Details

sample62.0ms

Algorithm

intervals

Results

11.0ms	112×	body	320	valid
9.0ms	551×	pre	80	true
9.0ms	295×	body	80	nan
6.0ms	94×	body	160	valid
3.0ms	23×	body	640	valid
1.0ms	27×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9
done	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
27.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5002	674
done	5002	674

prune172.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

22.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
153.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify108.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5003	2388
done	5003	2388

prune386.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `add-cube-cbrt` `div-exp`
4×	`sub-neg` `flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `associate-l`
2×	`distribute-rgt-in` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-prod` `associate-/r/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `times-frac` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

22.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
41.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
156.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify92.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	512	1105
1	3243	867
2	5001	860
done	5001	860

prune218.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.5b	(* (* 4.0 (* a c)) (* 4.0 (* a c)))
0.5b	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))

rewrite423.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt` `times-frac`
118×	`pow1`
92×	`*-un-lft-identity`
66×	`pow-prod-down`
56×	`add-exp-log` `add-cbrt-cube`
52×	`add-cube-cbrt`
42×	`difference-of-squares`
39×	`associate-/l*`
29×	`prod-exp` `cbrt-unprod`
20×	`sqrt-prod` `distribute-lft-out--`
12×	`associate-/r*`
10×	`distribute-rgt-neg-in`
9×	`pow-sqr` `pow-prod-up`
8×	`cbrt-undiv` `div-exp` `associate-/r/`
5×	`div-inv` `associate-/l/`
4×	`unpow-prod-down` `flip3--` `flip--` `add-log-exp` `sqr-pow`
3×	`frac-2neg` `pow-plus` `clear-num`
2×	`flip3-+` `flip-+`
1×	`pow2` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 235

Calls

4 calls:

175.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
118.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
79.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))
38.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
236.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
41.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))
96.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Counts

247 → 247

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	994	5277
1	5002	4702
done	5002	4702

prune653.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes81.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	27	13
done	27	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

359.0ms	3649×	body	320	valid
275.0ms	16213×	pre	80	true
260.0ms	8213×	body	80	nan
194.0ms	2944×	body	160	valid
65.0ms	493×	body	640	valid
30.0ms	914×	body	80	valid