Details

Time bar (total: 10.3s)

sample34.0ms

Algorithm
intervals
Results
15.0ms282×body80valid
4.0ms86×body80nan

simplify82.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
02038
13538
26537
311437
413637
514837
614937
done14937

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize114.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-log-exp
8×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
75 → 75
Iterations

Useful iterations: 3 (486.0ms)

IterNodesCost
01061330
12411181
27831110
329571090
done50001090

prune264.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.1b

localize117.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.3b
(/ (/ (- (- (* 2.0 (/ (* a c) b)) b) b) 2.0) a)
4.5b
(/ (* a c) b)
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
92×add-sqr-sqrt
91×*-un-lft-identity
63×add-cube-cbrt
20×associate-/l*
14×add-exp-log add-cbrt-cube distribute-lft-out-- difference-of-squares
8×add-log-exp
6×associate-/r* div-inv
5×pow1 cbrt-undiv div-exp
4×sqrt-prod
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log prod-exp cbrt-unprod associate-/l/
Counts
4 → 149
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms
(/ (/ (- (- (* 2.0 (/ (* a c) b)) b) b) 2.0) a)
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(/ (/ (- (- (* 2.0 (/ (* a c) b)) b) b) 2.0) a)
19.0ms
(/ (* a c) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify730.0ms

Counts
161 → 161
Iterations

Useful iterations: 2 (313.0ms)

IterNodesCost
03093560
17333400
223813238
done50013238

prune598.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.3b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.8b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log associate-*r* pow-prod-down prod-exp 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 sqrt-pow1 pow1/2 associate-*l* neg-log *-commutative
Counts
4 → 63
Calls
4 calls:
7.0ms
(* (* 4.0 a) c)
3.0ms
(- (* 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)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 4.0 a) c)
49.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
75 → 75
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01261083
1298989
21071899
34573889
done5000889

prune247.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
27.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* 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))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify679.0ms

Counts
88 → 88
Iterations

Useful iterations: done (676.0ms)

IterNodesCost
01471693
13611585
212151413
done50001395

prune278.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes185.0ms

Accuracy

89.2% (1.6b remaining)

Error of 7.7b against oracle of 6.1b and baseline of 21.2b

bsearch272.0ms

Steps
ItersRangePoint
9
1.790439840991813e+53
4.6520850645607246e+61
2.8436139815832302e+57
10
-4.825160222524179e-304
4.983370065797432e-302
-1.2159818839962e-310
7
-3.550313394724354e+57
-2.3888623512096697e+55
-3.124283374205192e+57

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
050132
16498
done6498

end0.0ms

sample891.0ms

Algorithm
intervals
Results
482.0ms8732×body80valid
145.0ms2890×body80nan