Details

sample40.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
6	2002
5	808
4	236
3	88
2	44
1	19
0	8

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.5b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (/ b a) (/ b a))
9.5b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

2 → 86

Calls

2 calls:

28.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series62.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(* (/ b a) (/ b a))
19.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	2001
3	2001
2	1310
1	407
0	134

prune454.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 9.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ b a) b)
6.2b	(* (* (/ b a) b) (/ 1 a))
9.5b	(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
29×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
22×	`prod-exp`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`associate-r`
14×	`associate-l`
12×	`cbrt-unprod`
11×	`pow1` `div-exp`
6×	`cbrt-undiv`
4×	`pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `rec-exp` `1-exp` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `un-div-inv`

Counts

3 → 100

Calls

3 calls:

27.0ms	(* (/ b a) b)
51.0ms	(* (* (/ b a) b) (/ 1 a))
2.0ms	(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

series82.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (/ b a) b)
32.0ms	(* (* (/ b a) b) (/ 1 a))
13.0ms	(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

simplify1.4s

Counts

109 → 109

Iterations

Iter	Nodes
done	2024
3	2024
2	1084
1	404
0	159

prune492.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 9.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ b a) b)
6.2b	(* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))
9.5b	(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
46.9b	(posit16->real (real->posit16 (* (/ b a) b)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`times-frac` `add-cube-cbrt`
18×	`add-exp-log`
16×	`associate-r` `associate-l`
14×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `sqrt-prod`
2×	`cbrt-undiv` `pow-prod-down` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-l/` `associate-r/` `un-div-inv` `remove-posit16`

Counts

4 → 101

Calls

4 calls:

10.0ms	(* (/ b a) b)
9.0ms	(* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))
1.0ms	(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (/ b a) b)
46.0ms	(* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))
21.0ms	(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
26.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

simplify1.1s

Counts

113 → 113

Iterations

Iter	Nodes
done	2005
3	2005
2	1075
1	367
0	160

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.4b

localize102.0ms

Local error

Found 4 expressions with local error:

9.5b	(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
46.9b	(posit16->real (real->posit16 (* (/ b a) b)))
46.9b	(posit16->real (real->posit16 (* (/ b a) b)))
46.9b	(posit16->real (real->posit16 (* (/ b a) b)))

rewrite5.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `remove-posit16`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 49

Calls

4 calls:

2.0ms	(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
1.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
35.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
33.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
36.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

simplify1.3s

Counts

61 → 61

Iterations

Iter	Nodes
done	2010
4	2010
3	723
2	180
1	69
0	46

prune921.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.4b

regimes191.0ms

Accuracy

0% (0.1b remaining)

Error of 7.3b against oracle of 7.2b and baseline of 7.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

979.0ms	8000×	body	80	valid
341.0ms	8000×	pre	80	true