Details

sample103.0ms

Algorithm

intervals

Results

20.0ms	153×	body	160	valid
18.0ms	278×	body	80	nan
16.0ms	534×	pre	80	true
8.0ms	40×	body	320	valid
4.0ms	63×	body	80	valid

simplify133.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (52.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize14.0ms

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))))

rewrite139.0ms

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:

9.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(* (* 3.0 a) c)
83.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 3.0 a) c))
24.0ms	(* (* 3.0 a) c)
117.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
94.0ms	(+ (- 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

prune306.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

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)))))

rewrite253.0ms

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)
17.0ms	(* 3.0 (* a c))
106.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
90.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (* 3.0 a) c)
34.0ms	(* 3.0 (* a c))
210.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
299.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify1.4s

Counts

177 → 177

Iterations

Useful iterations: done (1.4s)

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

prune546.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

285×	`times-frac`
138×	`add-sqr-sqrt` `distribute-rgt-neg-in` `*-un-lft-identity`
122×	`distribute-lft-neg-in`
74×	`add-cube-cbrt`
38×	`neg-mul-1`
32×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/l*`
30×	`associate-/r/`
25×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-prod` `div-inv`
15×	`flip3--` `flip--`
14×	`pow1`
13×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
6×	`associate-r` `pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `associate-/l/` `distribute-neg-frac`

Counts

4 → 308

Calls

4 calls:

21.0ms	(* (* 3.0 a) c)
29.0ms	(* (* 3.0 a) c)
191.0ms	(/ (- (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (- (* 3.0 a)))
61.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
24.0ms	(* (* 3.0 a) c)
203.0ms	(/ (- (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (- (* 3.0 a)))
233.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify3.5s

Counts

320 → 320

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	473	10963
1	1164	10383
2	4869	10009
done	5000	9995

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 3.0 a) c)
0.3b	(* (/ (* 3.0 (- a)) -1) (/ (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a)))
0.4b	(/ (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
90×	`add-exp-log` `add-cbrt-cube`
79×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
41×	`add-cube-cbrt`
34×	`cbrt-undiv` `div-exp` `associate-r`
31×	`prod-exp` `cbrt-unprod`
27×	`associate-/l*`
18×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1`
9×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`associate-l`
6×	`associate-/r/` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `pow-prod-down` `flip--` `log1p-expm1-u`
2×	`*-commutative`
1×	`distribute-lft-neg-out` `frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-r/` `distribute-frac-neg` `prod-diff` `associate-l/` `clear-num` `associate-/r*` `distribute-rgt-neg-out` `associate-/l/` `unswap-sqr`

Counts

4 → 196

Calls

4 calls:

17.0ms	(- (* b b) (* (* 3.0 a) c))
36.0ms	(* (* 3.0 a) c)
215.0ms	(* (/ (* 3.0 (- a)) -1) (/ (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a)))
111.0ms	(/ (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series710.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* b b) (* (* 3.0 a) c))
39.0ms	(* (* 3.0 a) c)
237.0ms	(* (/ (* 3.0 (- a)) -1) (/ (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a)))
356.0ms	(/ (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify3.5s

Counts

208 → 208

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	339	5771
1	967	5514
2	4519	4247
done	5000	4245

prune663.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes261.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	46
1	33	46
2	38	46
3	42	46
4	45	46
5	47	46
6	49	46
done	49	46

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.1s	8059×	body	80	nan
979.0ms	16059×	pre	80	true
910.0ms	4875×	body	160	valid
336.0ms	1337×	body	320	valid
156.0ms	1788×	body	80	valid