Details

sample114.0ms

Algorithm

intervals

Results

45.0ms	308×	body	80	nan
18.0ms	564×	pre	80	true
17.0ms	137×	body	160	valid
8.0ms	119×	body	80	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
27.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `add-log-exp`
9×	`pow1`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 93

Calls

4 calls:

13.0ms	(- (* b b) (* (* 3.0 a) c))
19.0ms	(* (* 3.0 a) c)
103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 3.0 a) c))
35.0ms	(* (* 3.0 a) c)
148.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
126.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.8s

Counts

105 → 105

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	167	1559
1	440	1478
2	1681	1247
done	5000	1234

prune421.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
0.4b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down` `associate-/r/`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 165

Calls

4 calls:

27.0ms	(* 3.0 (* a c))
18.0ms	(* (* 3.0 a) c)
128.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
67.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* 3.0 (* a c))
33.0ms	(* (* 3.0 a) c)
219.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
247.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify1.9s

Counts

177 → 177

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	251	4838
1	622	4351
2	2624	3972
done	5001	3970

prune651.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(* (* 3.0 a) c)
0.4b	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
132×	`add-exp-log`
76×	`add-sqr-sqrt` `*-un-lft-identity`
68×	`add-cbrt-cube`
63×	`div-exp`
45×	`associate-/l*`
44×	`add-cube-cbrt`
40×	`prod-exp`
27×	`cbrt-undiv`
20×	`cbrt-unprod`
16×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`div-inv`
8×	`rec-exp` `distribute-rgt-neg-in` `1-exp` `sqrt-prod`
6×	`associate-r` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `associate-/r/` `-commutative`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 202

Calls

4 calls:

129.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
35.0ms	(* (* 3.0 a) c)
36.0ms	(* (* 3.0 a) c)
175.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

series463.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
31.0ms	(* (* 3.0 a) c)
37.0ms	(* (* 3.0 a) c)
214.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

simplify2.2s

Counts

214 → 214

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	348	5826
1	890	5517
2	3256	4292
done	5002	4290

prune648.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
0.3b	(/ 1 (/ 1 (* 3.0 a)))
0.4b	(* (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) (* 3.0 a))
0.4b	(/ (/ 1 (/ 1 (* 3.0 a))) (* (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) (* 3.0 a)))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

576×	`add-exp-log`
316×	`div-exp`
195×	`prod-exp`
143×	`times-frac`
132×	`add-cbrt-cube`
80×	`rec-exp` `1-exp`
73×	`add-sqr-sqrt` `*-un-lft-identity`
62×	`cbrt-undiv`
61×	`add-cube-cbrt`
37×	`cbrt-unprod`
32×	`associate-/l*`
25×	`associate-l`
16×	`pow1` `div-inv`
9×	`associate-/r*`
8×	`pow-flip`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-neg-in` `frac-2neg` `clear-num` `sqrt-prod` `inv-pow`
2×	`associate-*l/`
1×	`associate-r` `*-commutative` `associate-/l/` `remove-double-div`

Counts

4 → 348

Calls

4 calls:

24.0ms	(/ 1 (* 3.0 a))
41.0ms	(/ 1 (/ 1 (* 3.0 a)))
132.0ms	(* (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) (* 3.0 a))
120.0ms	(/ (/ 1 (/ 1 (* 3.0 a))) (* (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) (* 3.0 a)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (* 3.0 a))
24.0ms	(/ 1 (/ 1 (* 3.0 a)))
181.0ms	(* (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) (* 3.0 a))
253.0ms	(/ (/ 1 (/ 1 (* 3.0 a))) (* (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) (* 3.0 a)))

simplify2.6s

Counts

360 → 360

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	440	9391
1	1067	7508
2	3261	5193
done	5001	5193

prune584.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes220.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	18	17
done	18	17

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	16618×	pre	80	true
725.0ms	4489×	body	160	valid
570.0ms	8618×	body	80	nan
285.0ms	3511×	body	80	valid