Details

sample98.0ms

Algorithm

intervals

Results

17.0ms	143×	body	160	valid
17.0ms	537×	pre	80	true
16.0ms	281×	body	80	nan
8.0ms	47×	body	320	valid
4.0ms	66×	body	80	valid

simplify128.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 3.0 a) c)
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
36.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite166.0ms

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:

15.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(* (* 3.0 a) c)
88.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
40.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b b) (* (* 3.0 a) c))
33.0ms	(* (* 3.0 a) c)
152.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
123.0ms	(+ (- 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

prune278.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 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))

rewrite256.0ms

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:

31.0ms	(* (* 3.0 a) c)
74.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.0ms	(* 3.0 (* a c))
120.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series514.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* 3.0 a) c)
260.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.0ms	(* 3.0 (* a c))
199.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify2.1s

Counts

177 → 177

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	251	4838
1	622	4351
2	2621	3972
done	5001	3970

prune622.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
0.3b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
0.4b	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

214×	`times-frac`
161×	`add-exp-log`
111×	`add-sqr-sqrt` `*-un-lft-identity`
80×	`div-exp`
77×	`add-cbrt-cube`
63×	`add-cube-cbrt`
48×	`associate-/l*`
46×	`prod-exp`
34×	`cbrt-undiv`
24×	`distribute-lft-out--` `difference-of-squares`
20×	`cbrt-unprod`
15×	`div-inv`
13×	`associate-/r*`
12×	`rec-exp` `distribute-rgt-neg-in` `1-exp` `sqrt-prod`
10×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l/`
1×	`flip3--` `pow-flip` `div-sub` `associate-l` `*-commutative` `flip--` `inv-pow`

Counts

4 → 260

Calls

4 calls:

18.0ms	(* (* 3.0 a) c)
74.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
105.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
153.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

series531.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (* 3.0 a) c)
211.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
130.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
162.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

simplify2.2s

Counts

272 → 272

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	374	8131
1	959	7621
2	3479	6149
done	5000	6146

prune683.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)
0.1b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.2b	(* (* 3.0 a) c)
0.3b	(/ (/ 1 1) (* 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-exp-log`
92×	`add-sqr-sqrt` `*-un-lft-identity`
72×	`add-cube-cbrt`
70×	`div-exp`
60×	`prod-diff`
52×	`times-frac`
39×	`1-exp`
35×	`sqrt-prod`
32×	`add-cbrt-cube`
31×	`prod-exp`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
20×	`associate-/l*`
12×	`cbrt-undiv`
10×	`rec-exp` `fma-neg` `distribute-lft-out--` `difference-of-squares`
9×	`pow1`
8×	`add-log-exp`
7×	`neg-mul-1` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`associate-r` `pow-prod-down` `associate-/l/`
2×	`flip3--` `frac-2neg` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `div-sub` `associate-r/` `associate-l` `neg-log` `associate-/r/` `-commutative`

Counts

4 → 240

Calls

4 calls:

136.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)
41.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.0ms	(* (* 3.0 a) c)
49.0ms	(/ (/ 1 1) (* 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)
117.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
27.0ms	(* (* 3.0 a) c)
190.0ms	(/ (/ 1 1) (* 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))

simplify2.1s

Counts

252 → 252

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	384	8894
1	808	6401
2	1903	5231
done	5000	4487

prune522.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes145.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	14	17
1	19	15
done	19	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

452.0ms	4792×	body	160	valid
423.0ms	16477×	pre	80	true
378.0ms	8477×	body	80	nan
189.0ms	1366×	body	320	valid
86.0ms	1842×	body	80	valid