Details

Time bar (total: 16.6s)

sample79.0ms

Algorithm
intervals
Results
34.0ms287×body80valid
11.0ms108×body80nan

simplify219.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize131.0ms

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)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
38.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
32.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series857.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
486.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
177 → 177
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02086992
14584570
212263570
done50002949

prune527.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize108.0ms

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)))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
32×add-sqr-sqrt
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log add-cbrt-cube
9×times-frac
7×associate-/l*
6×fma-neg add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u 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 → 113
Calls
4 calls:
105.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
91.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
20.0ms
(/ (* a c) b)
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
29.0ms
(/ (* a c) b)
133.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
125 → 125
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02172386
15442081
219591775
done50011679

prune627.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize120.0ms

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)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/r* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
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 → 105
Calls
4 calls:
80.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
9.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series530.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
62.0ms
(- (* b b) (* (* 4.0 a) c))
99.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
117 → 117
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01862435
14392125
213421819
done50001750

prune612.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize172.0ms

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)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
81×times-frac
73×*-un-lft-identity
72×add-sqr-sqrt
63×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
6×fma-neg div-inv add-log-exp
5×pow1 cbrt-undiv div-exp distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u 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 → 162
Calls
4 calls:
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms
(/ (- (- b) (- b (* 2.0 (/ a (/ b c))))) (* 2.0 a))
18.0ms
(/ a (/ b c))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
88.0ms
(/ (- (- b) (- b (* 2.0 (/ a (/ b c))))) (* 2.0 a))
28.0ms
(/ a (/ b c))
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
174 → 174
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03233080
17512717
225162399
done50002298

prune802.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

regimes321.0ms

Accuracy

91% (1.4b remaining)

Error of 7.3b against oracle of 5.9b and baseline of 21.5b

bsearch435.0ms

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

simplify15.0ms

Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
057175
168129
done68129

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.4s8706×body80valid
264.0ms2996×body80nan