Details

sample98.0ms

Algorithm

intervals

Results

60.0ms

256×

body

valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	4227
4	1000
3	308
2	129
1	52
0	22

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* l (/ 2.0 Om)) 2.0)
0.3b	(* l (/ 2.0 Om))
2.0b	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
6.8b	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r`
10×	`pow1` `times-frac`
9×	`add-cbrt-cube`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l` `pow-exp` `sqrt-prod`
2×	`pow-pow` `div-exp` `pow-prod-down` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `unpow-prod-down` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

7.0ms	(pow (* l (/ 2.0 Om)) 2.0)
12.0ms	(* l (/ 2.0 Om))
0.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
4.0ms	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (* l (/ 2.0 Om)) 2.0)
36.0ms	(* l (/ 2.0 Om))
328.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
548.0ms	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify2.8s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
3	4742
2	1147
1	378
0	160

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt Om)
0.6b	(cbrt Om)
2.0b	(fma (pow (* (/ l (* (cbrt Om) (cbrt Om))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
6.8b	(sqrt (fma (pow (* (/ l (* (cbrt Om) (cbrt Om))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `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:

1.0ms	(cbrt Om)
1.0ms	(cbrt Om)
0.0ms	(fma (pow (* (/ l (* (cbrt Om) (cbrt Om))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
1.0ms	(sqrt (fma (pow (* (/ l (* (cbrt Om) (cbrt Om))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

283.0ms	(cbrt Om)
264.0ms	(cbrt Om)
403.0ms	(fma (pow (* (/ l (* (cbrt Om) (cbrt Om))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
590.0ms	(sqrt (fma (pow (* (/ l (* (cbrt Om) (cbrt Om))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify1.9s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	1397
2	471
1	188
0	94

prune794.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.0b

localize164.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt Om)
1.0b	(expm1 (log1p (cbrt Om)))
2.0b	(fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
6.3b	(sqrt (fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`*-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-prod` `sqrt-prod`
1×	`rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2` `pow1/3` `fma-udef` `expm1-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt Om)
0.0ms	(expm1 (log1p (cbrt Om)))
1.0ms	(fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
3.0ms	(sqrt (fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

313.0ms	(cbrt Om)
478.0ms	(expm1 (log1p (cbrt Om)))
579.0ms	(fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
836.0ms	(sqrt (fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (cbrt Om))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify1.9s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	1412
2	483
1	200
0	106

prune707.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.0b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b	(expm1 (log1p (cbrt Om)))
1.0b	(expm1 (log1p (cbrt Om)))
2.0b	(fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (expm1 (log1p (cbrt Om))))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
6.3b	(sqrt (fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (expm1 (log1p (cbrt Om))))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

0.0ms	(expm1 (log1p (cbrt Om)))
0.0ms	(expm1 (log1p (cbrt Om)))
0.0ms	(fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (expm1 (log1p (cbrt Om))))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
1.0ms	(sqrt (fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (expm1 (log1p (cbrt Om))))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series2.5s

Counts

4 → 12

Calls

4 calls:

468.0ms	(expm1 (log1p (cbrt Om)))
481.0ms	(expm1 (log1p (cbrt Om)))
591.0ms	(fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (expm1 (log1p (cbrt Om))))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
915.0ms	(sqrt (fma (pow (* (/ l (* (cbrt Om) (expm1 (log1p (cbrt Om))))) (/ 2.0 (expm1 (log1p (cbrt Om))))) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify2.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	5003
3	1369
2	466
1	186
0	94

prune742.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.0b

regimes721.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.3b and baseline of 1.6b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.4s

8000×

body

valid