Details

Time bar (total: 6.7s)

sample42.0ms

Algorithm
intervals
Results
9.0ms180×body80valid
7.0ms34×body2560valid
5.0ms30×body1280valid
3.0ms85×body80nan
2.0ms16×body640valid
0.0ms4×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify62.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

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:
66.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify830.0ms

Counts
82 → 82
Iterations

Useful iterations: done (827.0ms)

IterNodesCost
01541565
14011461
213531245
done50011233

prune223.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0b
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite183.0ms

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:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series512.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
178.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
166 → 166
Iterations

Useful iterations: 2 (479.0ms)

IterNodesCost
02575113
16344541
226394211
done50014211

prune388.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
47×add-sqr-sqrt
36×*-un-lft-identity
26×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×sqrt-prod add-log-exp
7×flip3-- flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 118
Calls
4 calls:
56.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify813.0ms

Counts
130 → 130
Iterations

Useful iterations: done (804.0ms)

IterNodesCost
02203137
14972801
214612561
done50002481

prune225.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.0b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 6.0b

regimes183.0ms

Accuracy

81.9% (4.9b remaining)

Error of 11.0b against oracle of 6.0b and baseline of 33.2b

bsearch89.0ms

Steps
ItersRangePoint
8
1.7227097696114035e-146
1.4073942755830443e-143
1.3880700472259379e-143
7
-1.6239005782062206e+154
-7.680972122048022e+152
-2.6152573735422387e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02739
13339
done3339

end0.0ms

sample1.2s

Algorithm
intervals
Results
232.0ms1092×body2560valid
219.0ms5865×body80valid
161.0ms916×body1280valid
103.0ms2944×body80nan
64.0ms460×body640valid
30.0ms116×body5120valid
21.0ms209×body320valid
7.0ms105×body160valid