Details

Time bar (total: 15.9s)

sample72.0ms

Algorithm
intervals
Results
22.0ms30×body1280valid
9.0ms184×body80valid
9.0ms32×body2560valid
6.0ms83×body80nan
5.0ms24×body640valid
1.0ms7×body320valid
0.0ms4×body160valid

simplify34.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize19.0ms

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))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite159.0ms

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-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
98.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(- (* b_2 b_2) (* a c))
34.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
54.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify700.0ms

Counts
103 → 103

prune415.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.5b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 184
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
122.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
96.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series684.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b_2 b_2) (* a c))
265.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
273.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
99.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
196 → 196

prune825.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.5b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
3.4b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
831×times-frac
545×add-sqr-sqrt
448×*-un-lft-identity
352×add-cube-cbrt
96×difference-of-squares
74×associate-/l*
51×sqrt-prod
48×distribute-lft-out--
25×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 437
Calls
4 calls:
11.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
60.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series658.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* b_2 b_2) (* a c))
242.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
284.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify939.0ms

Counts
449 → 449

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.6b
(- (* b_2 b_2) (* a c))
19.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
745×times-frac
479×add-sqr-sqrt
392×*-un-lft-identity
306×add-cube-cbrt
86×difference-of-squares
46×sqrt-prod
43×distribute-lft-out--
38×div-inv
37×add-exp-log
29×div-exp
22×associate-/r*
16×add-cbrt-cube
13×associate-/l*
10×1-exp
8×cbrt-undiv add-log-exp
5×pow1
4×rec-exp
3×flip3-- flip--
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/ associate-/l/
Counts
4 → 393
Calls
4 calls:
81.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
110.0ms
(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
11.0ms
(- (* b_2 b_2) (* a c))
25.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
169.0ms
(/ (/ 1 1) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
41.0ms
(- (* b_2 b_2) (* a c))
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify906.0ms

Counts
405 → 405

prune923.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

regimes251.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.6b

bsearch193.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.7151811081882383e+78
9
3.6976431258031608e-267
1.8292500652683027e-260
7.061692521831336e-266
8
-6.990724105819741e+111
-2.6156774686163576e+108
-5.674469085146397e+110

simplify1.4s

end0.0ms

sample2.8s

Algorithm
intervals
Results
642.0ms3009×body80nan
572.0ms1082×body2560valid
456.0ms5908×body80valid
379.0ms891×body1280valid
106.0ms472×body640valid
45.0ms107×body5120valid
37.0ms212×body320valid
12.0ms104×body160valid