Average Error: 5.8 → 4.5
Time: 1.4m
Precision: 64
Internal Precision: 576
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.0538225245659302 \cdot 10^{-63} \lor \neg \left(x \le 5.779470874550678 \cdot 10^{-224}\right):\\ \;\;\;\;c \cdot b + \left(\left(\left(k \cdot j\right) \cdot \left(-27.0\right) + \left(4.0 \cdot x\right) \cdot \left(-i\right)\right) + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(\left(x \cdot 18.0\right) \cdot y\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - i \cdot \left(4.0 \cdot x\right)\right) - k \cdot \left(27.0 \cdot j\right)\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -1.0538225245659302e-63 or 5.779470874550678e-224 < x

    1. Initial program 8.2

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Initial simplification6.2

      \[\leadsto \left(c \cdot b - \left(27.0 \cdot \left(k \cdot j\right) + \left(x \cdot 4.0\right) \cdot i\right)\right) + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot t\]
    3. Using strategy rm

    4. Applied sub-neg6.2

      \[\leadsto \color{blue}{\left(c \cdot b + \left(-\left(27.0 \cdot \left(k \cdot j\right) + \left(x \cdot 4.0\right) \cdot i\right)\right)\right)} + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot t\]

    5. Applied associate-+l+6.2

      \[\leadsto \color{blue}{c \cdot b + \left(\left(-\left(27.0 \cdot \left(k \cdot j\right) + \left(x \cdot 4.0\right) \cdot i\right)\right) + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot t\right)}\]

    if -1.0538225245659302e-63 < x < 5.779470874550678e-224

    1. Initial program 1.1

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.0538225245659302 \cdot 10^{-63} \lor \neg \left(x \le 5.779470874550678 \cdot 10^{-224}\right):\\ \;\;\;\;c \cdot b + \left(\left(\left(k \cdot j\right) \cdot \left(-27.0\right) + \left(4.0 \cdot x\right) \cdot \left(-i\right)\right) + \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right) - a \cdot 4.0\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(\left(x \cdot 18.0\right) \cdot y\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - i \cdot \left(4.0 \cdot x\right)\right) - k \cdot \left(27.0 \cdot j\right)\\ \end{array}\]

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018225 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))