Details

Time bar (total: 6.7s)

sample44.0ms

Algorithm
intervals
Results
8.0ms34×body2560valid
8.0ms41×body1280valid
7.0ms174×body80valid
3.0ms94×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms6×body160valid

simplify93.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
311917
414117
514717
615017
done15017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
2.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
46.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify786.0ms

Counts
169 → 169
Iterations

Useful iterations: done (780.0ms)

IterNodesCost
02436690
15904755
218123760
done50013759

prune368.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.1b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune16.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
2.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
30.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
217 → 217
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03118365
17186209
221485076
done50015068

prune382.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
1.0b
(fma b b (- (* 4.0 (* a c))))
2.2b
(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
26.1b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv flip3-- diff-log div-exp flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv
Counts
4 → 149
Calls
4 calls:
31.0ms
(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
0.0ms
(fma b b (- (* 4.0 (* a c))))
12.0ms
(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
1.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
53.0ms
(fma b b (- (* 4.0 (* a c))))
89.0ms
(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
83.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify737.0ms

Counts
161 → 161
Iterations

Useful iterations: done (728.0ms)

IterNodesCost
02216500
15144586
214313612
done50003603

prune318.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.0b

regimes228.0ms

Accuracy

82.5% (4.6b remaining)

Error of 10.1b against oracle of 5.5b and baseline of 31.9b

bsearch204.0ms

Steps
ItersRangePoint
10
9.447687191993962e+42
3.6320219268964787e+53
3.3356876929369832e+53
8
-5.624252222434776e-141
-8.495612805601153e-144
-5.527751925950661e-141
3
-1.5135282028271172e-83
-1.144585171485834e-83
-1.1676441109446642e-83
8
-3.5277292732751733e+22
-1.8186532677649703e+19
-1.6260438117910197e+21

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
04080
15576
26376
done6376

end0.0ms

sample1.2s

Algorithm
intervals
Results
269.0ms1076×body2560valid
237.0ms5778×body80valid
192.0ms967×body1280valid
107.0ms2868×body80nan
76.0ms460×body640valid
33.0ms109×body5120valid
29.0ms234×body320valid
8.0ms107×body160valid