317	2299
2	723	2094
3	2039	2088
done	5000	2088

prune421.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
8.7b	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
8.7b	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
8.7b	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

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

series1.4s

Counts

4 → 12

Calls

4 calls:

353.0ms	(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
337.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
340.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
331.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify1.3s

Counts

73 → 73

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	82	1961
1	157	1774
2	341	1571
3	939	1560
4	3159	1536
done	5000	1528

prune427.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.5b	(log (exp (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
1.3b	(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
8.7b	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `log-pow`
6×	`exp-prod` `sqrt-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `log-prod`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp` `fma-udef` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

1.0ms	(pow (sin ky) 2.0)
2.0ms	(log (exp (sqrt (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)
1.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (sin ky) 2.0)
348.0ms	(log (exp (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
233.0ms	(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
349.0ms	(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify703.0ms

Counts

76 → 76

Iterations

Useful iterations: 3 (214.0ms)

Iter	Nodes	Cost
0	136	1586
1	253	1425
2	582	1246
3	1745	1240
done	5001	1240

prune374.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.0b

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 1.0b

regimes333.0ms

Accuracy

0% (0.4b remaining)

Error of 1.6b against oracle of 1.2b and baseline of 1.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	71
1	29	71
done	29	71

end0.0ms

sample1.0s

Algorithm

intervals

Results

782.0ms

8000×

body

valid