Details

Time bar (total: 16.3s)

sample97.0ms

Algorithm
intervals
Results
36.0ms40×body2560valid
12.0ms178×body80valid
11.0ms36×body1280valid
6.0ms88×body80nan
3.0ms15×body640valid
1.0ms7×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify65.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize35.0ms

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)))

rewrite163.0ms

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:
76.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
10.0ms
(- (* b b) (* (* c a) 4.0))
56.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
8.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
64.0ms
(- (* b b) (* (* c a) 4.0))
109.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
99.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.3s

Counts
161 → 161
Iterations
IterNodes
done5002
23070
1692
0280

prune980.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize28.0ms

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))))

rewrite123.0ms

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:
19.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
7.0ms
(- (* b b) (* 4.0 (* a c)))
88.0ms
(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)) (/ (/ b 2.0) a))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
51.0ms
(- (* b b) (* 4.0 (* a c)))
143.0ms
(- (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)) (/ (/ b 2.0) a))
85.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify772.0ms

Counts
85 → 85
Iterations
IterNodes
done5000
21571
1435
0170

prune504.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize44.0ms

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))))

rewrite125.0ms

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:
41.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
60.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series410.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
103.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
88.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts
72 → 72
Iterations
IterNodes
done5001
34455
2793
1198
080

prune604.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite364.0ms

Algorithm
rewrite-expression-head
Rules
137×times-frac
95×add-sqr-sqrt
69×sqrt-prod
61×*-un-lft-identity
52×add-cube-cbrt
16×sqrt-div
15×associate-/r/
13×add-cbrt-cube add-exp-log
12×associate-/r* difference-of-squares
10×flip3-- flip--
8×div-inv add-log-exp
6×associate-/l*
5×pow1 cbrt-undiv div-exp
2×sub-neg diff-log distribute-lft-out--
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp frac-sub cbrt-unprod
Counts
4 → 161
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(/ (sqrt 1) (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c))))))
317.0ms
(- (/ (sqrt 1) (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (/ b 2.0) a))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series545.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (* b b) (* 4.0 (* a c)))
155.0ms
(/ (sqrt 1) (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c))))))
188.0ms
(- (/ (sqrt 1) (/ (* a 2.0) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (/ b 2.0) a))
118.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
173 → 173
Iterations
IterNodes
done5000
22648
1713
0278

prune775.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes461.0ms

Accuracy

83.2% (4.8b remaining)

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

bsearch180.0ms

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

simplify3.0ms

Iterations
IterNodes
done38
138
032

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s5902×body80valid
637.0ms1052×body2560valid
450.0ms898×body1280valid
242.0ms2839×body80nan
183.0ms451×body640valid
100.0ms111×body5120valid
54.0ms239×body320valid
17.0ms105×body160valid