Details

Time bar (total: 15.7s)

sample86.0ms

Algorithm
intervals
Results
17.0ms40×body2560valid
13.0ms36×body1280valid
12.0ms178×body80valid
6.0ms88×body80nan
4.0ms15×body640valid
2.0ms7×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify129.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
0.2b
(- (* b b) (* (* c a) 4.0))
0.7b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.4b
(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 149
Calls
4 calls:
92.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
6.0ms
(- (* b b) (* (* c a) 4.0))
43.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
84.0ms
(- (* b b) (* (* c a) 4.0))
148.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
112.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.8s

Counts
161 → 161
Iterations
IterNodes
done5002
23070
1692
0280

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
0.2b
(- (* b b) (* 4.0 (* a c)))
6.8b
(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)) (/ (/ b 2.0) a))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
11×*-un-lft-identity
9×times-frac add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
8×add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div flip--
3×difference-of-squares
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 prod-exp frac-sub cbrt-unprod div-inv distribute-lft-out--
Counts
4 → 73
Calls
4 calls:
16.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
11.0ms
(- (* b b) (* 4.0 (* a c)))
104.0ms
(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)) (/ (/ b 2.0) a))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
67.0ms
(- (* b b) (* 4.0 (* a c)))
141.0ms
(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)) (/ (/ b 2.0) a))
98.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify812.0ms

Counts
85 → 85
Iterations
IterNodes
done5000
21571
1435
0170

prune556.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.7b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
33.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
32.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
13.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
103.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
114.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.6s

Counts
72 → 72
Iterations
IterNodes
done5001
34455
2793
1198
080

prune502.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
0.2b
(/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.9b
(- (/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (/ b 2.0) a))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
61×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
25×add-exp-log
15×sqrt-prod
13×add-cbrt-cube
12×associate-/r* div-exp
10×sqrt-div
9×associate-/r/ difference-of-squares
8×add-log-exp
7×flip3-- flip--
6×pow1 div-inv
5×cbrt-undiv
3×rec-exp 1-exp prod-exp associate-/l* distribute-lft-out--
2×sub-neg diff-log
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 frac-sub cbrt-unprod pow-flip inv-pow
Counts
4 → 128
Calls
4 calls:
6.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c))))))
164.0ms
(- (/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (/ b 2.0) a))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* b b) (* 4.0 (* a c)))
139.0ms
(/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c))))))
168.0ms
(- (/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (/ b 2.0) a))
86.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts
140 → 140
Iterations
IterNodes
done5001
22557
1639
0245

prune662.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes566.0ms

Accuracy

83.2% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 34.1b

bsearch166.0ms

Steps
ItersRangePoint
7
4.7547400806771625e-82
1.9034131584556183e-80
3.0476772566360775e-81
7
-9.685109581380507e+154
-1.5171851739610474e+153
-2.0256498248166784e+153

simplify6.0ms

Iterations
IterNodes
done38
138
032

end0.0ms

sample3.1s

Algorithm
intervals
Results
906.0ms1052×body2560valid
562.0ms5902×body80valid
383.0ms898×body1280valid
262.0ms2839×body80nan
192.0ms451×body640valid
90.0ms111×body5120valid
86.0ms239×body320valid
42.0ms105×body160valid