Details

sample90.0ms

Algorithm

intervals

Results

23.0ms	37×	body	2560	valid
18.0ms	194×	body	80	valid
14.0ms	28×	body	1280	valid
8.0ms	86×	body	80	nan
6.0ms	18×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize39.0ms

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)))

rewrite159.0ms

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:

70.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
47.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
91.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(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

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize32.0ms

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)))

rewrite129.0ms

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:

86.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
21.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
86.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
47.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(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

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt a) (cbrt 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)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
61×	`prod-diff`
58×	`*-un-lft-identity`
54×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`cbrt-prod`
12×	`pow1`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `pow-prod-down` `pow-sqr` `pow-prod-up` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `pow2` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 169

Calls

4 calls:

8.0ms	(* (cbrt a) (cbrt a))
26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (cbrt a) (cbrt a))
106.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	2003
3	2003
2	1307
1	525
0	232

prune2.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.6b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
10.9b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (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)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`fma-neg` `prod-diff`
10×	`add-log-exp`
6×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `neg-mul-1` `sub-neg` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 91

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (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)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	2000
3	2000
2	872
1	309
0	131

prune1.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.6b

regimes628.0ms

Accuracy

83.6% (4.6b remaining)

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

bsearch180.0ms

Steps

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

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample3.8s

Algorithm

intervals

Results

886.0ms	949×	body	1280	valid
806.0ms	1094×	body	2560	valid
668.0ms	5822×	body	80	valid
459.0ms	99×	body	5120	valid
372.0ms	2994×	body	80	nan
176.0ms	445×	body	640	valid
111.0ms	224×	body	320	valid
23.0ms	115×	body	160	valid