Details

Time bar (total: 12.5s)

sample112.0ms

Algorithm
intervals
Results
24.0ms40×body2560valid
18.0ms183×body80valid
18.0ms35×body1280valid
8.0ms79×body80nan
6.0ms16×body640valid
2.0ms2×body5120valid
1.0ms5×body160valid
1.0ms2×body320valid

simplify113.0ms

Counts
1 → 1
Iterations
IterNodes
done107
5107
499
379
244
124
014

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.3b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite157.0ms

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:
99.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms
(- (* b b) (* 4.0 (* a c)))
29.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
70.0ms
(- (* b b) (* 4.0 (* a c)))
109.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
113.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify799.0ms

Counts
82 → 82
Iterations
IterNodes
done5001
21723
1419
0152

prune451.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.7b

localize45.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
3.6b
(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))) (* 2.0 a))
7.8b
(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))
24.2b
(sqrt (- (pow b 2) (* 4.0 (* c a))))

rewrite291.0ms

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:
37.0ms
(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
121.0ms
(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))) (* 2.0 a))
96.0ms
(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))
24.0ms
(sqrt (- (pow b 2) (* 4.0 (* c a))))

series863.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
307.0ms
(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))) (* 2.0 a))
325.0ms
(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))
95.0ms
(sqrt (- (pow b 2) (* 4.0 (* c a))))

simplify1.9s

Counts
166 → 166
Iterations
IterNodes
done5002
23634
1650
0253

prune949.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
0.2b
(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (/ 1 a) 2.0))
1.3b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
54×add-sqr-sqrt
50×*-un-lft-identity
43×associate-*r*
41×add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
10×add-log-exp
7×pow1
6×div-exp
5×associate-*l* prod-exp
4×div-inv distribute-lft-out unswap-sqr
3×cbrt-undiv flip3-+ sqrt-prod cbrt-unprod flip-+
2×frac-times sum-log distribute-rgt-neg-in flip3-- sqrt-div associate-*l/ flip--
1×neg-sub0 +-commutative rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down neg-log associate-*r/ *-commutative associate-+l-
Counts
4 → 116
Calls
4 calls:
14.0ms
(- (* b b) (* 4.0 (* a c)))
127.0ms
(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (/ 1 a) 2.0))
33.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series510.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b b) (* 4.0 (* a c)))
192.0ms
(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (/ 1 a) 2.0))
149.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
102.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify485.0ms

Counts
128 → 128
Iterations
IterNodes
done5001
1779
0264

prune794.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune1.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

regimes392.0ms

Accuracy

83.1% (5.0b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 34.6b

bsearch141.0ms

Steps
ItersRangePoint
7
1.726360512453143e-63
2.3465896586148578e-61
1.3696631973385881e-61
5
-4.0529501114613944e+21
-1.3554105129294137e+21
-3.9950858563514354e+21

simplify4.0ms

Iterations
IterNodes
done37
137
029

end0.0ms

sample3.7s

Algorithm
intervals
Results
891.0ms931×body1280valid
671.0ms5779×body80valid
666.0ms1094×body2560valid
363.0ms2886×body80nan
143.0ms448×body640valid
142.0ms226×body320valid
108.0ms93×body5120valid
68.0ms125×body160valid