Details

Time bar (total: 19.5s)

sample118.0ms

Algorithm
intervals
Results
26.0ms8×body320valid
21.0ms35×body2560valid
19.0ms184×body80valid
14.0ms28×body1280valid
9.0ms86×body80nan
6.0ms15×body640valid
3.0ms4×body5120valid
1.0ms5×body160valid

simplify89.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
377
244
125
014

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.8b
(fma b b (* (* a -4) c))
1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
24.6b
(sqrt (fma b b (* (* a -4) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
27.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms
(fma b b (* (* a -4) c))
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
85.0ms
(fma b b (* (* a -4) c))
105.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
99.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify1.3s

Counts
126 → 126
Iterations
IterNodes
done2006
32006
21007
1423
0180

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma c (* -4 a) (* b b))
0.1b
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
1.7b
(- (sqrt (fma c (* -4 a) (* b b))) b)
24.6b
(sqrt (fma c (* -4 a) (* b b)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
0.0ms
(fma c (* -4 a) (* b b))
40.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
15.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(fma c (* -4 a) (* b b))
105.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
110.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
117.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
done2003
32003
2782
1337
0157

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize34.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.7b
(- (sqrt (fma b b (* (* a -4) c))) b)
24.6b
(sqrt (fma b b (* (* a -4) c)))
24.6b
(sqrt (fma b b (* (* a -4) c)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
112.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
99.0ms
(sqrt (fma b b (* (* a -4) c)))
106.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify1.1s

Counts
128 → 128
Iterations
IterNodes
done2003
42003
31446
2484
1225
0100

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize61.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.7b
(- (sqrt (fma c (* -4 a) (* b b))) b)
24.6b
(sqrt (fma c (* -4 a) (* b b)))
24.6b
(sqrt (fma c (* -4 a) (* b b)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
24.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
15.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
129.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
112.0ms
(sqrt (fma c (* -4 a) (* b b)))
85.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.1s

Counts
128 → 128
Iterations
IterNodes
done2001
42001
3908
2311
1168
085

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes414.0ms

Accuracy

84.4% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.4b

bsearch207.0ms

Steps
ItersRangePoint
10
8.296670056881522e-85
2.5972983117194536e-74
2.326372645943808e-74
7
-1.8217288728729631e+111
-6.606823090402082e+109
-1.0027271082217074e+110

simplify9.0ms

Iterations
IterNodes
done29
129
026

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.9s1126×body2560valid
917.0ms5836×body80valid
743.0ms915×body1280valid
421.0ms2976×body80nan
234.0ms417×body640valid
148.0ms119×body5120valid
116.0ms236×body320valid
60.0ms115×body160valid