Details

Time bar (total: 13.2s)

sample72.0ms

Algorithm
intervals
Results
24.0ms192×body80valid
11.0ms37×body2560valid
7.0ms30×body1280valid
4.0ms81×body80nan
2.0ms12×body640valid
2.0ms13×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify51.0ms

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: 35.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
0.6b
(- (* b b) (* (* c a) 4.0))
1.2b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
22.4b
(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite131.0ms

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:
63.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
6.0ms
(- (* b b) (* (* c a) 4.0))
47.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
53.0ms
(- (* b b) (* (* c a) 4.0))
98.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
77.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.5s

Counts
161 → 161
Iterations
IterNodes
done5002
23070
1692
0280

prune926.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
9×*-un-lft-identity div-exp
8×pow1 add-log-exp
7×add-cube-cbrt
6×prod-exp
4×cbrt-undiv sqrt-prod
3×rec-exp times-frac flip3-- 1-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log cbrt-unprod pow-flip difference-of-squares
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-/r/ div-inv distribute-lft-out-- inv-pow
Counts
4 → 75
Calls
4 calls:
66.0ms
(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
9.0ms
(- (* b b) (* 4.0 (* a c)))
58.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
69.0ms
(- (* b b) (* 4.0 (* a c)))
98.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
116.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify932.0ms

Counts
87 → 87
Iterations
IterNodes
done5001
21728
1410
0155

prune445.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
62×add-sqr-sqrt
46×*-un-lft-identity
43×associate-*r*
41×add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
8×add-log-exp
7×pow1
6×div-exp associate-*l*
5×flip3-- prod-exp sqrt-prod flip--
4×div-inv difference-of-squares unswap-sqr
3×cbrt-undiv cbrt-unprod
2×frac-times sub-neg sqrt-div diff-log associate-*l/ distribute-lft-out--
1×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ *-commutative
Counts
4 → 117
Calls
4 calls:
173.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
14.0ms
(- (* b b) (* 4.0 (* a c)))
34.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
65.0ms
(- (* b b) (* 4.0 (* a c)))
127.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
127.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify438.0ms

Counts
129 → 129
Iterations
IterNodes
done5001
1760
0263

prune793.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.9b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod
2×flip3-- pow1/3 sqrt-div flip-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
59.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
13.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series235.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
124.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
111.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify701.0ms

Counts
60 → 60
Iterations
IterNodes
done5000
2892
1236
099

prune426.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.9b

regimes577.0ms

Accuracy

84% (4.5b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 34.3b

bsearch216.0ms

Steps
ItersRangePoint
9
7.795577680554411e-96
2.7755025870893585e-88
3.5618278271730353e-90
10
-6.622314338184697e+74
-4.7924972520805885e+61
-2.063494556122609e+74

simplify4.0ms

Iterations
IterNodes
done35
135
028

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s936×body1280valid
706.0ms1070×body2560valid
547.0ms5837×body80valid
343.0ms2814×body80nan
135.0ms453×body640valid
98.0ms94×body5120valid
96.0ms223×body320valid
17.0ms113×body160valid