Details

Time bar (total: 17.8s)

sample244.0ms

Algorithm
intervals
Results
28.0ms35×body2560valid
25.0ms184×body80valid
21.0ms28×body1280valid
14.0ms86×body80nan
8.0ms15×body640valid
4.0ms4×body5120valid
3.0ms8×body320valid
1.0ms5×body160valid

simplify83.0ms

Counts
1 → 1
Iterations
IterNodes
done34
534
432
330
223
115
010

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize34.0ms

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)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u 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 → 122
Calls
4 calls:
78.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
51.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts
134 → 134
Iterations
IterNodes
done2015
32015
21393
1494
0199

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

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)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u 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 → 122
Calls
4 calls:
78.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms
(- (* b_2 b_2) (* a c))
57.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
43.0ms
(- (* b_2 b_2) (* a c))
130.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts
134 → 134
Iterations
IterNodes
done2015
32015
21393
1494
0199

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize25.0ms

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)))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u 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 → 123
Calls
4 calls:
161.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
16.0ms
(- (* b_2 b_2) (* a c))
46.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
55.0ms
(- (* b_2 b_2) (* a c))
116.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
135 → 135
Iterations
IterNodes
done2001
32001
21630
1559
0219

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.6b

localize26.0ms

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)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 120
Calls
4 calls:
42.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
115.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
132 → 132
Iterations
IterNodes
done2003
32003
2878
1287
0112

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.6b

regimes299.0ms

Accuracy

84.5% (4.3b remaining)

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

bsearch147.0ms

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

simplify4.0ms

Iterations
IterNodes
done26
126
023

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.1s917×body1280valid
902.0ms5834×body80valid
874.0ms1125×body2560valid
379.0ms2970×body80nan
214.0ms416×body640valid
129.0ms119×body5120valid
109.0ms237×body320valid
24.0ms115×body160valid