Details

sample395.0ms

Algorithm

intervals

Results

85.0ms	195×	body	80	valid
59.0ms	29×	body	2560	valid
23.0ms	28×	body	1280	valid
14.0ms	97×	body	80	nan
11.0ms	18×	body	640	valid
3.0ms	8×	body	320	valid
3.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize40.0ms

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))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite187.0ms

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:

92.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
62.0ms	(- (* b_2 b_2) (* a c))
127.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
119.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

187 → 187

Iterations

Iter	Nodes
done	2004
3	2004
2	1521
1	578
0	248

prune872.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `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-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 173

Calls

4 calls:

114.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
16.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
57.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

185 → 185

Iterations

Iter	Nodes
done	2011
3	2011
2	1654
1	640
0	267

prune810.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize63.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 145

Calls

4 calls:

38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

157 → 157

Iterations

Iter	Nodes
done	2003
3	2003
2	985
1	383
0	163

prune800.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`cbrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `pow1/3` `sqrt-div` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 137

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
33.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series893.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(cbrt a)
353.0ms	(cbrt a)
115.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

149 → 149

Iterations

Iter	Nodes
done	2000
3	2000
2	1083
1	424
0	187

prune660.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.5b

regimes490.0ms

Accuracy

81.6% (5.1b remaining)

Error of 10.6b against oracle of 5.4b and baseline of 33.4b

bsearch120.0ms

Steps

Iters	Range		Point
4	2.0351360940656854e+23	4.0047314049975276e+23	3.912332224813067e+23
8	-9.258644314597195e-129	-3.187950860214187e-133	-8.424937854855119e-129

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.6s	904×	body	1280	valid
1.1s	1113×	body	2560	valid
831.0ms	5811×	body	80	valid
364.0ms	2982×	body	80	nan
241.0ms	445×	body	640	valid
103.0ms	208×	body	320	valid
98.0ms	107×	body	5120	valid
59.0ms	112×	body	160	valid