Details

Time bar (total: 15.7s)

sample99.0ms

Algorithm
intervals
Results
17.0ms186×body80valid
16.0ms29×body2560valid
11.0ms24×body1280valid
9.0ms102×body80nan
5.0ms14×body640valid
4.0ms5×body5120valid
2.0ms9×body320valid
1.0ms4×body160valid

simplify93.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize43.0ms

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)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
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×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* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
71.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms
(- (* b b) (* (* 3.0 a) c))
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
50.0ms
(- (* b b) (* (* 3.0 a) c))
93.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
107.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify899.0ms

Counts
82 → 82
Iterations

Useful iterations: done (895.0ms)

IterNodesCost
01541565
14141463
218811247
done50001241

prune462.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize31.0ms

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)))

rewrite216.0ms

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-cbrt-cube add-exp-log
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×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 → 154
Calls
4 calls:
20.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
110.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
68.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series665.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
206.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
247.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
102.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts
166 → 166
Iterations

Useful iterations: 2 (721.0ms)

IterNodesCost
02535113
16564543
237044211
done50004211

prune824.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize46.0ms

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)))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
376×times-frac
192×add-sqr-sqrt
191×*-un-lft-identity
131×add-cube-cbrt
44×associate-/l*
33×add-cbrt-cube add-exp-log
30×distribute-lft-out-- difference-of-squares
26×associate-/r/
18×sqrt-prod div-inv
15×cbrt-undiv distribute-rgt-neg-in flip3-- div-exp flip--
10×associate-/r*
8×add-log-exp
6×prod-exp cbrt-unprod
5×pow1
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 → 262
Calls
4 calls:
20.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
135.0ms
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
86.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series768.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
224.0ms
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
318.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
108.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify662.0ms

Counts
274 → 274
Iterations

Useful iterations: done (639.0ms)

IterNodesCost
04989706
112829049
done50008631

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
49×add-sqr-sqrt
48×*-un-lft-identity
41×add-cbrt-cube add-exp-log
32×add-cube-cbrt
27×associate-*r*
15×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
10×pow1
8×distribute-lft-out-- add-log-exp difference-of-squares
7×sqrt-prod associate-/l*
6×div-inv
4×distribute-rgt-neg-in
3×associate-/r* flip3-- pow-prod-down flip--
2×sqrt-div diff-log associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 associate-*l* neg-log associate-*r/ *-commutative associate-/l/
Counts
4 → 134
Calls
4 calls:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
79.0ms
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
55.0ms
(/ (/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) 3.0) a)
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series740.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
287.0ms
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
212.0ms
(/ (/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) 3.0) a)
118.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify513.0ms

Counts
146 → 146
Iterations

Useful iterations: done (506.0ms)

IterNodesCost
02883760
18313595
done50003079

prune853.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

regimes740.0ms

Accuracy

87.7% (3.3b remaining)

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

bsearch322.0ms

Steps
ItersRangePoint
7
1.9371672431899034e+133
5.16149553175908e+134
1.958082194924451e+133
8
-3.651460945740179e-298
-7.119429034068498e-301
-7.691767660118564e-301
9
-3.792961868720521e+75
-7.261872368850313e+67
-3.5695008721667037e+75

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03667
14267
done4267

end0.0ms

sample3.2s

Algorithm
intervals
Results
647.0ms5958×body80valid
643.0ms451×body640valid
558.0ms1053×body2560valid
404.0ms880×body1280valid
201.0ms2946×body80nan
109.0ms216×body320valid
54.0ms97×body5120valid
18.0ms113×body160valid