Details

Time bar (total: 20.8s)

sample115.0ms

Algorithm
intervals
Results
27.0ms102×body80nan
17.0ms186×body80valid
16.0ms29×body2560valid
11.0ms24×body1280valid
5.0ms14×body640valid
3.0ms5×body5120valid
2.0ms9×body320valid
1.0ms4×body160valid

simplify71.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01217
12217
24216
38316
411216
512016
done12016

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
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×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
80.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
13.0ms
(- (* b b) (* (* 3.0 a) c))
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
61.0ms
(- (* b b) (* (* 3.0 a) c))
130.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
93.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01671697
14451590
220991363
done50001354

prune694.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.5b
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.9b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite241.0ms

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-cbrt-cube add-exp-log
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×clear-num frac-2neg sqrt-div diff-log prod-exp cbrt-unprod
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
125.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
72.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series822.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
248.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
339.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
107.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts
244 → 244
Iterations

Useful iterations: 2 (852.0ms)

IterNodesCost
033410067
18477629
247256518
done50006518

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.5b
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
10.9b
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
376×times-frac
233×add-sqr-sqrt
232×*-un-lft-identity
172×add-cube-cbrt
60×prod-diff
48×sqrt-prod
44×associate-/l*
36×distribute-rgt-neg-in
33×add-cbrt-cube add-exp-log
30×distribute-lft-out-- difference-of-squares
26×associate-/r/
21×distribute-lft-neg-in
18×div-inv
15×cbrt-undiv flip3-- div-exp flip--
10×associate-/r* fma-neg
8×add-log-exp
7×neg-mul-1
6×prod-exp cbrt-unprod
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×clear-num frac-2neg sqrt-div diff-log
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 340
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
119.0ms
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
67.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series691.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
219.0ms
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
264.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
106.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify785.0ms

Counts
352 → 352
Iterations

Useful iterations: done (753.0ms)

IterNodesCost
057914652
1147112136
done500111029

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize47.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.6b
(/ (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
3.5b
(/ (/ (/ (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)) 3.0) a)
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
1261×times-frac
604×add-sqr-sqrt
603×*-un-lft-identity
431×add-cube-cbrt
95×associate-/l*
86×distribute-lft-out-- difference-of-squares
76×sqrt-prod
64×distribute-rgt-neg-in
60×prod-diff
41×add-cbrt-cube add-exp-log
32×div-inv
28×associate-/r*
23×cbrt-undiv div-exp
21×distribute-lft-neg-in
13×associate-/r/
10×fma-neg
8×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
2×clear-num frac-2neg flip3-- sqrt-div diff-log flip--
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 583
Calls
4 calls:
34.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
52.0ms
(/ (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
111.0ms
(/ (/ (/ (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)) 3.0) a)
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
271.0ms
(/ (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
303.0ms
(/ (/ (/ (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)) 3.0) a)
122.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts
595 → 595
Iterations

Useful iterations: done (1.4s)

IterNodesCost
092723856
1245921278
done500019959

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

regimes501.0ms

Accuracy

87.5% (3.3b remaining)

Error of 8.8b against oracle of 5.5b and baseline of 32.0b

bsearch261.0ms

Steps
ItersRangePoint
7
1.9371672431899034e+133
5.16149553175908e+134
1.958082194924451e+133
10
-4.750525065312607e-249
-1.830196375340447e-262
-2.3007108173901322e-262
9
-3.792961868720521e+75
-7.261872368850313e+67
-3.5695008721667037e+75

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03667
14167
done4167

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s1053×body2560valid
551.0ms5958×body80valid
505.0ms97×body5120valid
433.0ms880×body1280valid
290.0ms2946×body80nan
120.0ms451×body640valid
47.0ms216×body320valid
15.0ms113×body160valid