Average Error: 4.2 → 0.1
Time: 7.7s
Precision: 64
Internal Precision: 320
\[\left(a \cdot {x}^{2} + b \cdot x\right) + c\]
\[x \cdot \left(x \cdot a\right) + \left(x \cdot b + c\right)\]

Error

Bits error versus a

Bits error versus x

Bits error versus b

Bits error versus c

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.2

    \[\left(a \cdot {x}^{2} + b \cdot x\right) + c\]
  2. Initial simplification4.2

    \[\leadsto \left(x \cdot x\right) \cdot a + \left(b \cdot x + c\right)\]
  3. Using strategy rm
  4. Applied associate-*l*0.1

    \[\leadsto \color{blue}{x \cdot \left(x \cdot a\right)} + \left(b \cdot x + c\right)\]
  5. Final simplification0.1

    \[\leadsto x \cdot \left(x \cdot a\right) + \left(x \cdot b + c\right)\]

Runtime

Time bar (total: 7.7s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a x b c)
  :name "a*x^2+b*x+c"
  (+ (+ (* a (pow x 2)) (* b x)) c))