Details

Time bar (total: 8.6s)

sample65.0ms

Algorithm
intervals
Results
14.0ms533×pre80true
12.0ms112×body320valid
9.0ms277×body80nan
7.0ms98×body160valid
3.0ms19×body640valid
1.0ms27×body80valid

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify521.0ms

Counts
102 → 102
Iterations

Useful iterations: done (519.0ms)

IterNodesCost
01671697
14361584
215011361
done50001351

prune228.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
19.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
53.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series422.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
169.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
128.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify998.0ms

Counts
243 → 243
Iterations

Useful iterations: done (989.0ms)

IterNodesCost
034510784
18528200
229736673
done50016650

prune575.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×cbrt-undiv times-frac diff-log div-exp prod-exp cbrt-unprod associate-/l*
2×sub-neg sqrt-div associate-*r/ associate-/r/ associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 neg-log clear-num associate-/r* flip-+ div-inv
Counts
4 → 152
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
32.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
122.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify847.0ms

Counts
164 → 164
Iterations

Useful iterations: done (841.0ms)

IterNodesCost
02697056
16864938
225073819
done50003804

prune530.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma (* c 4.0) a 0) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (fma (* c 4.0) a 0) (* 2.0 a))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt *-un-lft-identity
76×times-frac
71×add-cube-cbrt
61×prod-diff
39×sqrt-prod
30×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube distribute-lft-out-- difference-of-squares
11×fma-neg
10×div-inv associate-/l* add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg frac-2neg prod-exp clear-num associate-/r/ cbrt-unprod
1×associate--l- neg-sub0 neg-log associate-/l/
Counts
4 → 213
Calls
4 calls:
28.0ms
(/ (/ (fma (* c 4.0) a 0) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(/ (fma (* c 4.0) a 0) (* 2.0 a))

series346.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (/ (fma (* c 4.0) a 0) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(/ (fma (* c 4.0) a 0) (* 2.0 a))

simplify829.0ms

Counts
225 → 225
Iterations

Useful iterations: done (821.0ms)

IterNodesCost
03159204
17397212
225535980
done50015979

prune481.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
11717
done1717

end0.0ms

sample1.6s

Algorithm
intervals
Results
385.0ms3624×body320valid
302.0ms16210×pre80true
278.0ms8210×body80nan
210.0ms2991×body160valid
67.0ms472×body640valid
36.0ms913×body80valid