Details

sample102.0ms

Algorithm

intervals

Results

33.0ms	159×	body	160	valid
17.0ms	266×	body	80	nan
14.0ms	522×	pre	80	true
6.0ms	37×	body	320	valid
4.0ms	60×	body	80	valid

simplify91.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* 4.0 (* c a))))
0.2b	(- (* b b) (* 4.0 (* c a)))
0.2b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
39.6b	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

rewrite189.0ms

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:

15.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
13.0ms	(- (* b b) (* 4.0 (* c a)))
108.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
45.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

series405.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))
66.0ms	(- (* b b) (* 4.0 (* c a)))
149.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
116.0ms	(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

simplify1.9s

Counts

195 → 195

Iterations

Iter	Nodes
done	5002
2	2305
1	797
0	321

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.0b

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

prune142.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite59.0ms

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:

19.0ms	(/ (* a c) b)
35.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series76.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (* a c) b)
39.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify1.6s

Counts

83 → 83

Iterations

Iter	Nodes
done	5049
2	1836
1	456
0	171

prune569.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 6.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ -2.0 (sqrt a))
0.2b	(/ (* a c) b)
0.3b	(* (/ -2.0 (sqrt a)) (/ (/ (/ (* a c) b) 2.0) (sqrt a)))
0.4b	(/ (/ (/ (* a c) b) 2.0) (sqrt a))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

757×	`times-frac`
377×	`add-sqr-sqrt`
319×	`*-un-lft-identity` `add-cube-cbrt`
185×	`sqrt-prod`
154×	`associate-r`
70×	`add-cbrt-cube` `add-exp-log`
57×	`div-inv`
35×	`cbrt-undiv` `div-exp`
29×	`associate-/l*`
22×	`associate-l`
15×	`associate-/r*` `unswap-sqr`
14×	`prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

9.0ms	(/ -2.0 (sqrt a))
9.0ms	(/ (* a c) b)
155.0ms	(* (/ -2.0 (sqrt a)) (/ (/ (/ (* a c) b) 2.0) (sqrt a)))
33.0ms	(/ (/ (/ (* a c) b) 2.0) (sqrt a))

series252.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ -2.0 (sqrt a))
37.0ms	(/ (* a c) b)
68.0ms	(* (/ -2.0 (sqrt a)) (/ (/ (/ (* a c) b) 2.0) (sqrt a)))
94.0ms	(/ (/ (/ (* a c) b) 2.0) (sqrt a))

simplify2.0s

Counts

503 → 503

Iterations

Iter	Nodes
done	5002
1	2097
0	674

prune2.7s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 5.9b

regimes904.0ms

Accuracy

10.6% (6.1b remaining)

Error of 11.1b against oracle of 5.0b and baseline of 11.8b

bsearch36.0ms

Steps

Iters	Range		Point
3	0.03179800884184028	0.046932425441303355	0.03274390987930672

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample3.7s

Algorithm

intervals

Results

897.0ms	8410×	body	80	nan
803.0ms	4857×	body	160	valid
717.0ms	1385×	body	320	valid
618.0ms	16410×	pre	80	true
159.0ms	1758×	body	80	valid