Details

Time bar (total: 35.9s)

sample190.0ms

Algorithm
intervals
Results
16.0ms35×body2560valid
15.0ms188×body80valid
11.0ms28×body1280valid
6.0ms85×body80nan
4.0ms14×body640valid
2.0ms5×body5120valid
2.0ms10×body320valid
1.0ms4×body160valid

simplify163.0ms

Counts
1 → 1
Iterations
IterNodes
done29
529
427
325
222
114
010

prune47.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize45.0ms

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)))

rewrite302.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 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 → 88
Calls
4 calls:
177.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
20.0ms
(- (* b_2 b_2) (* a c))
85.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
85.0ms
(- (* b_2 b_2) (* a c))
179.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
113.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify6.5s

Counts
100 → 100
Iterations
IterNodes
done5008
34077
21022
1378
0158

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize34.0ms

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)))

rewrite408.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp insert-posit16 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 → 89
Calls
4 calls:
320.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
10.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
56.0ms
(- (* b_2 b_2) (* a c))
138.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
119.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify7.5s

Counts
101 → 101
Iterations
IterNodes
done5000
34775
21357
1446
0178

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize40.0ms

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)))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 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 → 88
Calls
4 calls:
179.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
20.0ms
(- (* b_2 b_2) (* a c))
111.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
58.0ms
(- (* b_2 b_2) (* a c))
142.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
133.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify6.3s

Counts
100 → 100
Iterations
IterNodes
done5008
34077
21022
1378
0158

prune978.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize83.0ms

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)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
133.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
135.0ms
(sqrt (- (* b_2 b_2) (* a c)))
120.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts
76 → 76
Iterations
IterNodes
done5000
31654
2536
1185
080

prune933.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

regimes980.0ms

Accuracy

83.9% (4.7b remaining)

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

bsearch134.0ms

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

simplify9.0ms

Iterations
IterNodes
done28
128
024

end0.0ms

sample2.9s

Algorithm
intervals
Results
968.0ms1082×body2560valid
523.0ms5804×body80valid
354.0ms933×body1280valid
167.0ms2985×body80nan
119.0ms492×body640valid
92.0ms108×body5120valid
73.0ms245×body320valid
13.0ms120×body160valid