Details

Time bar (total: 15.3s)

sample154.0ms

Algorithm
intervals
Results
43.0ms43×body2560valid
32.0ms190×body80valid
21.0ms25×body1280valid
13.0ms85×body80nan
9.0ms13×body640valid
6.0ms11×body320valid
4.0ms3×body5120valid
1.0ms2×body160valid

simplify143.0ms

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: 34.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (sqrt (fma b b (* (* a -4) c))) b) a) 2)
0.5b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.3b
(fma b b (* (* a -4) c))
24.5b
(sqrt (fma b b (* (* a -4) c)))

rewrite56.0ms

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*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
33.0ms
(/ (/ (- (sqrt (fma b b (* (* a -4) c))) b) a) 2)
15.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms
(fma b b (* (* a -4) c))
2.0ms
(sqrt (fma b b (* (* a -4) c)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (/ (- (sqrt (fma b b (* (* a -4) c))) b) a) 2)
150.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
90.0ms
(fma b b (* (* a -4) c))
136.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify1.4s

Counts
191 → 191
Iterations
IterNodes
done2015
32015
21850
1693
0297

prune972.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (- (sqrt (fma (* -4 a) c (* b b))) b) (/ 1/2 a))
0.5b
(- (sqrt (fma (* -4 a) c (* b b))) b)
24.5b
(sqrt (fma (* -4 a) c (* b b)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
8×add-cbrt-cube add-exp-log
6×pow1 fma-neg associate-*l*
5×add-log-exp
4×difference-of-squares
3×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative div-inv
Counts
3 → 100
Calls
3 calls:
56.0ms
(* (- (sqrt (fma (* -4 a) c (* b b))) b) (/ 1/2 a))
15.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series454.0ms

Counts
3 → 9
Calls
3 calls:
179.0ms
(* (- (sqrt (fma (* -4 a) c (* b b))) b) (/ 1/2 a))
133.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
141.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify1.0s

Counts
109 → 109
Iterations
IterNodes
done2004
32004
21144
1372
0162

prune636.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* (- (sqrt (fma (* -4 a) c (* b b))) b) 1/2) a)
0.5b
(- (sqrt (fma (* -4 a) c (* b b))) b)
24.5b
(sqrt (fma (* -4 a) c (* b b)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
8×add-cbrt-cube add-exp-log
6×fma-neg
5×add-log-exp
4×pow1
3×expm1-log1p-u associate-/r* times-frac insert-posit16 log1p-expm1-u
2×cbrt-undiv flip3-- div-exp associate-*l/ flip-- difference-of-squares associate-/l/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod div-inv associate-/l* distribute-lft-out--
Counts
3 → 84
Calls
3 calls:
28.0ms
(/ (* (- (sqrt (fma (* -4 a) c (* b b))) b) 1/2) a)
8.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series404.0ms

Counts
3 → 9
Calls
3 calls:
152.0ms
(/ (* (- (sqrt (fma (* -4 a) c (* b b))) b) 1/2) a)
129.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
122.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify1.2s

Counts
93 → 93
Iterations
IterNodes
done2012
32012
2927
1326
0139

prune341.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize51.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1/2 a) (- (sqrt (fma (* -4 a) c (* b b))) b))
0.5b
(- (sqrt (fma (* -4 a) c (* b b))) b)
24.5b
(sqrt (fma (* -4 a) c (* b b)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
54×*-un-lft-identity prod-diff
50×add-cube-cbrt
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
13×associate-*l*
10×times-frac
8×add-cbrt-cube add-exp-log
6×pow1 fma-neg associate-*r*
5×add-log-exp
4×difference-of-squares
3×expm1-log1p-u sub-neg flip3-- insert-posit16 log1p-expm1-u flip--
2×frac-times prod-exp associate-*r/ cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
3 → 140
Calls
3 calls:
52.0ms
(* (/ 1/2 a) (- (sqrt (fma (* -4 a) c (* b b))) b))
15.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series427.0ms

Counts
3 → 9
Calls
3 calls:
169.0ms
(* (/ 1/2 a) (- (sqrt (fma (* -4 a) c (* b b))) b))
120.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
138.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify1.3s

Counts
149 → 149
Iterations
IterNodes
done2001
32001
21443
1513
0199

prune600.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

regimes329.0ms

Accuracy

80.9% (5.0b remaining)

Error of 10.3b against oracle of 5.3b and baseline of 31.5b

bsearch209.0ms

Steps
ItersRangePoint
10
1.3859530517218358e-142
9.527435083115218e-125
9.354082991670835e-125
8
-4.336983712965787e+155
-6.488343844980391e+152
-9.088000531423294e+152

simplify4.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.1s1069×body2560valid
902.0ms5926×body80valid
660.0ms874×body1280valid
631.0ms108×body5120valid
427.0ms218×body320valid
405.0ms3004×body80nan
243.0ms467×body640valid
53.0ms112×body160valid