Details

sample173.0ms

Algorithm

intervals

Results

19.0ms	187×	body	80	valid
17.0ms	36×	body	2560	valid
13.0ms	30×	body	1280	valid
6.0ms	79×	body	80	nan
3.0ms	10×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify99.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 171

Calls

4 calls:

78.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
53.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
45.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2152
1	583
0	244

prune663.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 257

Calls

4 calls:

78.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
37.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

269 → 269

Iterations

Iter	Nodes
done	5000
2	4146
1	850
0	351

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
0.5b	(* (cbrt a) (cbrt a))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
60×	`prod-diff`
59×	`*-un-lft-identity`
55×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
19×	`cbrt-prod`
12×	`pow1`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
2×	`flip3--` `sqrt-div` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `pow2` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow-plus` `pow1/2` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 162

Calls

4 calls:

1.0ms	(cbrt a)
14.0ms	(* (cbrt a) (cbrt a))
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series838.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt a)
358.0ms	(* (cbrt a) (cbrt a))
108.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	2273
1	526
0	222

prune683.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.1b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 219

Calls

4 calls:

51.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
311.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
78.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
226.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
272.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

231 → 231

Iterations

Iter	Nodes
done	5000
2	4923
1	879
0	340

prune1.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.8b

regimes367.0ms

Accuracy

93.1% (1.7b remaining)

Error of 7.5b against oracle of 5.8b and baseline of 30.5b

bsearch276.0ms

Steps

Iters	Range	Point
9	3.768382185355077e+69	1.107955803311012e+78	1.082532154480776e+78
9	-2.926605843992264e-247	-1.2769153513311889e-254	-1.548986092369567e-252
9	-3.7162343696193017e+68	-4.7924972520805885e+61	-1.9495061528188055e+68

Iters

Range

Point

3.768382185355077e+69

1.107955803311012e+78

1.082532154480776e+78

-2.926605843992264e-247

-1.2769153513311889e-254

-1.548986092369567e-252

-3.7162343696193017e+68

-4.7924972520805885e+61

-1.9495061528188055e+68

simplify8.0ms

Iterations

Iter	Nodes
done	41
1	41
0	34

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	5896×	body	80	valid
491.0ms	1048×	body	2560	valid
300.0ms	877×	body	1280	valid
156.0ms	2811×	body	80	nan
156.0ms	121×	body	5120	valid
132.0ms	229×	body	320	valid
107.0ms	446×	body	640	valid
12.0ms	105×	body	160	valid