Details

sample55.0ms

Algorithm

intervals

Results

12.0ms	137×	body	160	valid
10.0ms	570×	pre	80	true
10.0ms	314×	body	80	nan
4.0ms	119×	body	80	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

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:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(- (* b b) (* (* 4.0 a) c))
102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify686.0ms

Counts

82 → 82

Iterations

Useful iterations: done (683.0ms)

Iter	Nodes	Cost
0	154	1565
1	406	1461
2	1361	1245
done	5000	1235

prune192.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

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:

2.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
125.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
162.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify884.0ms

Counts

163 → 163

Iterations

Useful iterations: done (878.0ms)

Iter	Nodes	Cost
0	254	5790
1	670	5273
2	2387	4513
done	5000	4511

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
136×	`add-sqr-sqrt`
135×	`*-un-lft-identity`
75×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
18×	`sqrt-prod`
15×	`distribute-rgt-neg-in`
13×	`associate-/l*`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`associate-/r*`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`cbrt-undiv` `diff-log` `div-exp`
2×	`sub-neg` `sqrt-div` `div-sub` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 174

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(/ (/ (- (* 4.0 (* a c)) 0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(/ (/ (- (* 4.0 (* a c)) 0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify869.0ms

Counts

186 → 186

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	283	6373
1	700	5705
2	2726	5501
done	5001	5500

prune504.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
205×	`add-sqr-sqrt`
152×	`*-un-lft-identity`
118×	`pow1`
92×	`add-cube-cbrt`
66×	`pow-prod-down`
57×	`difference-of-squares`
47×	`add-exp-log` `add-cbrt-cube`
30×	`sqrt-prod` `distribute-lft-out--`
27×	`prod-exp` `cbrt-unprod`
19×	`associate-/l*`
15×	`distribute-rgt-neg-in`
11×	`associate-/r*` `div-inv`
9×	`pow-sqr` `pow-prod-up`
8×	`add-log-exp`
4×	`cbrt-undiv` `unpow-prod-down` `div-exp` `associate-/r/` `sqr-pow`
3×	`flip3--` `pow-plus` `div-sub` `flip--` `associate-/l/`
2×	`frac-2neg` `diff-log` `clear-num`
1×	`associate--l-` `pow2` `neg-sub0` `sub-neg` `flip3-+` `swap-sqr` `associate-r` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 266

Calls

4 calls:

80.0ms	(/ (/ (- (* 4.0 (* a c)) 0) a) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c))))))
35.0ms	(- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))))
19.0ms	(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))
37.0ms	(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series431.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (/ (- (* 4.0 (* a c)) 0) a) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c))))))
122.0ms	(- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))))
89.0ms	(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))
34.0ms	(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify1.5s

Counts

278 → 278

Iterations

Useful iterations: 2 (742.0ms)

Iter	Nodes	Cost
0	424	13288
1	1088	12312
2	4465	11700
done	5000	11700

prune820.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes139.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	28	61
1	36	59
done	36	59

end0.0ms

sample1.4s

Algorithm

intervals

Results

301.0ms	4461×	body	160	valid
298.0ms	8802×	body	80	nan
295.0ms	16802×	pre	80	true
122.0ms	3538×	body	80	valid
0.0ms	1×	body	320	valid