Details

Time bar (total: 15.2s)

sample218.0ms

Algorithm
intervals
Results
67.0ms180×body80valid
22.0ms37×body1280valid
18.0ms24×body2560valid
10.0ms93×body80nan
9.0ms19×body640valid
4.0ms4×body5120valid
2.0ms5×body320valid
1.0ms4×body160valid

simplify48.0ms

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

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite228.0ms

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:
112.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms
(- (* b_2 b_2) (* a c))
78.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
59.0ms
(- (* b_2 b_2) (* a c))
132.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
117.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
134 → 134
Iterations
IterNodes
done2015
32015
21393
1494
0199

prune483.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.4b
(- (* b_2 b_2) (* a c))
1.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite266.0ms

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:
160.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
16.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
57.0ms
(- (* b_2 b_2) (* a c))
127.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
135 → 135
Iterations
IterNodes
done2001
32001
21630
1559
0219

prune587.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.7b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

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:
79.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
127.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms
(sqrt (- (* b_2 b_2) (* a c)))
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
132 → 132
Iterations
IterNodes
done2003
32003
2878
1287
0112

prune648.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize95.0ms

Local error

Found 4 expressions with local error:

22.1b
(cbrt (- (* b_2 b_2) (* a c)))
22.1b
(cbrt (- (* b_2 b_2) (* a c)))
22.1b
(cbrt (- (* b_2 b_2) (* a c)))
22.5b
(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 59
Calls
4 calls:
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))
9.0ms
(cbrt (- (* b_2 b_2) (* a c)))
11.0ms
(cbrt (- (* b_2 b_2) (* a c)))
0.0ms
(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))

series495.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(cbrt (- (* b_2 b_2) (* a c)))
127.0ms
(cbrt (- (* b_2 b_2) (* a c)))
112.0ms
(cbrt (- (* b_2 b_2) (* a c)))
121.0ms
(fma (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (- b_2))

simplify1.3s

Counts
71 → 71
Iterations
IterNodes
done2005
42005
31456
2502
1194
084

prune813.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.5b

regimes417.0ms

Accuracy

84.6% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.3b

bsearch224.0ms

Steps
ItersRangePoint
9
1.9857735944483347e-57
1.377205241174095e-49
2.1478963185043958e-57
9
-6.068663549431906e+113
-2.857502301579116e+107
-6.778998599359054e+108

simplify8.0ms

Iterations
IterNodes
done31
131
025

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.5s1062×body2560valid
770.0ms5860×body80valid
554.0ms914×body1280valid
380.0ms3004×body80nan
283.0ms467×body640valid
92.0ms109×body5120valid
79.0ms225×body320valid
55.0ms102×body160valid