Details

Time bar (total: 9.9s)

sample347.0ms

Algorithm
intervals
Results
7.0ms180×body80valid
6.0ms34×body2560valid
4.0ms30×body1280valid
2.0ms85×body80nan
2.0ms16×body640valid
0.0ms4×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

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:
60.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(- (* b_2 b_2) (* a c))
25.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
71.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
92 → 92
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01511534
13551440
210011266
327921252
done50001249

prune208.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.4b
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0b
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite141.0ms

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:
21.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
43.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
138.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
166.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
148 → 148
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02403445
15963204
220022940
done50012870

prune303.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.6b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

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:
36.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms
(- (* b_2 b_2) (* a c))
24.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
34.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01511775
13251672
28691558
322541540
done50011534

prune223.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
34×*-un-lft-identity
27×associate-*r*
23×times-frac
17×add-cube-cbrt
13×add-exp-log
10×add-log-exp
9×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
7×pow1 sqrt-prod
4×flip3-- distribute-rgt-neg-in prod-exp flip--
3×diff-log associate-*l* unswap-sqr
2×sub-neg sqrt-div div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 95
Calls
4 calls:
83.0ms
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
7.0ms
(- (* b_2 b_2) (* a c))
24.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
34.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
107 → 107
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01731703
14111478
210021318
324921302
done50001296

prune208.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.0b

regimes138.0ms

Accuracy

96% (1.0b remaining)

Error of 6.9b against oracle of 6.0b and baseline of 29.9b

bsearch130.0ms

Steps
ItersRangePoint
9
8.777746745010686e+110
1.2290467223415774e+117
4.945382427151992e+116
8
-4.2540360580362335e-213
-6.123213242466048e-217
-6.213463787515188e-217
9
-2.0347159842260902e+119
-8.425139364787487e+113
-8.514236331386388e+118

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03459
14155
done4155

end0.0ms

sample1.0s

Algorithm
intervals
Results
194.0ms1092×body2560valid
178.0ms5864×body80valid
135.0ms920×body1280valid
83.0ms2939×body80nan
50.0ms459×body640valid
25.0ms116×body5120valid
17.0ms210×body320valid
6.0ms103×body160valid