Details

Time bar (total: 9.3s)

sample64.0ms

Algorithm
intervals
Results
26.0ms268×body80valid
7.0ms85×body80nan

simplify121.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize85.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
75 → 75
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01001330
12461186
27801089
327401070
done50011066

prune274.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.0b

localize90.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.3b
(/ (* a c) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×times-frac
5×pow1
4×cbrt-undiv div-exp associate-/r* sqrt-prod associate-/l*
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 78
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
190.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
9.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
20.0ms
(/ (* a c) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify830.0ms

Counts
90 → 90
Iterations

Useful iterations: done (827.0ms)

IterNodesCost
01821467
14761375
217521211
done50001165

prune346.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize87.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite86.0ms

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:
42.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify780.0ms

Counts
88 → 88
Iterations

Useful iterations: done (778.0ms)

IterNodesCost
01491693
13601585
212461413
done50001395

prune302.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize87.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
32×*-un-lft-identity
27×associate-*r*
26×add-exp-log
21×times-frac
16×add-cube-cbrt add-cbrt-cube
12×prod-exp
10×pow1 add-log-exp
8×distribute-lft-out-- difference-of-squares
7×sqrt-prod
6×cbrt-unprod
4×flip3-- distribute-rgt-neg-in div-exp flip--
3×diff-log pow-prod-down
2×cbrt-undiv sub-neg rec-exp sqrt-div 1-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l* neg-log un-div-inv *-commutative div-inv
Counts
4 → 97
Calls
4 calls:
76.0ms
(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
109 → 109
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01862126
14811868
215991610
done50001596

prune299.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.7b

regimes261.0ms

Accuracy

93.4% (1.0b remaining)

Error of 7.7b against oracle of 6.8b and baseline of 21.4b

bsearch290.0ms

Steps
ItersRangePoint
9
8.777746745010686e+110
1.2290467223415774e+117
2.9765366996267504e+116
11
-1.5896185090842948e-298
2.4041921185404804e-297
-2.3942156153022e-310
7
-1.6239005782062206e+154
-7.680972122048022e+152
-2.6152573735422387e+153

simplify15.0ms

Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
051159
167124
done67124

end0.0ms

sample891.0ms

Algorithm
intervals
Results
432.0ms8763×body80valid
131.0ms2944×body80nan