Details

sample116.0ms

Algorithm

intervals

Results

38.0ms	313×	body	80	nan
17.0ms	135×	body	160	valid
16.0ms	569×	pre	80	true
8.0ms	121×	body	80	valid

simplify107.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

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))
27.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite163.0ms

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)))
103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
162.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
66.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(+ (- 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	401	1461
2	1341	1245
done	5000	1233

prune324.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite324.0ms

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:

118.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
44.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
134.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
111.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(- (* b b) (* (* 4.0 a) c))
285.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.5s

Counts

163 → 163

Iterations

Useful iterations: 2 (543.0ms)

Iter	Nodes	Cost
0	250	5048
1	625	4510
2	2764	4166
done	5001	4166

prune567.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c))))))
0.3b	(/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c)))
0.4b	(* (* c c) (* (* 4.0 a) (* 4.0 a)))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

113×	`pow1`
62×	`pow-prod-down`
60×	`add-sqr-sqrt`
49×	`add-exp-log` `add-cbrt-cube`
45×	`*-un-lft-identity`
38×	`times-frac`
31×	`prod-exp` `cbrt-unprod`
25×	`add-cube-cbrt`
15×	`difference-of-squares`
14×	`pow-prod-up`
11×	`associate-/r*`
10×	`pow-plus` `sqrt-prod` `distribute-lft-out--`
8×	`pow-sqr` `add-log-exp`
6×	`associate-/l*`
5×	`distribute-rgt-neg-in`
4×	`associate-/r/` `associate-/l/`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `div-sub` `associate-r` `associate-l` `neg-log` `*-commutative` `unswap-sqr`

Counts

4 → 160

Calls

4 calls:

60.0ms	(- (- b) (sqrt (/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c)))))
180.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c))))))
55.0ms	(/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c)))
153.0ms	(* (* c c) (* (* 4.0 a) (* 4.0 a)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (- b) (sqrt (/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c)))))
285.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c))))))
129.0ms	(/ (- (pow b 4) (* (* c c) (* (* 4.0 a) (* 4.0 a)))) (+ (* b b) (* (* 4.0 a) c)))
43.0ms	(* (* c c) (* (* 4.0 a) (* 4.0 a)))

simplify2.0s

Counts

172 → 172

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	276	6038
1	692	5672
2	3235	5089
done	5001	5087

prune847.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

692×	`times-frac`
298×	`add-exp-log`
249×	`add-sqr-sqrt` `*-un-lft-identity`
200×	`div-exp`
181×	`add-cube-cbrt`
106×	`add-cbrt-cube`
73×	`prod-exp`
58×	`cbrt-undiv`
49×	`div-inv`
45×	`1-exp` `associate-/r/`
34×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
23×	`cbrt-unprod`
18×	`rec-exp`
17×	`flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
14×	`associate-/l*`
10×	`add-log-exp`
4×	`pow1`
3×	`diff-log`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`associate--l-` `neg-sub0` `neg-log` `associate-/l/`

Counts

4 → 421

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(/ (/ 1 1) (/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
70.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(- (* b b) (* (* 4.0 a) c))
237.0ms	(/ (/ 1 1) (/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
256.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify3.2s

Counts

433 → 433

Iterations

Useful iterations: 2 (1.8s)

Iter	Nodes	Cost
0	686	18157
1	1704	15092
2	4170	13714
done	5000	13714

prune552.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes244.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	41
1	34	39
done	34	39

end0.0ms

sample4.1s

Algorithm

intervals

Results

924.0ms	8809×	body	80	nan
853.0ms	3519×	body	80	valid
807.0ms	4481×	body	160	valid
677.0ms	16809×	pre	80	true