Details

sample92.0ms

Algorithm

intervals

Results

20.0ms	522×	pre	80	true
16.0ms	137×	body	160	valid
15.0ms	266×	body	80	nan
7.0ms	119×	body	80	valid

simplify118.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
28.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite145.0ms

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:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
145.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
72.0ms	(- (* b b) (* (* 4.0 a) c))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	154	1565
1	419	1461
2	1906	1245
done	5000	1239

prune342.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite233.0ms

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:

33.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
165.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms	(- (* b b) (* (* 4.0 a) c))
269.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.2s

Counts

163 → 163

Iterations

Useful iterations: 2 (648.0ms)

Iter	Nodes	Cost
0	247	5048
1	654	4512
2	3774	4174
done	5000	4174

prune665.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
153×	`add-exp-log`
87×	`add-cbrt-cube`
77×	`div-exp`
73×	`add-sqr-sqrt` `*-un-lft-identity`
43×	`prod-exp`
41×	`add-cube-cbrt`
40×	`cbrt-undiv`
38×	`associate-/r*`
23×	`cbrt-unprod`
20×	`associate-/r/`
16×	`distribute-lft-out--` `difference-of-squares`
13×	`div-inv`
9×	`rec-exp` `1-exp`
8×	`flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
6×	`add-log-exp`
5×	`pow1` `associate-/l*`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

4 → 223

Calls

4 calls:

73.0ms	(/ 1 (/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
93.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(- (* b b) (* (* 4.0 a) c))
98.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series706.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ 1 (/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
140.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms	(- (* b b) (* (* 4.0 a) c))
257.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify708.0ms

Counts

235 → 235

Iterations

Useful iterations: done (698.0ms)

Iter	Nodes	Cost
0	357	7828
1	1120	7279
done	5001	6319

prune893.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b	(- (* b b) (* (* 4.0 a) c))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

285×	`times-frac`
185×	`add-sqr-sqrt` `*-un-lft-identity`
121×	`add-exp-log`
97×	`add-cube-cbrt`
63×	`add-cbrt-cube`
60×	`div-exp`
44×	`distribute-lft-out--` `difference-of-squares`
36×	`prod-exp`
34×	`div-inv`
27×	`cbrt-undiv`
22×	`distribute-rgt-neg-in` `sqrt-prod`
21×	`associate-/l*`
18×	`cbrt-unprod`
10×	`associate-/r/` `add-log-exp`
8×	`associate-/r*`
7×	`rec-exp` `1-exp`
4×	`pow1`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`associate--l-` `neg-sub0` `neg-log` `associate-/l/`

Counts

4 → 265

Calls

4 calls:

49.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
171.0ms	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
33.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))

series464.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
252.0ms	(/ (/ 1 (/ (* 2.0 a) (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
72.0ms	(- (* b b) (* (* 4.0 a) c))

simplify676.0ms

Counts

277 → 277

Iterations

Useful iterations: done (664.0ms)

Iter	Nodes	Cost
0	426	10126
1	1253	9402
done	5001	8315

prune678.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes211.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	23
1	23	23
done	23	23

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	8578×	body	80	nan
780.0ms	4399×	body	160	valid
721.0ms	16578×	pre	80	true
275.0ms	3601×	body	80	valid