Details

Time bar (total: 34.6s)

sample493.0ms

Algorithm
intervals
Results
188.0ms188×body80valid
50.0ms35×body2560valid
39.0ms14×body640valid
12.0ms28×body1280valid
8.0ms85×body80nan
4.0ms5×body5120valid
3.0ms10×body320valid
1.0ms4×body160valid

simplify234.0ms

Counts
1 → 1
Iterations
IterNodes
done34
534
432
330
223
115
010

prune58.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite457.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
174.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms
(- (* b_2 b_2) (* a c))
227.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series602.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
68.0ms
(- (* b_2 b_2) (* a c))
160.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
195.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts
134 → 134
Iterations
IterNodes
done5028
21493
1497
0199

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 123
Calls
4 calls:
213.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
22.0ms
(- (* b_2 b_2) (* a c))
105.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
30.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series535.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
68.0ms
(- (* b_2 b_2) (* a c))
140.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify7.2s

Counts
135 → 135
Iterations
IterNodes
done5000
34962
21533
1562
0219

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 122
Calls
4 calls:
186.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
11.0ms
(- (* b_2 b_2) (* a c))
118.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
82.0ms
(- (* b_2 b_2) (* a c))
153.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
133.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts
134 → 134
Iterations
IterNodes
done5028
21493
1497
0199

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize94.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 120
Calls
4 calls:
100.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
130.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
147.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))
121.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify5.2s

Counts
132 → 132
Iterations
IterNodes
done5000
32450
2763
1287
0112

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.8b

regimes1.1s

Accuracy

83.9% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 34.6b

bsearch180.0ms

Steps
ItersRangePoint
6
1.5727591416233446e-143
1.789606490082599e-142
1.744031351412433e-142
8
-1.3198903247987554e+155
-1.1250773400730914e+152
-1.2705286994550075e+152

simplify8.0ms

Iterations
IterNodes
done25
125
023

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.0s1082×body2560valid
679.0ms933×body1280valid
493.0ms5804×body80valid
303.0ms2985×body80nan
122.0ms492×body640valid
53.0ms108×body5120valid
45.0ms245×body320valid
15.0ms120×body160valid