Details

sample89.0ms

Algorithm

intervals

Results

18.0ms	15×	body	640	valid
16.0ms	182×	body	80	valid
14.0ms	35×	body	1280	valid
14.0ms	26×	body	2560	valid
8.0ms	91×	body	80	nan
3.0ms	4×	body	5120	valid
2.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite160.0ms

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:

73.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(- (* b_2 b_2) (* a c))
31.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
82.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

187 → 187

Iterations

Iter	Nodes
3	4198
2	1440
1	577
0	248

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.6b	(- (* b_2 b_2) (* a c))
4.0b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

1339×	`times-frac`
946×	`add-sqr-sqrt`
940×	`*-un-lft-identity`
926×	`add-cube-cbrt`
749×	`prod-diff`
323×	`sqrt-prod`
210×	`distribute-rgt-neg-in`
207×	`distribute-lft-neg-in`
69×	`neg-mul-1`
60×	`div-inv`
35×	`fma-neg`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `div-exp` `frac-sub` `sub-div`

Counts

4 → 893

Calls

4 calls:

14.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
8.0ms	(- (* b_2 b_2) (* a c))
34.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
39.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

905 → 905

Iterations

Iter	Nodes
1	2006
0	907

prune13.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
1.6b	(- (* b_2 b_2) (* a c))
10.9b	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
69×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
35×	`fma-neg` `prod-diff`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`associate-r` `add-exp-log`
10×	`sqrt-div`
9×	`add-cbrt-cube` `sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `flip3--` `flip--`
6×	`neg-mul-1` `associate-l` `frac-sub` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `prod-exp` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-*r/` `un-div-inv`
2×	`sub-neg` `diff-log` `div-exp` `cbrt-unprod` `sub-div`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `1-exp` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 177

Calls

4 calls:

50.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
22.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
61.0ms	(- (* b_2 b_2) (* a c))
133.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify689.0ms

Counts

189 → 189

Iterations

Iter	Nodes
2	2256
1	787
0	309

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.8b

localize40.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
14.0b	(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
48×	`add-sqr-sqrt`
46×	`*-un-lft-identity` `add-cube-cbrt`
35×	`fma-neg` `prod-diff`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`sqrt-div`
8×	`add-log-exp`
6×	`pow1` `neg-mul-1` `flip3--` `sqrt-prod` `flip--`
5×	`frac-sub`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l/` `associate-r/` `div-inv`
1×	`associate--l-` `neg-sub0` `div-sub` `sub-div`

Counts

4 → 143

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b_2 b_2) (* a c))
125.0ms	(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

155 → 155

Iterations

Iter	Nodes
3	4967
2	1628
1	596
0	245

prune1.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.8b

regimes970.0ms

Accuracy

84% (4.6b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 34.6b

bsearch76.0ms

Steps

Iters	Range		Point
6	2.332248586404817e+54	2.734436825826664e+55	2.6656023684116586e+55
4	-1.803902702675876e-57	-1.171727155116065e-57	-1.229142930221511e-57

simplify5.0ms

Iterations

Iter	Nodes
2	34
1	34
0	28

end0.0ms

sample3.5s

Algorithm

intervals

Results

804.0ms	1042×	body	2560	valid
714.0ms	5889×	body	80	valid
567.0ms	475×	body	640	valid
509.0ms	935×	body	1280	valid
331.0ms	2911×	body	80	nan
171.0ms	207×	body	320	valid
84.0ms	110×	body	5120	valid
43.0ms	107×	body	160	valid