Average Error: 13.0 → 1.6
Time: 25.8s
Precision: 64
Internal Precision: 576
\[\left(a \cdot {x}^{2} + \left(\left(2 \cdot c\right) \cdot x\right) \cdot y\right) + b \cdot {y}^{2}\]
\[\begin{array}{l} \mathbf{if}\;x \le -6.963685818077932 \cdot 10^{+86}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y \cdot 2\right)\right) + \left(\left(y \cdot y\right) \cdot b + x \cdot \left(a \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y \cdot 2\right) + \left(x \cdot \left(a \cdot x\right) + y \cdot \left(b \cdot y\right)\right)\\ \end{array}\]

Error

Bits error versus a

Bits error versus x

Bits error versus c

Bits error versus y

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes
  2. if x < -6.963685818077932e+86

    1. Initial program 34.3

      \[\left(a \cdot {x}^{2} + \left(\left(2 \cdot c\right) \cdot x\right) \cdot y\right) + b \cdot {y}^{2}\]
    2. Initial simplification34.3

      \[\leadsto \left(\left(x \cdot x\right) \cdot a + b \cdot \left(y \cdot y\right)\right) + \left(c \cdot x\right) \cdot \left(2 \cdot y\right)\]
    3. Using strategy rm
    4. Applied associate-*l*11.7

      \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot a\right)} + b \cdot \left(y \cdot y\right)\right) + \left(c \cdot x\right) \cdot \left(2 \cdot y\right)\]
    5. Using strategy rm
    6. Applied associate-*l*4.0

      \[\leadsto \left(x \cdot \left(x \cdot a\right) + b \cdot \left(y \cdot y\right)\right) + \color{blue}{c \cdot \left(x \cdot \left(2 \cdot y\right)\right)}\]

    if -6.963685818077932e+86 < x

    1. Initial program 11.3

      \[\left(a \cdot {x}^{2} + \left(\left(2 \cdot c\right) \cdot x\right) \cdot y\right) + b \cdot {y}^{2}\]
    2. Initial simplification11.3

      \[\leadsto \left(\left(x \cdot x\right) \cdot a + b \cdot \left(y \cdot y\right)\right) + \left(c \cdot x\right) \cdot \left(2 \cdot y\right)\]
    3. Using strategy rm
    4. Applied associate-*l*7.2

      \[\leadsto \left(\color{blue}{x \cdot \left(x \cdot a\right)} + b \cdot \left(y \cdot y\right)\right) + \left(c \cdot x\right) \cdot \left(2 \cdot y\right)\]
    5. Using strategy rm
    6. Applied associate-*r*1.4

      \[\leadsto \left(x \cdot \left(x \cdot a\right) + \color{blue}{\left(b \cdot y\right) \cdot y}\right) + \left(c \cdot x\right) \cdot \left(2 \cdot y\right)\]
  3. Recombined 2 regimes into one program.
  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.963685818077932 \cdot 10^{+86}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y \cdot 2\right)\right) + \left(\left(y \cdot y\right) \cdot b + x \cdot \left(a \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot c\right) \cdot \left(y \cdot 2\right) + \left(x \cdot \left(a \cdot x\right) + y \cdot \left(b \cdot y\right)\right)\\ \end{array}\]

Runtime

Time bar (total: 25.8s)Debug log

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