Details

Time bar (total: 17.8s)

sample130.0ms

Algorithm
intervals
Results
12.0ms190×body80valid
12.0ms36×body2560valid
7.0ms28×body1280valid
5.0ms92×body80nan
3.0ms16×body640valid
2.0ms7×body320valid
1.0ms1×body5120valid
0.0ms3×body160valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite226.0ms

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:
123.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms
(- (* b_2 b_2) (* a c))
57.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
56.0ms
(- (* b_2 b_2) (* a c))
111.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts
92 → 92
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01511534
13551440
210011266
327921252
done50001249

prune414.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.4b
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.2b
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite232.0ms

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:
34.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
124.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
58.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series681.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
216.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
282.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
72.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
148 → 148
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02403445
15963204
220022940
done50012870

prune552.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.2b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite121.0ms

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:
59.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
17.0ms
(- (* b_2 b_2) (* a c))
32.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
45.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
116.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
102 → 102
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01511775
13251672
28691558
322541540
done50011534

prune394.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.2b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite217.0ms

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:
143.0ms
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms
(- (* b_2 b_2) (* a c))
44.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(* c (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
68.0ms
(- (* b_2 b_2) (* a c))
106.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
107 → 107
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01731703
14111478
210021318
324921302
done50001296

prune285.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.5b

regimes246.0ms

Accuracy

86.8% (3.3b remaining)

Error of 8.5b against oracle of 5.2b and baseline of 30.2b

bsearch226.0ms

Steps
ItersRangePoint
9
1.3206820209921783e+153
1.5782810135998455e+159
6.190496209585126e+153
6
-9.655534078733555e-134
-6.854174842211803e-135
-3.438769587726376e-134
10
-7.296408209838224e+27
-1014094955833491.1
-1.2846701741855862e+20

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03767
14461
done4461

end0.0ms

sample3.0s

Algorithm
intervals
Results
776.0ms466×body640valid
587.0ms1077×body2560valid
488.0ms5880×body80valid
263.0ms850×body1280valid
218.0ms2914×body80nan
51.0ms107×body5120valid
37.0ms212×body320valid
14.0ms123×body160valid