Details

Time bar (total: 24.8s)

sample101.0ms

Algorithm
intervals
Results
33.0ms176×body80valid
18.0ms43×body2560valid
10.0ms31×body1280valid
7.0ms106×body80nan
4.0ms18×body640valid
2.0ms4×body5120valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify97.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01417
12817
27016
312716
414016
done14016

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize24.0ms

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)))

rewrite181.0ms

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:
100.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms
(- (* b b) (* (* 4.0 a) c))
49.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms
(- (* b b) (* (* 4.0 a) c))
130.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01671697
110781560
done50011407

prune479.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite283.0ms

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
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 pow1/2 neg-log associate-/l/
Counts
4 → 230
Calls
4 calls:
57.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
134.0ms
(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
54.0ms
(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series1.4s

Counts
4 → 12
Calls
4 calls:
561.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
367.0ms
(/ (/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
346.0ms
(/ (fma (* 4.0 a) c 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify6.5s

Counts
242 → 242
Iterations

Useful iterations: 1 (1.9s)

IterNodesCost
03289831
149536957
done50006957

prune996.0ms

Pruning

7 alts after pruning (7 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))))
15.0b
(/ (* 2.0 a) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite136.0ms

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 log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div 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 → 150
Calls
4 calls:
18.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(/ (* 2.0 a) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (* b b) (* (* 4.0 a) c))
102.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(/ (* 2.0 a) (* (* 4.0 a) c))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts
162 → 162
Iterations

Useful iterations: done (3.8s)

IterNodesCost
02416256
124713633
done50013450

prune586.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ 1 1) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ (/ (* 2.0 a) (* 4.0 a)) c)))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
228×add-exp-log
140×div-exp
77×add-cbrt-cube
70×prod-exp
65×add-sqr-sqrt
64×*-un-lft-identity
61×prod-diff
60×add-cube-cbrt
39×cbrt-undiv
35×1-exp
34×sqrt-prod
31×times-frac
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
20×cbrt-unprod
14×rec-exp
13×associate-/l*
11×fma-neg
10×add-log-exp
7×neg-mul-1
5×pow1 flip3-- associate-/r/ flip--
4×expm1-log1p-u log1p-expm1-u
3×diff-log div-inv
2×frac-times sub-neg sqrt-div associate-*l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ neg-log clear-num associate-/r* associate-/l/
Counts
4 → 231
Calls
4 calls:
81.0ms
(/ (/ 1 1) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ (/ (* 2.0 a) (* 4.0 a)) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (/ 1 1) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ (/ (* 2.0 a) (* 4.0 a)) c)))
80.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
243 → 243
Iterations

Useful iterations: done (2.7s)

IterNodesCost
04189986
done50016996

prune747.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

regimes191.0ms

Accuracy

93.3% (1.6b remaining)

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

bsearch213.0ms

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04268
15368
done5368

end0.0ms

sample3.4s

Algorithm
intervals
Results
868.0ms1074×body2560valid
726.0ms885×body1280valid
576.0ms5876×body80valid
321.0ms3010×body80nan
161.0ms492×body640valid
81.0ms218×body320valid
54.0ms107×body5120valid
12.0ms92×body160valid