Details

Time bar (total: 13.2s)

sample40.0ms

Algorithm
intervals
Results
9.0ms39×body2560valid
6.0ms36×body1280valid
6.0ms165×body80valid
3.0ms87×body80nan
2.0ms13×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms4×body160valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
1.0b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 183
Calls
4 calls:
39.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
48.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify929.0ms

Counts
195 → 195
Iterations

Useful iterations: done (922.0ms)

IterNodesCost
03194967
17514592
221594283
done50004264

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) (/ (/ 1 2.0) a))
1.3b
(fma b b (- (* 4.0 (* a c))))
1.6b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
22.6b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
71×times-frac
60×*-un-lft-identity
55×add-cube-cbrt
43×associate-*r*
19×add-exp-log
18×prod-diff
17×sqrt-prod
13×add-cbrt-cube
7×pow1
6×fma-neg div-exp associate-*l* add-log-exp
5×prod-exp
4×expm1-log1p-u log1p-expm1-u div-inv difference-of-squares unswap-sqr
3×cbrt-undiv flip3-- flip-- cbrt-unprod
2×frac-times associate-*l/ distribute-lft-out--
1×sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp associate-*r/ pow-prod-down *-commutative fma-udef
Counts
4 → 143
Calls
4 calls:
34.0ms
(* (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) (/ (/ 1 2.0) a))
0.0ms
(fma b b (- (* 4.0 (* a c))))
6.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
1.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) (/ (/ 1 2.0) a))
57.0ms
(fma b b (- (* 4.0 (* a c))))
92.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
81.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify997.0ms

Counts
155 → 155
Iterations

Useful iterations: done (993.0ms)

IterNodesCost
02823455
17142972
219902592
done50002565

prune416.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
3251×times-frac
1774×add-sqr-sqrt
1519×*-un-lft-identity
1265×add-cube-cbrt
254×difference-of-squares
142×sqrt-prod
129×div-inv
127×distribute-lft-out--
71×associate-/r*
64×add-exp-log
54×div-exp
25×add-cbrt-cube
19×prod-diff
15×cbrt-undiv 1-exp associate-/r/
13×associate-/l*
8×add-log-exp
7×fma-neg
6×rec-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip--
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 1122
Calls
4 calls:
52.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0)))
49.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.2s

Counts
1134 → 1134
Iterations

Useful iterations: done (4.2s)

IterNodesCost
0152248578
1451438703
done500038649

prune714.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.6b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

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×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
128 → 128
Iterations

Useful iterations: 3 (639.0ms)

IterNodesCost
01122856
12612310
27561948
328861774
done50001774

prune348.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes199.0ms

Accuracy

81.5% (5.2b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 33.8b

bsearch108.0ms

Steps
ItersRangePoint
9
2.365685850767504e-168
1.2053288471691685e-161
1.1860189201379418e-161
8
-1.4395777107888637e+138
-2.299948591329529e+133
-1.9827654008890006e+134

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13940
24740
done4740

end0.0ms

sample1.3s

Algorithm
intervals
Results
422.0ms5914×body80valid
235.0ms1025×body2560valid
165.0ms891×body1280valid
106.0ms2997×body80nan
70.0ms450×body640valid
29.0ms107×body5120valid
22.0ms209×body320valid
7.0ms104×body160valid