Details

Time bar (total: 15.9s)

sample86.0ms

Algorithm
intervals
Results
50.0ms273×body80valid
9.0ms69×body80nan

simplify178.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize119.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
12.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b b) (* (* 4.0 a) c))
62.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
66 → 66
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune439.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize148.0ms

Local error

Found 4 expressions with local error:

7.4b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log difference-of-squares
Counts
4 → 58
Calls
4 calls:
84.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
70 → 70
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune497.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize142.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.2b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
8.3b
(/ (* a c) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 71
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
29.0ms
(/ (* a c) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
38.0ms
(/ (* a c) b)
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
83 → 83
Iterations

Useful iterations: 2 (322.0ms)

IterNodesCost
01551221
13931165
21501997
done5000997

prune485.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize143.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.2b
(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
5.2b
(* a (/ c b))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
14×add-exp-log add-cbrt-cube
13×times-frac associate-*r*
7×pow1
6×add-log-exp
3×cbrt-undiv flip3-- div-exp associate-*l* prod-exp associate-/r* sqrt-prod flip-- cbrt-unprod
2×sqrt-div associate-/r/ div-inv unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 82
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
21.0ms
(* a (/ c b))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
29.0ms
(* a (/ c b))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
94 → 94
Iterations

Useful iterations: 2 (352.0ms)

IterNodesCost
01771312
14521246
216011078
done50001078

prune519.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

regimes366.0ms

Accuracy

92.3% (1.1b remaining)

Error of 7.8b against oracle of 6.7b and baseline of 21.3b

bsearch420.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
11
-2.859335985249397e-307
9.448397398655464e-278
-5.0660426096144e-310
9
-1.4642911230069481e+159
-8.435593739772907e+149
-1.4341281730542053e+153

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
058174
172139
done72139

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.8s8737×body80valid
339.0ms2941×body80nan