Details

Time bar (total: 18.8s)

sample130.0ms

Algorithm
intervals
Results
13.0ms188×body80valid
11.0ms35×body2560valid
8.0ms28×body1280valid
5.0ms85×body80nan
3.0ms14×body640valid
2.0ms5×body5120valid
1.0ms10×body320valid
0.0ms4×body160valid

simplify29.0ms

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

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize23.0ms

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)))

rewrite227.0ms

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:
143.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms
(- (* b_2 b_2) (* a c))
54.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
50.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
106.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
100 → 100
Iterations
IterNodes
done5003
34058
21029
1378
0158

prune607.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize42.0ms

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)))

rewrite279.0ms

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:
180.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
11.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
57.0ms
(- (* b_2 b_2) (* a c))
98.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
101 → 101
Iterations
IterNodes
done5002
34688
21305
1445
0178

prune595.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite213.0ms

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:
140.0ms
(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
14.0ms
(- (* b_2 b_2) (* c a))
43.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
43.0ms
(- (* b_2 b_2) (* c a))
92.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
86.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify3.0s

Counts
100 → 100
Iterations
IterNodes
done5003
34218
21044
1381
0159

prune467.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

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:
57.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
86.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* c a)))
18.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
115.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
82.0ms
(sqrt (- (* b_2 b_2) (* c a)))
83.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify1.5s

Counts
76 → 76
Iterations
IterNodes
done5000
31496
2512
1186
081

prune459.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

regimes453.0ms

Accuracy

83.8% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 34.0b

bsearch116.0ms

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

simplify4.0ms

Iterations
IterNodes
done28
128
024

end0.0ms

sample3.1s

Algorithm
intervals
Results
804.0ms2985×body80nan
603.0ms1082×body2560valid
507.0ms933×body1280valid
464.0ms5804×body80valid
220.0ms492×body640valid
59.0ms108×body5120valid
50.0ms245×body320valid
17.0ms120×body160valid