Details

Time bar (total: 11.0s)

sample35.0ms

Algorithm
intervals
Results
13.0ms269×body80valid
4.0ms85×body80nan

simplify123.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

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:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
75 → 75
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01061330
12411181
27481110
326611090
done50001085

prune275.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.1b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.3b
(/ (* a c) b)
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
11×*-un-lft-identity
9×add-cube-cbrt
6×times-frac add-log-exp
5×pow1
4×cbrt-undiv div-exp associate-/r* sqrt-prod associate-/l*
3×flip3-- flip--
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/ difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub distribute-lft-out--
Counts
4 → 75
Calls
4 calls:
42.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
49.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
9.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
78.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
24.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify846.0ms

Counts
87 → 87
Iterations

Useful iterations: done (844.0ms)

IterNodesCost
01751385
14561289
216501137
done50001097

prune315.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac associate-/r* sqrt-prod difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
46.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
10.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
46.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
83 → 83
Iterations

Useful iterations: 3 (866.0ms)

IterNodesCost
01451551
13461445
211411291
344741287
done50001287

prune282.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize94.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.9b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.1b
(/ (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)) (* 2.0 a))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
31×times-frac
30×add-exp-log
24×*-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×add-log-exp unswap-sqr
4×sqrt-prod
3×flip3-- flip-- div-inv associate-/l*
2×sqrt-div associate-/l/ difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative distribute-lft-out--
Counts
4 → 113
Calls
4 calls:
42.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
43.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
236.0ms
(/ (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)) (* 2.0 a))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
55.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
105.0ms
(/ (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)) (* 2.0 a))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
125 → 125
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02602462
17332333
228541821
done50001640

prune686.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

regimes191.0ms

Accuracy

93.2% (1.0b remaining)

Error of 7.8b against oracle of 6.8b and baseline of 21.3b

bsearch270.0ms

Steps
ItersRangePoint
9
8.777746745010686e+110
1.2290467223415774e+117
1.1912031425131646e+117
9
1.1467953016179043e-293
9.802722462678435e-287
1.160883915256953e-293
7
-1.6239005782062206e+154
-7.680972122048022e+152
-1.3333004218627638e+154

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
050169
160169
done60169

end0.0ms

sample934.0ms

Algorithm
intervals
Results
442.0ms8781×body80valid
137.0ms2958×body80nan