Details

sample163.0ms

Algorithm

intervals

Results

113.0ms

256×

body

valid

simplify9.0s

Counts

1 → 1

Iterations

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

prune63.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize169.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.5b	(/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))
2.1b	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
8.0b	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`pow1` `associate-/r*` `times-frac`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow-prod-down`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-to-exp` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `associate-r/` `fma-udef` `div-inv` `associate-/l` `sqr-pow` `associate-/l/`

Counts

4 → 80

Calls

4 calls:

11.0ms	(pow (sin ky) 2.0)
20.0ms	(/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))
1.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
5.0ms	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series3.5s

Counts

4 → 12

Calls

4 calls:

225.0ms	(pow (sin ky) 2.0)
1.4s	(/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))
703.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
1.1s	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify3.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5011
2	1449
1	434
0	176

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize288.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
7.5b	(sqrt (/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
8.0b	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
8.0b	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
8×	`pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div` `div-inv`

Counts

4 → 80

Calls

4 calls:

12.0ms	(sqrt (/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
13.0ms	(sqrt (/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
3.0ms	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
5.0ms	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

series5.7s

Counts

4 → 12

Calls

4 calls:

1.8s	(sqrt (/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
1.7s	(sqrt (/ (* 1.0 (/ 1.0 2.0)) (sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
1.0s	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))
1.2s	(sqrt (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))

simplify6.4s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
4	3818
3	1147
2	450
1	210
0	115

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize168.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* 1.0 (/ 1.0 2.0)) (sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))))
2.1b	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
8.0b	(sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
11.0b	(posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
6×	`associate-/r*` `times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `fma-udef` `div-inv` `remove-posit16` `associate-/l` `associate-/l/`

Counts

4 → 71

Calls

4 calls:

18.0ms	(/ (* 1.0 (/ 1.0 2.0)) (sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))))
1.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
3.0ms	(sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
1.0ms	(posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))

series4.3s

Counts

4 → 12

Calls

4 calls:

1.6s	(/ (* 1.0 (/ 1.0 2.0)) (sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))))
649.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
1.1s	(sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
994.0ms	(posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))

simplify3.6s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
2	1119
1	340
0	148

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize174.0ms

Local error

Found 4 expressions with local error:

2.1b	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
2.1b	(log (exp (/ (* 1.0 (/ 1.0 2.0)) (sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))))))
8.0b	(sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
11.0b	(posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`log-pow`
10×	`add-sqr-sqrt` `exp-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `times-frac` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `fma-udef` `div-inv` `remove-posit16`

Counts

4 → 63

Calls

4 calls:

1.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
15.0ms	(log (exp (/ (* 1.0 (/ 1.0 2.0)) (sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))))))
2.0ms	(sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
1.0ms	(posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))

series4.1s

Counts

4 → 12

Calls

4 calls:

619.0ms	(fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)
1.6s	(log (exp (/ (* 1.0 (/ 1.0 2.0)) (sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))))))
1.1s	(sqrt (posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0))))
685.0ms	(posit16->real (real->posit16 (fma (pow (* l (/ 2.0 Om)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) 1.0)))

simplify4.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5002
3	1443
2	489
1	232
0	140

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes2.2s

Accuracy

0% (1.1b remaining)

Error of 1.8b against oracle of 0.7b and baseline of 1.8b

bsearch0.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	27
1	27
0	23

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.6s

8000×

body

valid