Details

sample128.0ms

Algorithm

intervals

Results

45.0ms	278×	body	80	nan
21.0ms	153×	body	160	valid
17.0ms	534×	pre	80	true
7.0ms	40×	body	320	valid
4.0ms	63×	body	80	valid

simplify538.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize28.0ms

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))
37.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite199.0ms

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:

17.0ms	(- (* b b) (* (* 3.0 a) c))
26.0ms	(* (* 3.0 a) c)
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* b b) (* (* 3.0 a) c))
30.0ms	(* (* 3.0 a) c)
128.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
105.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.6s

Counts

105 → 105

Iterations

Useful iterations: done (1.6s)

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

prune258.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(* 3.0 (* a c))
0.3b	(/ (/ (+ 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)))))

rewrite219.0ms

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:

18.0ms	(* (* 3.0 a) c)
23.0ms	(* 3.0 (* a c))
95.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
68.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
36.0ms	(* 3.0 (* a c))
169.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
240.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify1.7s

Counts

177 → 177

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	251	4838
1	622	4351
2	2625	3972
done	5001	3970

prune662.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(* (* a 3.0) c)
0.3b	(/ (/ (+ 0 (* (* a 3.0) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
0.4b	(/ (+ 0 (* (* a 3.0) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite254.0ms

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×	`associate-r` `pow-prod-down` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 165

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
20.0ms	(* (* a 3.0) c)
125.0ms	(/ (/ (+ 0 (* (* a 3.0) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
82.0ms	(/ (+ 0 (* (* a 3.0) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* 3.0 a) c)
37.0ms	(* (* a 3.0) c)
190.0ms	(/ (/ (+ 0 (* (* a 3.0) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
219.0ms	(/ (+ 0 (* (* a 3.0) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify1.6s

Counts

177 → 177

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	253	4841
1	628	4352
2	2674	3973
done	5000	3971

prune625.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

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

rewrite426.0ms

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)
111.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
141.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
140.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

series572.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 3.0 a) c)
224.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
157.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))
170.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

simplify2.4s

Counts

272 → 272

Iterations

Useful iterations: done (2.3s)

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

prune660.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes238.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	18	25
1	23	17
done	23	17

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.4s	4875×	body	160	valid
706.0ms	16059×	pre	80	true
673.0ms	8059×	body	80	nan
271.0ms	1337×	body	320	valid
157.0ms	1788×	body	80	valid