Details

Time bar (total: 17.3s)

sample74.0ms

Algorithm
intervals
Results
31.0ms287×body80valid
10.0ms108×body80nan

simplify175.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize136.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-log-exp
8×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
40.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
75 → 75
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01061330
12411181
27481110
326611090
done50001085

prune519.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize153.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.6b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.8b
(/ (* a c) b)
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
9×add-cube-cbrt times-frac
7×associate-/l*
6×add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv div-exp associate-/r* sqrt-prod difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 81
Calls
4 calls:
59.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
438.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
10.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
88.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
22.0ms
(/ (* a c) b)
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
93 → 93
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01831536
14621432
216911274
done50001243

prune528.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize131.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac associate-/r* sqrt-prod difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
66.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
18.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
90.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
83 → 83
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01451551
13461445
211411291
344741287
done50001287

prune459.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize146.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.6b
(/ (- (- b) (- b (* 2.0 (/ a (/ b c))))) (* 2.0 a))
5.7b
(/ a (/ b c))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
81×times-frac
59×*-un-lft-identity
58×add-sqr-sqrt
49×add-cube-cbrt
14×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
6×div-inv add-log-exp
5×pow1 cbrt-undiv div-exp distribute-lft-out--
4×sqrt-prod difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div clear-num associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub prod-exp associate-/r/ cbrt-unprod
Counts
4 → 130
Calls
4 calls:
50.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms
(/ (- (- b) (- b (* 2.0 (/ a (/ b c))))) (* 2.0 a))
18.0ms
(/ a (/ b c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
95.0ms
(/ (- (- b) (- b (* 2.0 (/ a (/ b c))))) (* 2.0 a))
40.0ms
(/ a (/ b c))
133.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
142 → 142
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02892230
16692068
222381898
done50011865

prune844.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

regimes370.0ms

Accuracy

91% (1.4b remaining)

Error of 7.3b against oracle of 5.8b and baseline of 21.5b

bsearch534.0ms

Steps
ItersRangePoint
9
1.7084993271036838e+35
8.915315724770326e+40
8.75372275402518e+40
10
-9.54870507633444e-304
1.3079717882256375e-300
-3.20057348973956e-310
5
-2.3823986784004295e+101
-6.644598008915225e+100
-2.1851923969506957e+101

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
053182
161182
done61182

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s8706×body80valid
621.0ms2996×body80nan