Details

sample44.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify8.1s

Counts

1 → 1

Iterations

Iter	Nodes
8	6442
7	1455
6	631
5	341
4	166
3	86
2	44
1	19
0	8

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1 (* (/ b a) (/ b a)))
0.3b	(* (/ b a) (/ b a))
7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
35×	`*-un-lft-identity`
34×	`add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `fma-neg` `prod-diff` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`pow2` `frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

3 → 109

Calls

3 calls:

10.0ms	(- 1 (* (/ b a) (/ b a)))
28.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series125.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(- 1 (* (/ b a) (/ b a)))
44.0ms	(* (/ b a) (/ b a))
23.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.5s

Counts

118 → 118

Iterations

Iter	Nodes
3	5219
2	1454
1	482
0	167

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 7.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ b (sqrt a)) (/ b (sqrt a)))
0.5b	(* (/ 1 (sqrt a)) (/ 1 (sqrt a)))
7.9b	(sqrt (fabs (- 1 (* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (* (/ b (sqrt a)) (/ b (sqrt a)))))))
8.5b	(* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (* (/ b (sqrt a)) (/ b (sqrt a))))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

482×	`add-exp-log`
253×	`prod-exp`
242×	`add-sqr-sqrt`
220×	`times-frac`
168×	`div-exp`
158×	`add-cbrt-cube`
139×	`*-un-lft-identity`
117×	`add-cube-cbrt`
113×	`sqrt-prod`
73×	`cbrt-unprod`
63×	`pow1`
58×	`swap-sqr`
48×	`cbrt-undiv` `rec-exp` `1-exp`
45×	`associate-r` `associate-l`
35×	`unswap-sqr`
24×	`pow-flip`
23×	`frac-times`
20×	`pow-prod-down`
15×	`associate-*l/`
14×	`associate-*r/` `pow-prod-up`
10×	`div-inv`
9×	`sqrt-pow1` `pow1/2`
8×	`pow-sqr` `inv-pow`
6×	`pow-plus`
5×	`un-div-inv`
4×	`pow2` `expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`rem-sqrt-square`

Counts

4 → 432

Calls

4 calls:

37.0ms	(* (/ b (sqrt a)) (/ b (sqrt a)))
39.0ms	(* (/ 1 (sqrt a)) (/ 1 (sqrt a)))
2.0ms	(sqrt (fabs (- 1 (* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (* (/ b (sqrt a)) (/ b (sqrt a)))))))
145.0ms	(* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (* (/ b (sqrt a)) (/ b (sqrt a))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ b (sqrt a)) (/ b (sqrt a)))
35.0ms	(* (/ 1 (sqrt a)) (/ 1 (sqrt a)))
23.0ms	(sqrt (fabs (- 1 (* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (* (/ b (sqrt a)) (/ b (sqrt a)))))))
61.0ms	(* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (* (/ b (sqrt a)) (/ b (sqrt a))))

simplify2.8s

Counts

444 → 444

Iterations

Iter	Nodes
2	3880
1	1377
0	468

prune4.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 7.7b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (sqrt a)) (/ 1 (sqrt a)))
7.9b	(sqrt (fabs (- 1 (* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))))))
8.5b	(* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a))))))
44.8b	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
124×	`times-frac`
102×	`add-exp-log`
84×	`*-un-lft-identity`
65×	`sqrt-prod`
62×	`add-cube-cbrt`
49×	`prod-exp`
34×	`add-cbrt-cube`
33×	`pow1`
32×	`div-exp`
30×	`swap-sqr`
26×	`unswap-sqr`
25×	`associate-r`
24×	`pow-flip`
23×	`associate-l`
16×	`rec-exp` `1-exp`
13×	`cbrt-unprod`
9×	`sqrt-pow1` `pow1/2` `pow-prod-up`
8×	`cbrt-undiv` `pow-prod-down` `inv-pow`
6×	`associate-*l/` `div-inv`
5×	`pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `associate-r/` `un-div-inv` `-commutative`
1×	`pow2` `rem-sqrt-square` `pow-plus` `remove-posit16`

Counts

4 → 226

Calls

4 calls:

22.0ms	(* (/ 1 (sqrt a)) (/ 1 (sqrt a)))
2.0ms	(sqrt (fabs (- 1 (* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))))))
95.0ms	(* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a))))))
1.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ 1 (sqrt a)) (/ 1 (sqrt a)))
20.0ms	(sqrt (fabs (- 1 (* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))))))
52.0ms	(* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a))))))
52.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))

simplify4.6s

Counts

238 → 238

Iterations

Iter	Nodes
3	4309
2	1490
1	769
0	269

prune5.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.7b

localize90.0ms

Local error

Found 4 expressions with local error:

16.1b	(cbrt (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a))))))
44.8b	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))
44.8b	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))
44.8b	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `remove-posit16`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a))))))
0.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))
0.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))
1.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a))))))
54.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))
36.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))
60.0ms	(posit16->real (real->posit16 (* (/ b (sqrt a)) (/ b (sqrt a)))))

simplify1.2s

Counts

59 → 59

Iterations

Iter	Nodes
4	3038
3	984
2	350
1	149
0	74

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.7b

regimes231.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.3b and baseline of 7.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	8
0	8

end0.0ms

sample1.2s

Algorithm

intervals

Results

736.0ms	8000×	body	80	valid
297.0ms	8000×	pre	80	true