Details

Time bar (total: 8.5s)

sample35.0ms

Algorithm
intervals
Results
14.0ms275×body80valid
4.0ms92×body80nan

simplify91.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13538
26537
311437
413637
514837
614937
done14937

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize112.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
2.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
72 → 72
Iterations

Useful iterations: 3 (574.0ms)

IterNodesCost
0971211
12281091
27651009
33087998
done5000998

prune259.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize116.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.5b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.8b
(/ (* a c) b)
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
63.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
22.0ms
(/ (* a c) b)
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify756.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
01551221
13971165
21551997
done5000997

prune298.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize116.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.5b
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
7.4b
(/ a (/ b c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
50×add-sqr-sqrt
49×add-cube-cbrt *-un-lft-identity
16×associate-/r*
14×add-exp-log add-cbrt-cube
6×div-inv add-log-exp
5×pow1 cbrt-undiv div-exp
4×associate-/l*
3×flip3-- sqrt-prod associate-/r/ flip--
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod
Counts
4 → 120
Calls
4 calls:
2.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
8.0ms
(/ a (/ b c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
20.0ms
(/ a (/ b c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify759.0ms

Counts
132 → 132
Iterations

Useful iterations: 2 (238.0ms)

IterNodesCost
02581915
16171799
221431621
done50011621

prune527.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.6b

localize120.0ms

Local error

Found 4 expressions with local error:

7.4b
(/ a (/ b c))
12.6b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×add-cube-cbrt *-un-lft-identity
13×associate-/r*
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1 sqrt-prod
5×div-inv
4×sqrt-div
3×cbrt-undiv div-exp associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 sum-log flip--
1×+-commutative neg-sub0 associate-+l- frac-2neg flip3-+ neg-log clear-num associate-/r/ flip-+
Counts
4 → 113
Calls
4 calls:
5.0ms
(/ a (/ b c))
9.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ a (/ b c))
77.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify830.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (201.0ms)

IterNodesCost
02292023
15411583
217221479
done50011479

prune586.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.6b

regimes146.0ms

Accuracy

91.1% (1.3b remaining)

Error of 7.9b against oracle of 6.6b and baseline of 21.4b

bsearch181.0ms

Steps
ItersRangePoint
9
2.944023772201993e+37
9.447687191993962e+42
8.949232802794837e+42
8
-6.10058349091927e+155
-9.408528429616011e+151
-1.3696490745623736e+154

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
050157
162157
done62157

end0.0ms

sample832.0ms

Algorithm
intervals
Results
441.0ms8720×body80valid
138.0ms2864×body80nan