Details

Time bar (total: 19.5s)

sample128.0ms

Algorithm
intervals
Results
32.0ms36×body2560valid
30.0ms187×body80valid
18.0ms25×body1280valid
14.0ms86×body80nan
11.0ms17×body640valid
4.0ms8×body320valid
1.0ms4×body160valid

simplify89.0ms

Counts
1 → 1
Iterations
IterNodes
895
795
694
592
484
367
243
124
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize31.0ms

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))
0.9b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite180.0ms

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:
87.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
9.0ms
(- (* b b) (* (* 4 a) c))
67.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
64.0ms
(- (* b b) (* (* 4 a) c))
113.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
92.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
100 → 100
Iterations
IterNodes
33816
21126
1392
0161

prune558.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize48.0ms

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))
0.9b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite236.0ms

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:
169.0ms
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
7.0ms
(- (* b b) (* (* 4 a) c))
38.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
61.0ms
(- (* b b) (* (* 4 a) c))
90.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.2s

Counts
101 → 101
Iterations
IterNodes
34837
21437
1455
0181

prune581.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.9b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite116.0ms

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:
50.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
47.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
120.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
114.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify859.0ms

Counts
76 → 76
Iterations
IterNodes
32007
2604
1192
082

prune565.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.3b

localize65.0ms

Local error

Found 4 expressions with local error:

23.5b
(sqrt (- (* b b) (* (* 4 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series513.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
133.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
100.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
162.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify3.4s

Counts
70 → 70
Iterations
IterNodes
46322
31876
2580
1200
089

prune625.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.3b

regimes357.0ms

Accuracy

84.1% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 32.9b

bsearch234.0ms

Steps
ItersRangePoint
8
5.833527798943191e-77
3.6732813120885656e-72
3.1295384133612364e-73
9
-2.2174027590176242e+73
-8.164533525332822e+65
-3.063397748446981e+71

simplify9.0ms

Iterations
IterNodes
234
134
029

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.3s1026×body2560valid
1.3s5891×body80valid
648.0ms881×body1280valid
431.0ms2954×body80nan
297.0ms464×body640valid
154.0ms237×body320valid
140.0ms96×body5120valid
25.0ms104×body160valid