Details

sample81.0ms

Algorithm

intervals

Results

22.0ms	41×	body	2560	valid
15.0ms	183×	body	80	valid
14.0ms	31×	body	1280	valid
6.0ms	84×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize41.0ms

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))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

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--` `insert-posit16` `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 → 175

Calls

4 calls:

79.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
58.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	1521
1	578
0	248

prune698.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

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` `insert-posit16` `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 → 261

Calls

4 calls:

31.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
9.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
56.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

273 → 273

Iterations

Iter	Nodes
done	5023
2	2295
1	837
0	355

prune771.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize22.0ms

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))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
146×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`associate-l` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 296

Calls

4 calls:

78.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
39.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

308 → 308

Iterations

Iter	Nodes
done	5001
2	2073
1	1004
0	360

prune802.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
5.5b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))
23.4b	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

91×	`prod-diff`
75×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
68×	`log-prod` `exp-sum` `add-cube-cbrt`
37×	`sqrt-prod`
31×	`distribute-rgt-neg-in`
30×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`neg-mul-1` `add-log-exp`
7×	`pow1`
6×	`exp-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log` `log-pow` `difference-of-squares`
2×	`log-div` `sub-neg` `sqrt-pow1` `pow1/2` `exp-diff` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `neg-log` `rem-exp-log`

Counts

4 → 182

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
31.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b_2 b_2) (* a c))
89.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))

simplify3.0s

Counts

194 → 194

Iterations

Iter	Nodes
done	5000
3	4036
2	1257
1	564
0	261

prune669.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

regimes560.0ms

Accuracy

82.9% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 32.9b

bsearch122.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	7.052614559736995e+62
8	-9.498395151376604e-61	-6.25213087380725e-65	-1.6239127264630285e-63

simplify7.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5893×	body	80	valid
901.0ms	1104×	body	2560	valid
539.0ms	854×	body	1280	valid
364.0ms	3005×	body	80	nan
295.0ms	463×	body	640	valid
83.0ms	98×	body	5120	valid
71.0ms	221×	body	320	valid
24.0ms	115×	body	160	valid