Details

Time bar (total: 12.4s)

sample43.0ms

Algorithm
intervals
Results
9.0ms37×body2560valid
7.0ms177×body80valid
6.0ms31×body1280valid
3.0ms92×body80nan
2.0ms16×body640valid
1.0ms5×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

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:
38.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
25.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
85.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
51.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
195 → 195
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03214967
17594592
221934283
done50004264

prune600.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
452×add-sqr-sqrt
377×*-un-lft-identity
303×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
52×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
19×prod-diff
17×div-inv
15×div-exp
13×add-cbrt-cube
8×add-log-exp
7×fma-neg
6×pow1 cbrt-undiv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u
3×rec-exp flip3-- 1-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 388
Calls
4 calls:
37.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
23.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
49.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
400 → 400
Iterations

Useful iterations: done (2.5s)

IterNodesCost
061212852
1143611602
2404110561
done500010543

prune682.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (sqrt (fma b b (- (* c (* 4.0 a))))) b) (/ a (/ 1 2.0)))
0.4b
(- (sqrt (fma b b (- (* c (* 4.0 a))))) b)
1.0b
(fma b b (- (* c (* 4.0 a))))
27.3b
(sqrt (fma b b (- (* c (* 4.0 a)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
726×times-frac
494×add-sqr-sqrt
401×*-un-lft-identity
309×add-cube-cbrt
92×difference-of-squares
61×sqrt-prod
46×distribute-lft-out--
44×associate-/r*
29×div-inv
19×add-exp-log
18×prod-diff
13×add-cbrt-cube
11×div-exp
8×associate-/r/
6×cbrt-undiv fma-neg associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×flip3-- flip-- associate-/l/
1×sub-neg rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 diff-log 1-exp div-sub clear-num fma-udef
Counts
4 → 404
Calls
4 calls:
30.0ms
(/ (- (sqrt (fma b b (- (* c (* 4.0 a))))) b) (/ a (/ 1 2.0)))
6.0ms
(- (sqrt (fma b b (- (* c (* 4.0 a))))) b)
0.0ms
(fma b b (- (* c (* 4.0 a))))
1.0ms
(sqrt (fma b b (- (* c (* 4.0 a)))))

series343.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (- (sqrt (fma b b (- (* c (* 4.0 a))))) b) (/ a (/ 1 2.0)))
90.0ms
(- (sqrt (fma b b (- (* c (* 4.0 a))))) b)
56.0ms
(fma b b (- (* c (* 4.0 a))))
86.0ms
(sqrt (fma b b (- (* c (* 4.0 a)))))

simplify2.1s

Counts
416 → 416
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
062114308
1173712851
2486411877
done500011877

prune727.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.0b
(fma b b (- (* c (* 4.0 a))))
27.3b
(sqrt (fma b b (- (* c (* 4.0 a)))))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod add-log-exp
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 sqrt-div flip--
1×sub-neg fma-neg diff-log prod-diff fma-udef
Counts
4 → 58
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
0.0ms
(fma b b (- (* c (* 4.0 a))))
1.0ms
(sqrt (fma b b (- (* c (* 4.0 a)))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
55.0ms
(fma b b (- (* c (* 4.0 a))))
81.0ms
(sqrt (fma b b (- (* c (* 4.0 a)))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
70 → 70
Iterations

Useful iterations: done (1.3s)

IterNodesCost
091956
1192881
2623832
32532804
done5000801

prune300.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.9b

regimes270.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 33.8b

bsearch138.0ms

Steps
ItersRangePoint
11
4.489865195692553e-133
5.932607888300091e-106
2.0569776426586135e-106
8
-6.10058349091927e+155
-9.408528429616011e+151
-7.93152454634662e+153

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13840
24640
done4640

end0.0ms

sample1.1s

Algorithm
intervals
Results
235.0ms1046×body2560valid
226.0ms5918×body80valid
162.0ms861×body1280valid
109.0ms2864×body80nan
64.0ms452×body640valid
31.0ms113×body5120valid
24.0ms230×body320valid
7.0ms100×body160valid