Details

Time bar (total: 9.0s)

sample43.0ms

Algorithm
intervals
Results
10.0ms40×body2560valid
8.0ms187×body80valid
5.0ms23×body1280valid
3.0ms86×body80nan
2.0ms16×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms5×body160valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify695.0ms

Counts
82 → 82
Iterations

Useful iterations: done (688.0ms)

IterNodesCost
01541565
14061461
213591245
done50001235

prune216.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0b
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.8b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
36.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
159.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify765.0ms

Counts
166 → 166
Iterations

Useful iterations: done (759.0ms)

IterNodesCost
02615855
16775304
223634558
done50004556

prune454.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0b
(/ (+ (* 4.0 (* a c)) 0) a)
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×*-un-lft-identity
13×add-cube-cbrt
10×add-log-exp
9×times-frac
6×add-exp-log add-cbrt-cube
5×pow1
4×sqrt-prod
3×flip3-- diff-log associate-/r* flip-- associate-/l*
2×sub-neg sqrt-div associate-/l/ distribute-lft-out-- difference-of-squares
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 74
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (+ (* 4.0 (* a c)) 0) a)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(/ (+ (* 4.0 (* a c)) 0) a)
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify541.0ms

Counts
86 → 86
Iterations

Useful iterations: done (538.0ms)

IterNodesCost
01541396
13541204
213191116
done50001114

prune279.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.8b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 associate-*l* neg-log *-commutative
Counts
4 → 63
Calls
4 calls:
6.0ms
(* (* 4.0 a) c)
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (* 4.0 a) c)
45.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
75 → 75
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01261083
1298989
21071899
34573889
done5000889

prune183.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

regimes227.0ms

Accuracy

94% (1.4b remaining)

Error of 6.7b against oracle of 5.3b and baseline of 29.1b

bsearch191.0ms

Steps
ItersRangePoint
9
1.790439840991813e+53
4.6520850645607246e+61
4.144553567986907e+60
11
-2.5535425374078063e-212
-1.1714445965311569e-247
-1.273959369302109e-247
7
-3.550313394724354e+57
-2.3888623512096697e+55
-3.124283374205192e+57

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03664
14664
done4664

end0.0ms

sample1.2s

Algorithm
intervals
Results
264.0ms1074×body2560valid
250.0ms5844×body80valid
183.0ms907×body1280valid
117.0ms2890×body80nan
74.0ms452×body640valid
32.0ms102×body5120valid
28.0ms234×body320valid
9.0ms119×body160valid