Details

Time bar (total: 11.3s)

sample85.0ms

Algorithm
intervals
Results
22.0ms108×body80nan
13.0ms36×body2560valid
12.0ms188×body80valid
7.0ms24×body1280valid
4.0ms17×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
161.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
76.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: 2 (275.0ms)

IterNodesCost
01541592
14051496
217891332
done50011332

prune387.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
47×add-sqr-sqrt
36×*-un-lft-identity
26×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
9×associate-/r/
8×sqrt-prod add-log-exp
7×flip3-- flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 118
Calls
4 calls:
122.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
17.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
74.0ms
(- (* b b) (* (* 4.0 a) c))
116.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
130 → 130
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02203137
15712809
227562613
done50022611

prune415.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
12.0b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
1×difference-of-squares
Counts
4 → 55
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
124.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify896.0ms

Counts
67 → 67
Iterations

Useful iterations: done (892.0ms)

IterNodesCost
0941323
1243973
21100895
done5001893

prune350.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.1b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.1b

regimes228.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 33.8b

bsearch210.0ms

Steps
ItersRangePoint
9
4.939518845348872e-48
4.7173742985844417e-39
1.4070882317677973e-46
10
-2.8734245235493903e+48
-2.602501271628617e+37
-2.8472042802820317e+48

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample3.7s

Algorithm
intervals
Results
744.0ms1074×body2560valid
723.0ms2902×body80nan
674.0ms5856×body80valid
505.0ms903×body1280valid
228.0ms451×body640valid
115.0ms112×body5120valid
53.0ms223×body320valid
18.0ms111×body160valid