Details

Time bar (total: 17.9s)

sample145.0ms

Algorithm
intervals
Results
13.0ms35×body2560valid
12.0ms179×body80valid
9.0ms30×body1280valid
7.0ms76×body80nan
3.0ms8×body5120valid
3.0ms10×body640valid
2.0ms9×body320valid
0.0ms2×body160valid

simplify109.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
138.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
56.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b_2 b_2) (* a c))
145.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
111.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
118.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
92 → 92
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01511534
13551440
210061266
327891252
done50001249

prune340.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.5b
(/ (/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.9b
(/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
58×add-sqr-sqrt
57×*-un-lft-identity
29×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×associate-/l* distribute-lft-out-- difference-of-squares
10×associate-/r* sqrt-prod associate-/r/
8×add-log-exp
7×cbrt-undiv flip3-- distribute-rgt-neg-in div-exp flip--
6×div-inv
5×pow1
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 136
Calls
4 calls:
43.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
106.0ms
(/ (/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
69.0ms
(/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series707.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
251.0ms
(/ (/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
253.0ms
(/ (* c a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
148 → 148
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02423445
16073206
220392840
done50012802

prune501.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.3b
(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
62×*-un-lft-identity
44×times-frac
29×add-cube-cbrt
27×associate-*r*
17×add-exp-log
16×distribute-lft-out-- difference-of-squares
11×sqrt-prod add-cbrt-cube
8×pow1 distribute-rgt-neg-in add-log-exp
7×associate-/r*
4×flip3-- div-exp prod-exp associate-/r/ flip--
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div diff-log 1-exp cbrt-unprod div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log clear-num un-div-inv *-commutative inv-pow
Counts
4 → 132
Calls
4 calls:
118.0ms
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
59.0ms
(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
48.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series583.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
125.0ms
(/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
122.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
144 → 144
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01912567
14452238
210482054
324862028
done50012019

prune418.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(* c (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.5b
(/ (* c (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
25.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×*-un-lft-identity
27×associate-*r*
25×times-frac
19×add-cube-cbrt
18×add-exp-log add-cbrt-cube
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 sqrt-prod
5×cbrt-undiv div-exp
4×distribute-rgt-neg-in prod-exp cbrt-unprod
3×flip3-- associate-*l* associate-/r* flip--
2×sqrt-div diff-log associate-*r/ associate-/r/ div-inv unswap-sqr
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log clear-num *-commutative associate-/l/ associate-/l*
Counts
4 → 103
Calls
4 calls:
29.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
135.0ms
(* c (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
38.0ms
(/ (* c (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
244.0ms
(* c (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
232.0ms
(/ (* c (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts
115 → 115
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02062076
15211953
216611623
done50001601

prune331.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes255.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.9b

bsearch226.0ms

Steps
ItersRangePoint
8
1.538525478595148e+72
6.402915924844171e+74
6.326287366549383e+74
9
-7.006116511457938e-281
-2.476656944921405e-289
-3.3203606567416007e-289
6
-3.779251410483496e+105
-5.080294099506613e+104
-1.361733299857302e+105

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03556
14256
done4256

end0.0ms

sample3.2s

Algorithm
intervals
Results
723.0ms2910×body80nan
626.0ms5865×body80valid
604.0ms1026×body2560valid
359.0ms907×body1280valid
123.0ms439×body640valid
108.0ms127×body5120valid
48.0ms245×body320valid
15.0ms110×body160valid