Details

Time bar (total: 16.1s)

sample125.0ms

Algorithm
intervals
Results
24.0ms35×body2560valid
22.0ms85×body80nan
21.0ms188×body80valid
16.0ms28×body1280valid
6.0ms14×body640valid
4.0ms5×body5120valid
3.0ms10×body320valid
1.0ms4×body160valid

simplify108.0ms

Counts
1 → 1
Iterations
IterNodes
done95
795
694
592
484
367
243
124
014

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.8b
(- (* b b) (* (* 4 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite234.0ms

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:
108.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
14.0ms
(- (* b b) (* (* 4 a) c))
90.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
60.0ms
(- (* b b) (* (* 4 a) c))
124.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
88.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.3s

Counts
100 → 100
Iterations
IterNodes
done5000
21158
1394
0161

prune506.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
0.8b
(- (* b b) (* (* 4 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite249.0ms

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:
181.0ms
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
8.0ms
(- (* b b) (* (* 4 a) c))
47.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
89.0ms
(- (* b b) (* (* 4 a) c))
117.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
101 → 101
Iterations
IterNodes
done5003
21455
1458
0181

prune669.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize64.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite186.0ms

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:
64.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
86.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
17.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
139.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
115.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
112.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.2s

Counts
76 → 76
Iterations
IterNodes
done5002
32079
2595
1194
082

prune635.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

localize40.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
67.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
98.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
91.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts
76 → 76
Iterations
IterNodes
done5002
32079
2595
1194
082

prune523.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.7b

regimes451.0ms

Accuracy

82% (5.2b remaining)

Error of 10.6b against oracle of 5.4b and baseline of 34.1b

bsearch163.0ms

Steps
ItersRangePoint
6
1.5727591416233446e-143
1.789606490082599e-142
1.6528810740721013e-142
6
-2.971125736392027e+46
-1.937449214055594e+45
-2.900769547116861e+46

simplify10.0ms

Iterations
IterNodes
done36
136
029

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s1083×body2560valid
572.0ms5804×body80valid
550.0ms932×body1280valid
278.0ms2988×body80nan
236.0ms489×body640valid
68.0ms107×body5120valid
61.0ms247×body320valid
18.0ms121×body160valid