Details

Time bar (total: 14.0s)

sample120.0ms

Algorithm
intervals
Results
29.0ms83×body80nan
19.0ms32×body2560valid
18.0ms184×body80valid
14.0ms30×body1280valid
9.0ms24×body640valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify143.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite181.0ms

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:
117.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms
(- (* b b) (* 4.0 (* a c)))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series387.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
54.0ms
(- (* b b) (* 4.0 (* a c)))
110.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
106.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
169 → 169
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02436690
15874705
217533760
done50003113

prune570.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma b b (- (* 4.0 (* a c))))
2.5b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
9.1b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
19.7b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×flip3-- flip-- associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ fma-udef
Counts
4 → 140
Calls
4 calls:
0.0ms
(fma b b (- (* 4.0 (* a c))))
88.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
74.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
3.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series615.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma b b (- (* 4.0 (* a c))))
197.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
249.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
106.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.3s

Counts
152 → 152
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02424430
15763966
221943645
done50003641

prune583.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma b b (- (* 4.0 (* a c))))
2.6b
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
9.1b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
19.7b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
51×add-exp-log
42×*-un-lft-identity
40×times-frac
28×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp
14×difference-of-squares
10×sqrt-prod
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r* distribute-lft-out--
6×associate-/r*
4×expm1-log1p-u rec-exp 1-exp associate-/r/ log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+ fma-udef
Counts
4 → 138
Calls
4 calls:
0.0ms
(fma b b (- (* 4.0 (* a c))))
99.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
62.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
3.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series705.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(fma b b (- (* 4.0 (* a c))))
245.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
285.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
116.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.4s

Counts
150 → 150
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02474148
16353632
224273172
done50013169

prune532.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
0.8b
(fma b b (- (* 4.0 (* a c))))
11.9b
(/ (* (* a c) 4.0) (* 2.0 a))
19.7b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
24×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
16×sqrt-prod
9×prod-exp cbrt-unprod
6×cbrt-undiv fma-neg div-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×difference-of-squares
1×sub-neg rem-sqrt-square flip3-- frac-2neg sqrt-pow1 times-frac pow1/2 diff-log clear-num associate-/r* flip-- fma-udef div-inv associate-/l* distribute-lft-out--
Counts
4 → 93
Calls
4 calls:
11.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
0.0ms
(fma b b (- (* 4.0 (* a c))))
41.0ms
(/ (* (* a c) 4.0) (* 2.0 a))
2.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
77.0ms
(fma b b (- (* 4.0 (* a c))))
12.0ms
(/ (* (* a c) 4.0) (* 2.0 a))
115.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify923.0ms

Counts
105 → 105
Iterations

Useful iterations: done (918.0ms)

IterNodesCost
01681926
14131650
218081333
done50001266

prune390.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

regimes155.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.7b

bsearch249.0ms

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

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03657
14857
25657
done5657

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.0s5913×body80valid
599.0ms1081×body2560valid
360.0ms3009×body80nan
339.0ms891×body1280valid
129.0ms468×body640valid
104.0ms107×body5120valid
60.0ms100×body160valid
43.0ms216×body320valid