Details

Time bar (total: 19.2s)

sample74.0ms

Algorithm
intervals
Results
16.0ms43×body2560valid
12.0ms176×body80valid
10.0ms31×body1280valid
6.0ms106×body80nan
5.0ms18×body640valid
2.0ms4×body5120valid
1.0ms7×body320valid
0.0ms4×body160valid

simplify138.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite185.0ms

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:
127.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
58.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01671697
14331584
214881361
done50001347

prune497.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize41.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.1b
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.7b
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×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
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u 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 → 232
Calls
4 calls:
57.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
71.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
33.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series757.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
266.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
264.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
244 → 244
Iterations

Useful iterations: done (2.1s)

IterNodesCost
033810067
18117605
230636508
done50006422

prune896.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.7b
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
152×times-frac
150×*-un-lft-identity
109×add-cube-cbrt
94×add-exp-log
85×associate-*r*
61×prod-diff
58×add-cbrt-cube
43×sqrt-prod
39×div-exp
35×prod-exp
31×distribute-rgt-neg-in
21×cbrt-undiv distribute-lft-neg-in cbrt-unprod
20×distribute-lft-out-- difference-of-squares
11×fma-neg
10×add-log-exp
7×pow1 neg-mul-1 associate-*l*
6×flip3-- associate-/r/ flip--
5×div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u unswap-sqr
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 265
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
53.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
234.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
229.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
277 → 277
Iterations

Useful iterations: done (2.6s)

IterNodesCost
044210420
112257945
241806391
done50006342

prune997.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.8b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 152
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
54.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
230.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
164 → 164
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02566823
16484808
228753640
done50003555

prune459.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.2b

regimes262.0ms

Accuracy

93.4% (1.5b remaining)

Error of 7.4b against oracle of 5.8b and baseline of 29.1b

bsearch352.0ms

Steps
ItersRangePoint
9
1.7084993271036838e+35
8.915315724770326e+40
8.75372275402518e+40
9
-4.09118134758863e-163
-1.5699591568311042e-168
-1.5885810260222291e-168
6
-2.3823986784004295e+101
-2.936095699822542e+100
-1.555632367828989e+101

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04264
15264
done5264

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.3s1074×body2560valid
1.1s5876×body80valid
448.0ms885×body1280valid
250.0ms3010×body80nan
203.0ms492×body640valid
66.0ms107×body5120valid
56.0ms218×body320valid
52.0ms92×body160valid