Details

sample81.0ms

Algorithm

intervals

Results

19.0ms	175×	body	80	valid
17.0ms	43×	body	2560	valid
9.0ms	31×	body	1280	valid
7.0ms	106×	body	80	nan
4.0ms	18×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify524.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	12	17
1	24	17
2	66	16
3	103	16
4	114	16
done	114	16

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
16.0ms	(- (* b b) (* (* 3.0 a) c))
55.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 3.0 a) c)
82.0ms	(- (* b b) (* (* 3.0 a) c))
121.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	122	1001
1	713	883
done	5001	824

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.3b

localize34.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.2b	(/ (/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b	(/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

36.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
133.0ms	(/ (/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
127.0ms	(/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
26.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
210.0ms	(/ (/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
276.0ms	(/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
130.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts

166 → 166

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	253	5113
done	5000	4537

prune756.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.1b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.2b	(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
10.0b	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

376×	`times-frac`
192×	`add-sqr-sqrt`
191×	`*-un-lft-identity`
131×	`add-cube-cbrt`
44×	`associate-/l*`
33×	`add-exp-log` `add-cbrt-cube`
30×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r/`
18×	`sqrt-prod` `div-inv`
15×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `div-exp` `flip--`
10×	`associate-/r*`
8×	`add-log-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 262

Calls

4 calls:

43.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
154.0ms	(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
74.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
212.0ms	(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
281.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
111.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.7s

Counts

274 → 274

Iterations

Useful iterations: done (4.7s)

Iter	Nodes	Cost
0	500	9750
1	3782	9071
done	5000	8637

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.2b

localize49.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.2b	(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt 3.0)) a)
9.9b	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

733×	`times-frac`
355×	`add-sqr-sqrt`
354×	`*-un-lft-identity`
246×	`add-cube-cbrt`
156×	`cbrt-prod`
83×	`associate-/l*`
54×	`distribute-lft-out--` `difference-of-squares`
50×	`associate-/r/`
30×	`sqrt-prod` `div-inv`
27×	`flip3--` `distribute-rgt-neg-in` `flip--`
23×	`add-exp-log`
20×	`add-cbrt-cube`
11×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
8×	`add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 414

Calls

4 calls:

45.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
158.0ms	(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt 3.0)) a)
87.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
32.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series1.4s

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
834.0ms	(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt 3.0)) a)
315.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
110.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.5s

Counts

426 → 426

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	667	15912
1	4331	14666
done	5000	14364

prune2.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.6b

regimes735.0ms

Accuracy

84.9% (3.3b remaining)

Error of 12.6b against oracle of 9.3b and baseline of 31.3b

bsearch391.0ms

Steps

Iters	Range		Point
3	5.973091654032696e+157	8.116126331786576e+157	6.107031321392313e+157
9	1.8716994562120376e+60	1.989588560476957e+65	3.0585377634424225e+64
8	-8.323312449074226e-206	-4.4801366753311535e-209	-5.843373275880085e-209
6	-9.188861011096532e+114	-1.1922005359556833e+114	-7.949039921111462e+114

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	51	132
1	61	130
done	61	130

end0.0ms

sample3.3s

Algorithm

intervals

Results

774.0ms	885×	body	1280	valid
646.0ms	1076×	body	2560	valid
641.0ms	5872×	body	80	valid
283.0ms	3010×	body	80	nan
181.0ms	491×	body	640	valid
135.0ms	105×	body	5120	valid
45.0ms	218×	body	320	valid
13.0ms	95×	body	160	valid