Details

sample56.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
12.0ms	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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
7.2b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite22.0ms

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:

17.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series46.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(* (/ b a) (/ b a))
18.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.8s

Counts

88 → 88

Iterations

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

prune427.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

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:

9.0ms	(* b (/ b a))
1.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
11.0ms	(/ (* b (/ b a)) a)

series85.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* b (/ b a))
23.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
35.0ms	(/ (* b (/ b a)) a)

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1042
1	285
0	116

prune290.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ b a) (/ b a))
0.4b	(* (/ b a) (/ b a))
7.2b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
11.6b	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
80×	`times-frac`
61×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 161

Calls

4 calls:

22.0ms	(* (/ b a) (/ b a))
21.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
7.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ b a) (/ b a))
39.0ms	(* (/ b a) (/ b a))
16.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
20.0ms	(cbrt (* (fabs (- 1 (* (/ b a) (/ b a)))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))

simplify3.0s

Counts

173 → 173

Iterations

Iter	Nodes
done	5022
3	4017
2	1328
1	421
0	140

prune716.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
7.2b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
21.9b	(/ (- (* a a) (* b b)) (* a a))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`sqrt-prod` `insert-posit16` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

3 → 55

Calls

3 calls:

7.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
23.0ms	(/ (- (* a a) (* b b)) (* a a))

series126.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(- (* a a) (* b b))
13.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
54.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify1.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	801
1	247
0	93

prune227.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 7.0b

regimes396.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.3s

Algorithm

intervals

Results

749.0ms	8000×	body	80	valid
341.0ms	8000×	pre	80	true