Details

Time bar (total: 17.1s)

sample403.0ms

Algorithm
intervals
Results
66.0ms15×body640valid
57.0ms184×body80valid
32.0ms35×body2560valid
24.0ms28×body1280valid
18.0ms86×body80nan
4.0ms4×body5120valid
4.0ms8×body320valid
1.0ms5×body160valid

simplify53.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize872.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b
(- (* b_2 b_2) (* a c))
1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite240.0ms

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:
124.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
18.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
41.0ms
(- (* b_2 b_2) (* a c))
78.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
107.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done2003
32003
21029
1378
0158

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b
(- (* b_2 b_2) (* a c))
1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite162.0ms

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:
95.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms
(- (* b_2 b_2) (* a c))
51.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
53.0ms
(- (* b_2 b_2) (* a c))
106.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
100 → 100
Iterations
IterNodes
done2003
32003
21029
1378
0158

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.6b
(- (* b_2 b_2) (* a c))
1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite239.0ms

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:
176.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
7.0ms
(- (* b_2 b_2) (* a c))
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
61.0ms
(- (* b_2 b_2) (* a c))
101.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
101 → 101
Iterations
IterNodes
done2001
32001
21305
1445
0178

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.6b

localize53.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite120.0ms

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:
53.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
done2013
42013
31579
2536
1185
080

prune1.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.6b

regimes364.0ms

Accuracy

84.5% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.4b

bsearch139.0ms

Steps
ItersRangePoint
10
8.296670056881522e-85
2.5972983117194536e-74
2.326372645943808e-74
7
-1.542727211461463e+154
-9.467643560597781e+151
-1.056361093164439e+152

simplify8.0ms

Iterations
IterNodes
done28
128
024

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s1125×body2560valid
785.0ms5834×body80valid
563.0ms917×body1280valid
433.0ms2970×body80nan
200.0ms416×body640valid
97.0ms119×body5120valid
73.0ms237×body320valid
24.0ms115×body160valid