Details

sample86.0ms

Algorithm

intervals

Results

22.0ms	36×	body	2560	valid
15.0ms	187×	body	80	valid
11.0ms	30×	body	1280	valid
6.0ms	79×	body	80	nan
3.0ms	10×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	156
6	156
5	152
4	142
3	115
2	64
1	28
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.6b	(- (* b b) (* a (* 4.0 c)))
0.9b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
22.6b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

79.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
15.0ms	(- (* b b) (* a (* 4.0 c)))
38.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
21.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
63.0ms	(- (* b b) (* a (* 4.0 c)))
114.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
92.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify888.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1700
1	416
0	157

prune464.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
0.6b	(- (* b b) (* a (* 4.0 c)))
0.9b	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
22.6b	(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 125

Calls

4 calls:

85.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
13.0ms	(- (* b b) (* a (* 4.0 c)))
35.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
14.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))))
54.0ms	(- (* b b) (* a (* 4.0 c)))
121.0ms	(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
96.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify1.0s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	2588
1	595
0	228

prune654.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* a 2.0)) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))
0.6b	(- (* b b) (* 4.0 (* c a)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
22.6b	(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `rec-exp` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

99.0ms	(* (/ 1 (* a 2.0)) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))
20.0ms	(- (* b b) (* 4.0 (* c a)))
27.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (/ 1 (* a 2.0)) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))
61.0ms	(- (* b b) (* 4.0 (* c a)))
122.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
110.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2986
1	514
0	179

prune561.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 c) a))
8.3b	(+ (/ (/ (- b) a) 2.0) (/ (- (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a)))
22.6b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `times-frac` `associate-/l*`
15×	`add-cube-cbrt` `sqrt-prod`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`distribute-frac-neg`
5×	`pow1`
4×	`sqrt-div` `div-sub`
3×	`neg-sub0` `flip3--` `flip--`
2×	`cbrt-undiv` `neg-mul-1` `div-exp` `distribute-neg-frac` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `unsub-neg` `frac-add` `prod-exp` `associate-+l-` `cbrt-unprod` `flip-+` `div-inv` `distribute-neg-out` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 c) a))
207.0ms	(+ (/ (/ (- b) a) 2.0) (/ (- (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
81.0ms	(- (* b b) (* (* 4.0 c) a))
151.0ms	(+ (/ (/ (- b) a) 2.0) (/ (- (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a)))
87.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	2148
1	512
0	200

prune676.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

regimes388.0ms

Accuracy

85.4% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.3b

bsearch404.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	7.501979458872916e+77
6	-6.6625002027150184e-136	-1.2670716760605177e-136	-6.596302400897662e-136
9	-1.3974083100475422e-87	-7.780761669250176e-94	-7.877985662156599e-94
10	-4.6999773453873415e+54	-3.4259522644792056e+40	-5.84038254482515e+46

simplify16.0ms

Iterations

Iter	Nodes
done	64
3	64
2	60
1	58
0	44

end0.0ms

sample3.4s

Algorithm

intervals

Results

648.0ms	5898×	body	80	valid
635.0ms	1045×	body	2560	valid
598.0ms	448×	body	640	valid
458.0ms	875×	body	1280	valid
242.0ms	2811×	body	80	nan
151.0ms	121×	body	5120	valid
54.0ms	227×	body	320	valid
16.0ms	105×	body	160	valid