Details

Time bar (total: 17.7s)

sample121.0ms

Algorithm
intervals
Results
34.0ms31×body2560valid
23.0ms172×body80valid
19.0ms35×body1280valid
11.0ms82×body80nan
10.0ms20×body640valid
6.0ms5×body5120valid
3.0ms7×body320valid
1.0ms3×body160valid

simplify122.0ms

Counts
1 → 1
Iterations
IterNodes
done134
5134
4125
390
247
125
014

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.4b
(- (* b b) (* (* 4 a) c))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
61.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
17.0ms
(- (* b b) (* (* 4 a) c))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
69.0ms
(- (* b b) (* (* 4 a) c))
144.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
103.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
106 → 106
Iterations
IterNodes
done5000
22176
1446
0166

prune566.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
2.3b
(/ (/ (+ 0 (* (* 4 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (* 2 a))
8.8b
(/ (+ 0 (* (* 4 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-cbrt-cube add-exp-log
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×associate-/l/
2×clear-num frac-2neg sqrt-div diff-log prod-exp cbrt-unprod
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 236
Calls
4 calls:
19.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
73.0ms
(/ (/ (+ 0 (* (* 4 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (* 2 a))
89.0ms
(/ (+ 0 (* (* 4 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
27.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
211.0ms
(/ (/ (+ 0 (* (* 4 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (* 2 a))
264.0ms
(/ (+ 0 (* (* 4 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
101.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.0s

Counts
248 → 248
Iterations
IterNodes
done5000
24650
1857
0337

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
0.4b
(- (* b b) (* (* 4 a) c))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
16×add-cube-cbrt
13×associate-*r*
10×fma-def times-frac add-log-exp
9×add-cbrt-cube add-exp-log
7×pow1
5×distribute-rgt-neg-in associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ sqrt-prod flip-+
2×frac-times sum-log flip3-- sqrt-div associate-*l/ prod-exp cbrt-unprod flip-- unswap-sqr
1×neg-sub0 cbrt-undiv +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 pow1/2 fma-neg diff-log div-exp prod-diff pow-prod-down neg-log associate-*r/ *-commutative associate-+l- div-inv
Counts
4 → 104
Calls
4 calls:
109.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
8.0ms
(- (* b b) (* (* 4 a) c))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
62.0ms
(- (* b b) (* (* 4 a) c))
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
98.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.7s

Counts
116 → 116
Iterations
IterNodes
done5000
22896
1510
0191

prune652.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune0.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

regimes369.0ms

Accuracy

84.3% (4.2b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 32.0b

bsearch165.0ms

Steps
ItersRangePoint
6
1.6664801848567985e-94
1.3864776888564433e-93
1.3635892865650846e-93
7
-8.18523145413159e+143
-2.8208844788355687e+142
-5.517926393801403e+142

simplify8.0ms

Iterations
IterNodes
done30
130
025

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.2s1056×body2560valid
936.0ms5744×body80valid
823.0ms2913×body80nan
818.0ms978×body1280valid
273.0ms454×body640valid
174.0ms138×body5120valid
101.0ms257×body320valid
32.0ms119×body160valid