Average Error: 5.3 → 3.8
Time: 35.0s
Precision: 64
Internal Precision: 128
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.8757066058813413 \cdot 10^{+123} \lor \neg \left(t \le 6.313812657534764 \cdot 10^{-129}\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(18.0 \cdot \left(x \cdot y\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - 4.0 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - 4.0 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]

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 t < -1.8757066058813413e+123 or 6.313812657534764e-129 < t

    1. Initial program 2.7

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

    3. Applied associate-*l*2.7

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

    4. Taylor expanded around 0 2.7

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

    5. Taylor expanded around inf 2.6

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

    if -1.8757066058813413e+123 < t < 6.313812657534764e-129

    1. Initial program 7.0

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

    3. Applied associate-*l*7.0

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

    4. Taylor expanded around 0 7.0

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

    5. Taylor expanded around inf 7.0

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

    7. Applied associate-*l*4.5

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

  4. Final simplification3.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.8757066058813413 \cdot 10^{+123} \lor \neg \left(t \le 6.313812657534764 \cdot 10^{-129}\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(18.0 \cdot \left(x \cdot y\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - 4.0 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(18.0 \cdot \left(x \cdot y\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - 4.0 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]

Runtime

Time bar (total: 35.0s)Debug logProfile

herbie shell --seed 2018273 
(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)))