Details

sample369.0ms

Algorithm

intervals

Results

29.0ms	32×	body	2560	valid
26.0ms	176×	body	80	valid
22.0ms	29×	body	1280	valid
14.0ms	85×	body	80	nan
9.0ms	16×	body	640	valid
6.0ms	6×	body	5120	valid
4.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify92.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize29.0ms

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))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite474.0ms

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:

46.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
380.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
48.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

187 → 187

Iterations

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

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize27.0ms

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))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite180.0ms

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:

113.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
21.0ms	(- (* b_2 b_2) (* a c))
34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
54.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

185 → 185

Iterations

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

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize18.0ms

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))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

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:

48.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (* b_2 b_2) (* a c))
113.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

187 → 187

Iterations

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

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

9.0ms

(* -1/2 (/ c b_2))

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(* -1/2 (/ c b_2))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
done	2016
4	2016
3	1721
2	518
1	173
0	71

prune233.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.6b

regimes468.0ms

Accuracy

81.6% (5.1b remaining)

Error of 10.7b against oracle of 5.6b and baseline of 33.2b

bsearch177.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	2.559678284282607e+69
9	-2.273288360947074e-131	-1.9680749876012584e-137	-2.2415082771065304e-131

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	25

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5788×	body	80	valid
778.0ms	1053×	body	2560	valid
646.0ms	956×	body	1280	valid
410.0ms	2937×	body	80	nan
237.0ms	453×	body	640	valid
112.0ms	98×	body	5120	valid
92.0ms	216×	body	320	valid
22.0ms	108×	body	160	valid