Details

Time bar (total: 13.9s)

sample79.0ms

Algorithm
intervals
Results
13.0ms44×body2560valid
9.0ms167×body80valid
7.0ms32×body1280valid
5.0ms100×body80nan
3.0ms14×body640valid
1.0ms7×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
32.0ms
(* (* 4.0 a) c)
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (* 4.0 a) c)
151.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(- (* b b) (* (* 4.0 a) c))
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
72 → 72
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01221001
1328907
21722805
done5000799

prune372.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
3.3b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.3b
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
10.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
111.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series628.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* b b) (* (* 4.0 a) c))
221.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
245.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
160 → 160
Iterations

Useful iterations: 2 (632.0ms)

IterNodesCost
02514912
16674366
241904044
done50024044

prune604.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.4b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
3.3b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
11.6b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
122×add-exp-log
76×add-sqr-sqrt
75×*-un-lft-identity
63×div-exp
58×add-cbrt-cube
45×associate-/l*
43×add-cube-cbrt
34×prod-exp
27×cbrt-undiv
16×distribute-lft-out-- difference-of-squares
14×cbrt-unprod
11×sqrt-prod
10×div-inv
8×rec-exp distribute-rgt-neg-in 1-exp
6×add-log-exp
5×pow1
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div clear-num associate-/r* associate-/r/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 185
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
81.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
150.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
163.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify554.0ms

Counts
197 → 197
Iterations

Useful iterations: done (541.0ms)

IterNodesCost
03845941
111385598
done50014835

prune562.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
16.2b
(/ (* 4.0 (* a c)) a)
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
7×add-cube-cbrt
5×pow1
4×sqrt-prod
3×cbrt-undiv flip3-- times-frac diff-log div-exp prod-exp associate-/r* flip-- cbrt-unprod
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num div-inv associate-/l*
Counts
4 → 68
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(/ (* 4.0 (* a c)) a)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (* 4.0 (* a c)) a)
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
80 → 80
Iterations

Useful iterations: 2 (249.0ms)

IterNodesCost
01501194
14011105
22048945
done5001945

prune272.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

regimes318.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 30.1b

bsearch270.0ms

Steps
ItersRangePoint
8
1.051086597250448e+104
4.713735678910177e+106
3.7657312149088605e+106
10
-2.4810350231976038e-293
2.102313690554005e-306
-6.206784543730362e-301
10
-8.097032161796104e+150
-8.691973301260876e+137
-2.322469259707236e+143

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04168
14868
25068
35268
done5268

end0.0ms

sample3.0s

Algorithm
intervals
Results
720.0ms2905×body80nan
708.0ms1127×body2560valid
469.0ms5717×body80valid
353.0ms936×body1280valid
107.0ms448×body640valid
48.0ms111×body5120valid
42.0ms223×body320valid
14.0ms112×body160valid