Details

sample144.0ms

Algorithm

intervals

Results

10.0ms	206×	body	80	valid
7.0ms	29×	body	2560	valid
6.0ms	28×	body	1280	valid
4.0ms	96×	body	80	nan
2.0ms	12×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
105.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
48.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

103 → 103

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	156	1821
1	366	1727
2	1005	1611
3	2770	1595
done	5001	1593

prune458.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

75.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
55.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
116.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

189 → 189

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	266	4484
1	577	3936
2	1380	3617
3	3854	3507
done	5000	3507

prune483.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.3b	(/ (+ 0 (* a c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

17.0ms	(- (* b_2 b_2) (* a c))
52.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (+ 0 (* a c)) a)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (+ 0 (* a c)) a)
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts

83 → 83

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	144	1084
1	329	915
2	1070	825
3	3772	785
done	5000	785

prune313.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.2b	(- (* b_2 b_2) (* a c))
2.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

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-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

Calls

4 calls:

43.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(/ c (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
56.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

91 → 91

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	142	1485
1	323	1382
2	872	1211
3	2285	1195
done	5001	1189

prune673.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.6b

regimes377.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.3b

bsearch311.0ms

Steps

Iters	Range		Point
9	1.2073698495971617e+61	8.75865749938149e+67	5.099089738165329e+67
10	1.610059141238142e-239	1.618698210595833e-224	2.094358742794728e-239
10	-3.742210988141449e+103	-1.0235731023437291e+92	-3.359953003549157e+103

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	54
1	35	54
done	35	54

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	5837×	body	80	valid
526.0ms	898×	body	1280	valid
484.0ms	1052×	body	2560	valid
208.0ms	2844×	body	80	nan
116.0ms	464×	body	640	valid
89.0ms	112×	body	5120	valid
45.0ms	238×	body	320	valid
13.0ms	108×	body	160	valid