Details

sample328.0ms

Algorithm

intervals

Results

7.0ms	36×	body	2560	valid
6.0ms	191×	body	80	valid
4.0ms	77×	body	80	nan
3.0ms	20×	body	1280	valid
2.0ms	18×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7
done	29	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

74.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify39.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705
done	5001	705

prune228.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
61.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
143.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
171.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Counts

218 → 218

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269
done	5001	3269

prune487.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.7b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp` `sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`cbrt-undiv`
8×	`add-log-exp`
6×	`prod-exp` `div-inv`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `neg-log` `associate-/r/` `associate-/l/`

Counts

4 → 180

Calls

4 calls:

25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
49.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
40.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
182.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
157.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Counts

192 → 192

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	814	2587
1	3756	2402
2	5002	2379
done	5002	2379

prune408.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
32×	`add-exp-log`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
17×	`div-exp`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`1-exp` `associate-/r*`
6×	`pow1` `prod-exp`
5×	`cbrt-undiv` `div-inv`
4×	`rec-exp` `sqrt-prod`
3×	`flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `cbrt-unprod` `inv-pow`

Counts

4 → 104

Calls

4 calls:

52.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
9.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
34.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	521	1126
1	2188	976
2	5002	931
done	5002	931

prune192.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.3b

regimes185.0ms

Accuracy

82.5% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 30.1b

bsearch68.0ms

Steps

Iters	Range		Point
5	3.355600980676121e+98	1.2784432988208537e+99	6.385814412780331e+98
9	-7.880786648230988e-89	-3.5843833042003497e-96	-4.706781135059312e-92

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15
done	34	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

191.0ms	1121×	body	2560	valid
181.0ms	5760×	body	80	valid
130.0ms	903×	body	1280	valid
81.0ms	2849×	body	80	nan
57.0ms	476×	body	640	valid
30.0ms	129×	body	5120	valid
18.0ms	216×	body	320	valid
6.0ms	105×	body	160	valid