Details

Time bar (total: 21.0s)

sample68.0ms

Algorithm
intervals
Results
34.0ms266×body80valid
9.0ms94×body80nan

simplify152.0ms

Counts
1 → 1
Iterations
IterNodes
done176
6176
5174
4161
3122
266
136
020

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize150.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 151
Calls
4 calls:
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series440.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
163 → 163
Iterations
IterNodes
done5001
21833
1440
0179

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize171.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.9b
(/ (fma 2.0 (/ c (/ b a)) (* b -2)) (* 2.0 a))
3.8b
(/ c (/ b a))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
94×*-un-lft-identity
90×add-cube-cbrt
78×times-frac
60×prod-diff
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×associate-/r* add-cbrt-cube add-exp-log
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×div-inv associate-/l*
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u
2×clear-num frac-2neg flip3-- sqrt-div diff-log flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log prod-exp associate-/r/ cbrt-unprod
Counts
4 → 202
Calls
4 calls:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(/ (fma 2.0 (/ c (/ b a)) (* b -2)) (* 2.0 a))
14.0ms
(/ c (/ b a))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
109.0ms
(/ (fma 2.0 (/ c (/ b a)) (* b -2)) (* 2.0 a))
28.0ms
(/ c (/ b a))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
214 → 214
Iterations
IterNodes
done5000
23861
1877
0355

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize158.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×associate-/r* neg-mul-1 times-frac
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 156
Calls
4 calls:
66.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms
(- (* b b) (* (* 4.0 a) c))
53.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series584.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(- (* b b) (* (* 4.0 a) c))
139.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
168 → 168
Iterations
IterNodes
done5002
22850
1581
0235

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize159.0ms

Local error

Found 4 expressions with local error:

11.7b
(cbrt (/ b a))
11.7b
(cbrt (/ b a))
11.7b
(cbrt (/ b a))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 89
Calls
4 calls:
2.0ms
(cbrt (/ b a))
2.0ms
(cbrt (/ b a))
2.0ms
(cbrt (/ b a))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(cbrt (/ b a))
86.0ms
(cbrt (/ b a))
92.0ms
(cbrt (/ b a))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
101 → 101
Iterations
IterNodes
done5000
34588
2793
1256
0129

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

regimes533.0ms

Accuracy

86.1% (2.2b remaining)

Error of 7.7b against oracle of 5.5b and baseline of 21.2b

bsearch215.0ms

Steps
ItersRangePoint
3
5.437233749566996e+22
6.419404774371196e+22
6.358019085320933e+22
8
-6.412561728939963e+28
-6.810701174428621e+25
-6.336287344206649e+28

simplify13.0ms

Iterations
IterNodes
done60
160
050

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8708×body80valid
331.0ms2942×body80nan