Details

sample92.0ms

Algorithm

intervals

Results

23.0ms	146×	body	160	valid
17.0ms	310×	body	80	nan
14.0ms	566×	pre	80	true
7.0ms	110×	body	80	valid

simplify107.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* 4.0 (* c a))))
0.3b	(- (* b b) (* 4.0 (* c a)))
0.3b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
28.1b	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

rewrite204.0ms

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:

16.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
13.0ms	(- (* b b) (* 4.0 (* c a)))
82.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

series456.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
71.0ms	(- (* b b) (* 4.0 (* c a)))
153.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
113.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

simplify2.0s

Counts

195 → 195

Iterations

Iter	Nodes
done	5002
2	2305
1	797
0	321

prune1.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.3b

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

prune191.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 9.3b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

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:

39.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
15.0ms	(/ (* a c) b)

series45.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
22.0ms	(/ (* a c) b)

simplify1.8s

Counts

83 → 83

Iterations

Iter	Nodes
done	5026
2	1950
1	459
0	171

prune737.0ms

Pruning

37 alts after pruning (36 fresh and 1 done)

Merged error: 9.1b

localize32.0ms

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)
0.6b	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite132.0ms

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:

78.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
7.0ms	(/ (* a c) b)
7.0ms	(/ (* a c) b)
34.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (/ (* -2.0 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) 2.0) a)
33.0ms	(/ (* a c) b)
24.0ms	(/ (* a c) b)
88.0ms	(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.8s

Counts

176 → 176

Iterations

Iter	Nodes
done	5013
2	2188
1	566
0	237

prune963.0ms

Pruning

40 alts after pruning (39 fresh and 1 done)

Merged error: 9.1b

regimes1.2s

Accuracy

44.1% (7.8b remaining)

Error of 16.8b against oracle of 9.0b and baseline of 23.0b

bsearch39.0ms

Steps

Iters	Range		Point
2	59.54081762261222	70.62772712067056	60.5124483648276

simplify6.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	4385×	body	160	valid
935.0ms	8838×	body	80	nan
602.0ms	16838×	pre	80	true
253.0ms	3614×	body	80	valid
0.0ms	1×	body	320	valid