Details

Time bar (total: 1.8m)

sample99.0ms

Algorithm
intervals
Results
20.0ms37×body2560valid
18.0ms192×body80valid
13.0ms30×body1280valid
7.0ms81×body80nan
4.0ms12×body640valid
3.0ms13×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify94.0ms

Counts
1 → 1
Iterations
IterNodes
done111
5111
4102
378
244
124
014

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize36.0ms

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))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
84.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(- (* b b) (* (* 4.0 a) c))
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
70.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify932.0ms

Counts
82 → 82
Iterations
IterNodes
done5001
21926
1421
0154

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.0b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-cbrt-cube add-exp-log
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×clear-num frac-2neg sqrt-div diff-log prod-exp cbrt-unprod
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series665.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
191.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
274.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
166 → 166
Iterations
IterNodes
done5000
23736
1659
0254

prune964.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.7b
(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.2b
(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
54×add-cbrt-cube add-exp-log
42×add-sqr-sqrt
36×*-un-lft-identity
28×times-frac
27×associate-*r*
21×cbrt-undiv div-exp
20×add-cube-cbrt
16×prod-exp cbrt-unprod
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 associate-*l* sqrt-prod
4×distribute-rgt-neg-in
3×associate-/r* flip3-- div-inv flip-- associate-/l/
2×frac-times sqrt-div diff-log associate-*l/ associate-*r/ associate-/r/ unswap-sqr
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log *-commutative associate-/l*
Counts
4 → 127
Calls
4 calls:
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms
(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
81.0ms
(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series689.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
263.0ms
(* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
221.0ms
(/ (* (/ (* 4.0 a) 2.0) (/ c (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) a)
87.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify418.0ms

Counts
139 → 139
Iterations
IterNodes
done5001
1795
0262

prune845.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(/ (/ (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (cbrt a) (cbrt a)) (/ a (/ 2.0 4.0)))) (cbrt a))
1.3b
(/ (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (cbrt a) (cbrt a)) (/ a (/ 2.0 4.0))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite3.9s

Algorithm
rewrite-expression-head
Rules
50675×times-frac
19526×add-sqr-sqrt
19525×*-un-lft-identity
14805×add-cube-cbrt
3987×cbrt-prod
2360×distribute-lft-out-- difference-of-squares
1487×div-inv
1355×associate-/l*
1228×associate-/r/
1183×sqrt-prod
1180×distribute-rgt-neg-in
395×flip3-- flip--
150×add-exp-log
111×add-cbrt-cube
105×cbrt-undiv div-exp
55×associate-/r*
12×prod-exp cbrt-unprod
8×add-log-exp
5×pow1
2×clear-num frac-2neg sqrt-div diff-log associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log
Counts
4 → 10815
Calls
4 calls:
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
694.0ms
(/ (/ (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (cbrt a) (cbrt a)) (/ a (/ 2.0 4.0)))) (cbrt a))
157.0ms
(/ (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (cbrt a) (cbrt a)) (/ a (/ 2.0 4.0))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series1.2s

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
318.0ms
(/ (/ (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (cbrt a) (cbrt a)) (/ a (/ 2.0 4.0)))) (cbrt a))
603.0ms
(/ (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (cbrt a) (cbrt a)) (/ a (/ 2.0 4.0))))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify6.1s

Counts
10827 → 10827
Iterations
IterNodes
done11342
011342

prune1.4m

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

regimes524.0ms

Accuracy

92.3% (1.9b remaining)

Error of 7.8b against oracle of 5.9b and baseline of 30.2b

bsearch243.0ms

Steps
ItersRangePoint
9
3.768382185355077e+69
1.107955803311012e+78
4.2871760960662547e+77
3
-5.1570355596853615e-201
-3.8052178173245655e-201
-4.565615297402514e-201
8
-1.0455781936591884e+110
-3.8601914758440924e+107
-3.828737593568667e+109

simplify11.0ms

Iterations
IterNodes
done62
162
052

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.1s5837×body80valid
892.0ms936×body1280valid
631.0ms1070×body2560valid
338.0ms2814×body80nan
183.0ms453×body640valid
57.0ms94×body5120valid
51.0ms223×body320valid
21.0ms113×body160valid