Details

sample119.0ms

Algorithm

intervals

Results

33.0ms	37×	body	2560	valid
24.0ms	194×	body	80	valid
16.0ms	28×	body	1280	valid
10.0ms	86×	body	80	nan
9.0ms	18×	body	640	valid
5.0ms	5×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite156.0ms

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:

99.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
97.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

187 → 187

Iterations

Iter	Nodes
done	2003
3	2003
2	1504
1	577
0	248

prune743.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite131.0ms

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:

81.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

185 → 185

Iterations

Iter	Nodes
done	2002
3	2002
2	1665
1	640
0	267

prune681.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
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`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 71

Calls

4 calls:

18.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

83 → 83

Iterations

Iter	Nodes
done	2004
4	2004
3	1558
2	467
1	166
0	69

prune596.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 a))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
53×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`cbrt-prod`
11×	`fma-neg`
10×	`add-log-exp`
9×	`times-frac`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `neg-log` `div-inv`

Counts

4 → 151

Calls

4 calls:

2.0ms	(cbrt (/ 1 a))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt (/ 1 a))
99.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
47.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

163 → 163

Iterations

Iter	Nodes
done	2002
3	2002
2	1168
1	497
0	238

prune600.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.6b

regimes579.0ms

Accuracy

83.6% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.3b

bsearch213.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	2.5703497435733685e+102
10	-1.094129558870314e-56	-1.2317994276347943e-74	-1.8774910265390396e-73

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample3.4s

Algorithm

intervals

Results

858.0ms	1094×	body	2560	valid
752.0ms	2994×	body	80	nan
615.0ms	5822×	body	80	valid
539.0ms	949×	body	1280	valid
223.0ms	445×	body	640	valid
70.0ms	99×	body	5120	valid
64.0ms	224×	body	320	valid
24.0ms	115×	body	160	valid