Details

Time bar (total: 18.4s)

sample137.0ms

Algorithm
intervals
Results
16.0ms45×body1280valid
16.0ms184×body80valid
11.0ms25×body2560valid
5.0ms69×body80nan
4.0ms17×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify95.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite196.0ms

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:
98.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
56.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
114.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms
(- (* b_2 b_2) (* a c))
104.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts
92 → 92
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01511534
13551440
210011266
327841252
done50011249

prune397.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.5b
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.2b
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
54×add-sqr-sqrt
53×*-un-lft-identity
29×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×associate-/l*
12×distribute-lft-out-- difference-of-squares
10×associate-/r* associate-/r/
9×sqrt-prod
7×cbrt-undiv flip3-- div-exp flip--
6×distribute-rgt-neg-in div-inv add-log-exp
5×pow1
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 130
Calls
4 calls:
15.0ms
(- (* b_2 b_2) (* a c))
121.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
79.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series649.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* b_2 b_2) (* a c))
232.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
270.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
142 → 142
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02333254
15803035
220072773
done50002709

prune516.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/r*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/l*
2×sub-neg sqrt-div associate-/r/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp neg-log clear-num div-inv
Counts
4 → 90
Calls
4 calls:
69.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
119.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms
(- (* b_2 b_2) (* a c))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
102 → 102
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01511775
13251672
28711558
322581540
done50001534

prune407.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
128×add-sqr-sqrt
127×*-un-lft-identity
75×add-cube-cbrt
26×distribute-lft-out-- difference-of-squares
25×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×add-cbrt-cube
7×div-exp
6×pow1
5×div-inv
3×cbrt-undiv flip3-- diff-log flip-- associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ inv-pow
Counts
4 → 169
Calls
4 calls:
92.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
46.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
74.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
181 → 181
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02614167
16043699
213873372
335063316
done50013314

prune402.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

regimes246.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.6b

bsearch180.0ms

Steps
ItersRangePoint
2
5.341589198600723e+134
5.967668210703041e+134
5.732888581164671e+134
10
-1.2529167750641135e-296
-2.859335985249397e-307
-3.5177987696791986e-300
9
-5.2045971803048284e+128
-5.738453298103652e+119
-1.406599291770867e+122

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03459
14055
done4055

end0.0ms

sample2.9s

Algorithm
intervals
Results
907.0ms5847×body80valid
506.0ms1056×body2560valid
335.0ms926×body1280valid
235.0ms477×body640valid
221.0ms2938×body80nan
112.0ms113×body5120valid
36.0ms209×body320valid
13.0ms108×body160valid