Details

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
6	2324
5	753
4	228
3	85
2	43
1	18
0	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
4.5b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite50.0ms

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×	`insert-posit16` `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 → 82

Calls

2 calls:

43.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series81.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(* (/ b a) (/ b a))
26.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
3	4058
2	1294
1	401
0	130

prune662.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b	(* b (/ b a))
4.5b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.2b	(/ (* b (/ b a)) a)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`times-frac` `associate-r`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-l*` `sqrt-prod` `insert-posit16` `add-log-exp`
2×	`associate-*r/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

3 → 72

Calls

3 calls:

26.0ms	(* b (/ b a))
2.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
27.0ms	(/ (* b (/ b a)) a)

series81.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* b (/ b a))
15.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
46.0ms	(/ (* b (/ b a)) a)

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1042
1	285
0	116

prune325.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 4.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* b (/ b a))
0.4b	(/ 1 (/ a (* b (/ b a))))
4.5b	(sqrt (fabs (- 1 (/ 1 (/ a (* b (/ b a)))))))
7.1b	(/ a (* b (/ b a)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
49×	`times-frac`
38×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
25×	`div-exp`
13×	`cbrt-undiv` `associate-r`
10×	`prod-exp`
9×	`associate-/r*`
8×	`pow1`
7×	`div-inv`
6×	`associate-r/` `associate-/r/` `cbrt-unprod` `associate-/l`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`associate-l` `sqrt-prod`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

13.0ms	(* b (/ b a))
23.0ms	(/ 1 (/ a (* b (/ b a))))
1.0ms	(sqrt (fabs (- 1 (/ 1 (/ a (* b (/ b a)))))))
18.0ms	(/ a (* b (/ b a)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* b (/ b a))
46.0ms	(/ 1 (/ a (* b (/ b a))))
16.0ms	(sqrt (fabs (- 1 (/ 1 (/ a (* b (/ b a)))))))
44.0ms	(/ a (* b (/ b a)))

simplify1.6s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	1627
1	454
0	195

prune615.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 4.5b

localize16.0ms

Local error

Found 3 expressions with local error:

4.5b	(sqrt (fabs (- 1 (/ (/ (* b b) a) a))))
7.2b	(/ (/ (* b b) a) a)
16.3b	(/ (* b b) a)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
17×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*` `div-inv`
4×	`pow1`
3×	`sqrt-prod` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

3 → 85

Calls

3 calls:

5.0ms	(sqrt (fabs (- 1 (/ (/ (* b b) a) a))))
13.0ms	(/ (/ (* b b) a) a)
18.0ms	(/ (* b b) a)

series86.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(sqrt (fabs (- 1 (/ (/ (* b b) a) a))))
44.0ms	(/ (/ (* b b) a) a)
27.0ms	(/ (* b b) a)

simplify1.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5023
2	1092
1	312
0	129

prune430.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 4.5b

regimes144.0ms

Accuracy

0% (0.1b remaining)

Error of 7.1b against oracle of 7.1b and baseline of 7.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample932.0ms

Algorithm

intervals

Results

506.0ms	8000×	body	80	valid
281.0ms	8000×	pre	80	true