Details

sample143.0ms

Algorithm

intervals

Results

28.0ms	159×	body	160	valid
26.0ms	303×	body	80	nan
21.0ms	559×	pre	80	true
11.0ms	44×	body	320	valid
5.0ms	53×	body	80	valid

simplify158.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	79
2	43
1	25
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* 4.0 (* c a))))
0.2b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
0.2b	(- (* b b) (* 4.0 (* c a)))
38.3b	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
19×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

10.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
70.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
15.0ms	(- (* b b) (* 4.0 (* c a)))
77.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

series432.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
142.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
81.0ms	(- (* b b) (* 4.0 (* c a)))
118.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

simplify2.1s

Counts

195 → 195

Iterations

Iter	Nodes
done	5001
2	2320
1	798
0	321

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.5b

localize5.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune144.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.5b

localize27.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b	(/ (* a c) b)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
6×	`associate-/r*` `div-inv`
5×	`prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 77

Calls

2 calls:

24.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
15.0ms	(/ (* a c) b)

series58.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
23.0ms	(/ (* a c) b)

simplify1.5s

Counts

83 → 83

Iterations

Iter	Nodes
done	5026
2	1950
1	459
0	171

prune602.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
0.3b	(/ (* a c) b)
0.3b	(/ (* a c) b)
0.5b	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
48×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `add-cube-cbrt`
34×	`sqrt-prod`
30×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
12×	`swap-sqr`
11×	`cbrt-undiv` `div-exp` `div-inv`
10×	`associate-r` `associate-l`
9×	`associate-/r` `associate-/l`
8×	`sqrt-pow1` `pow1/2`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `pow-prod-down` `pow-sqr`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

69.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
8.0ms	(/ (* a c) b)
8.0ms	(/ (* a c) b)
30.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
25.0ms	(/ (* a c) b)
22.0ms	(/ (* a c) b)
68.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.8s

Counts

176 → 176

Iterations

Iter	Nodes
done	5013
2	2188
1	566
0	237

prune908.0ms

Pruning

35 alts after pruning (33 fresh and 2 done)

Merged error: 5.4b

regimes1.1s

Accuracy

8.2% (6.4b remaining)

Error of 11.4b against oracle of 5.0b and baseline of 12.0b

bsearch37.0ms

Steps

Iters	Range		Point
4	6.789181744096528e-08	1.2662217397802895e-07	6.961131476357277e-08

simplify6.0ms

Iterations

Iter	Nodes
done	34
2	34
1	26
0	19

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.2s	4796×	body	160	valid
1.0s	16177×	pre	80	true
790.0ms	8177×	body	80	nan
361.0ms	1358×	body	320	valid
159.0ms	1846×	body	80	valid