Details

Time bar (total: 16.3s)

sample373.0ms

Algorithm
intervals
Results
63.0ms31×body2560valid
41.0ms84×body80nan
31.0ms190×body80valid
25.0ms31×body1280valid
9.0ms13×body640valid
4.0ms4×body5120valid
4.0ms8×body320valid
1.0ms4×body160valid

simplify40.0ms

Counts
1 → 1
Iterations
IterNodes
done44
444
341
232
118
010

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (* b_2 b_2) (* a c))
1.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- insert-posit16 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 → 95
Calls
4 calls:
175.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms
(- (* b_2 b_2) (* a c))
48.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms
(- (* b_2 b_2) (* a c))
135.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
145.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify862.0ms

Counts
107 → 107
Iterations
IterNodes
done2004
21046
1388
0162

prune478.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize48.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.9b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×distribute-lft-out--
11×add-cbrt-cube add-exp-log
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp insert-posit16
3×associate-/l/
2×clear-num frac-2neg sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 191
Calls
4 calls:
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
110.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
53.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series690.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
220.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
278.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify694.0ms

Counts
203 → 203
Iterations
IterNodes
done2000
1736
0308

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize77.0ms

Local error

Found 4 expressions with local error:

5.3b
(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.4b
(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
23.4b
(sqrt (- (* b_2 b_2) (* a c)))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
188×add-sqr-sqrt
154×*-un-lft-identity
122×add-cube-cbrt
118×sqrt-prod
36×associate-/l*
32×difference-of-squares
16×distribute-lft-out--
14×sqrt-div
12×associate-/r*
11×add-cbrt-cube add-exp-log
10×associate-/r/
7×flip3-- flip--
6×pow1 div-inv
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×flip3-+ flip-+
Counts
4 → 239
Calls
4 calls:
92.0ms
(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
139.0ms
(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series1.4s

Counts
4 → 12
Calls
4 calls:
585.0ms
(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
625.0ms
(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify813.0ms

Counts
251 → 251
Iterations
IterNodes
done2001
1841
0357

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

localize109.0ms

Local error

Found 4 expressions with local error:

23.4b
(sqrt (- (* b_2 b_2) (* a c)))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log insert-posit16 flip-- add-log-exp
Counts
4 → 64
Calls
4 calls:
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))
95.0ms
(sqrt (- (* b_2 b_2) (* a c)))
104.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify697.0ms

Counts
76 → 76
Iterations
IterNodes
done2002
31050
2357
1122
050

prune661.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.0b

regimes588.0ms

Accuracy

87.6% (3.3b remaining)

Error of 8.5b against oracle of 5.2b and baseline of 32.0b

bsearch261.0ms

Steps
ItersRangePoint
7
1.9723660647371773e+81
3.4101289177416236e+83
3.340270116328134e+83
9
-3.8385825784978356e-187
-1.5580723401690244e-192
-3.2374193672365033e-189
8
-4.372979365646395e-14
-8.411835944359371e-19
-4.2863876983616346e-14

simplify15.0ms

Iterations
IterNodes
done45
245
144
033

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.3s1054×body2560valid
825.0ms2980×body80nan
718.0ms5925×body80valid
661.0ms921×body1280valid
182.0ms420×body640valid
117.0ms116×body5120valid
96.0ms222×body320valid
26.0ms123×body160valid