Details

Time bar (total: 20.0s)

sample384.0ms

Algorithm
intervals
Results
31.0ms184×body80valid
28.0ms31×body2560valid
27.0ms35×body1280valid
11.0ms86×body80nan
7.0ms12×body640valid
3.0ms7×body320valid
3.0ms2×body5120valid
1.0ms3×body160valid

simplify61.0ms

Counts
1 → 1
Iterations
IterNodes
544
444
341
232
118
010

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize75.0ms

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))
1.1b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite207.0ms

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:
90.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
57.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
130.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify895.0ms

Counts
107 → 107
Iterations
IterNodes
32584
21011
1386
0162

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

localize33.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0b
(sqrt (- (* b_2 b_2) (* a c)))
21.0b
(sqrt (- (* b_2 b_2) (* a c)))
21.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
10×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 67
Calls
4 calls:
26.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
79 → 79
Iterations
IterNodes
43459
31467
2565
1200
086

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
1.0b
(- (* b_2 b_2) (* a c))
1.1b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
6×add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod insert-posit16
3×cbrt-prod flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 pow1/3 neg-log
Counts
4 → 60
Calls
4 calls:
1.0ms
(cbrt a)
10.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(cbrt a)
53.0ms
(- (* b_2 b_2) (* a c))
108.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
104.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts
72 → 72
Iterations
IterNodes
45131
31910
2706
1265
0119

prune949.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.4b

localize51.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.5b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite256.0ms

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:
44.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
95.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series729.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
229.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
303.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
203 → 203
Iterations
IterNodes
22212
1728
0308

prune2.2s

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 4.4b

regimes512.0ms

Accuracy

88.6% (3.2b remaining)

Error of 8.5b against oracle of 5.4b and baseline of 33.1b

bsearch220.0ms

Steps
ItersRangePoint
9
1.7155709022758137e+74
7.648947555279674e+80
5.704492581538356e+80
8
-6.469330140987597e-187
-1.8749838958168548e-190
-2.2033917388951676e-187
7
-1.445259435205163e+106
-1.1448563471736209e+104
-1.1643926003340064e+104

simplify10.0ms

Iterations
IterNodes
234
134
030

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s1093×body2560valid
1.2s864×body1280valid
788.0ms5873×body80valid
360.0ms2898×body80nan
219.0ms426×body640valid
121.0ms235×body320valid
90.0ms108×body5120valid
28.0ms122×body160valid