Details

sample100.0ms

Algorithm

intervals

Results

18.0ms	37×	body	2560	valid
17.0ms	23×	body	1280	valid
16.0ms	190×	body	80	valid
7.0ms	90×	body	80	nan
5.0ms	15×	body	640	valid
1.0ms	6×	body	160	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	320	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite245.0ms

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:

133.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
63.0ms	(- (* b_2 b_2) (* a c))
137.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	156	1821
1	387	1727
2	1508	1613
done	5001	1603

prune685.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

171.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
14.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
64.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

101 → 101

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	175	1741
1	456	1588
2	2159	1377
done	5000	1357

prune739.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite207.0ms

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:

97.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
24.0ms	(- (* b_2 b_2) (* a c))
47.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.0s

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
71.0ms	(- (* b_2 b_2) (* a c))
606.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
124.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

189 → 189

Iterations

Useful iterations: 2 (861.0ms)

Iter	Nodes	Cost
0	266	4484
1	665	3936
2	3528	3786
done	5002	3786

prune861.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.3b	(/ (+ 0 (* a c)) a)
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite129.0ms

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:

16.0ms	(- (* b_2 b_2) (* a c))
50.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(/ (+ 0 (* a c)) a)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b_2 b_2) (* a c))
131.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms	(/ (+ 0 (* a c)) a)
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

83 → 83

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	144	1084
1	368	917
2	1942	827
done	5000	791

prune673.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.6b

regimes520.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.7b

bsearch369.0ms

Steps

Iters	Range	Point
8	4.049254448328916e+76	2.3057443967677173e+80	1.2307425160882177e+80
9	-2.156528177776517e-300	1.8516868946851025e-307	1.3959529492205615e-308
10	-6.623625638726693e+82	-6.4709084601913214e+72	-4.6218828469248316e+82

Iters

Range

Point

4.049254448328916e+76

2.3057443967677173e+80

1.2307425160882177e+80

-2.156528177776517e-300

1.8516868946851025e-307

1.3959529492205615e-308

-6.623625638726693e+82

-6.4709084601913214e+72

-4.6218828469248316e+82

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	50
1	36	50
done	36	50

end0.0ms

sample3.9s

Algorithm

intervals

Results

982.0ms	904×	body	1280	valid
758.0ms	1110×	body	2560	valid
732.0ms	5910×	body	80	valid
308.0ms	3011×	body	80	nan
196.0ms	432×	body	640	valid
114.0ms	106×	body	5120	valid
52.0ms	220×	body	320	valid
17.0ms	110×	body	160	valid