Details

Time bar (total: 16.1s)

sample74.0ms

Algorithm
intervals
Results
19.0ms88×body80nan
11.0ms40×body2560valid
10.0ms178×body80valid
8.0ms36×body1280valid
3.0ms15×body640valid
1.0ms7×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify87.0ms

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

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:
87.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
17.0ms
(- (* b b) (* (* 4.0 a) c))
64.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
55.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
161 → 161
Iterations
IterNodes
done5001
23078
1690
0280

prune935.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize26.0ms

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))))

rewrite108.0ms

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:
17.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
6.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)) (/ (/ b 2.0) a))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
61.0ms
(- (* b b) (* 4.0 (* a c)))
126.0ms
(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)) (/ (/ b 2.0) a))
123.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify789.0ms

Counts
85 → 85
Iterations
IterNodes
done5000
21571
1435
0170

prune602.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize74.0ms

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))))

rewrite103.0ms

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:
38.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
36.0ms
(- (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))))

series460.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
123.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
110.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
115.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.3s

Counts
72 → 72
Iterations
IterNodes
done5001
34455
2793
1198
080

prune589.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize44.0ms

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))))

rewrite228.0ms

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:
13.0ms
(- (* b b) (* 4.0 (* a c)))
31.0ms
(/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c))))))
169.0ms
(- (/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (/ b 2.0) a))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series505.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* 4.0 (* a c)))
144.0ms
(/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c))))))
191.0ms
(- (/ 1 (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (/ b 2.0) a))
109.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify976.0ms

Counts
140 → 140
Iterations
IterNodes
done5001
22557
1639
0245

prune538.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.3b

regimes498.0ms

Accuracy

83.2% (4.8b remaining)

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

bsearch162.0ms

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

simplify7.0ms

Iterations
IterNodes
done38
138
032

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.2s5902×body80valid
610.0ms1052×body2560valid
411.0ms898×body1280valid
340.0ms2839×body80nan
169.0ms451×body640valid
63.0ms111×body5120valid
52.0ms239×body320valid
17.0ms105×body160valid