Average Error: 5.3 → 4.2
Time: 1.1m
Precision: 64
Internal Precision: 128
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.0465606956736276 \cdot 10^{-216} \lor \neg \left(x \le 6.675834613747172 \cdot 10^{-109}\right):\\ \;\;\;\;\left(c \cdot b - \left(j \cdot \left(k \cdot 27.0\right) + i \cdot \left(4.0 \cdot x\right)\right)\right) + \left(\left(\left(y \cdot 18.0\right) \cdot z\right) \cdot x - a \cdot 4.0\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(\left(x \cdot 18.0\right) \cdot y\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - i \cdot \left(4.0 \cdot x\right)\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]

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 < -3.0465606956736276e-216 or 6.675834613747172e-109 < x

    1. Initial program 7.3

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

    2. Initial simplification5.6

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

    4. Applied associate-*l*5.6

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

    6. Applied associate-*r*5.6

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

    8. Applied associate-*r*5.7

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

    if -3.0465606956736276e-216 < x < 6.675834613747172e-109

    1. Initial program 0.8

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

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.0465606956736276 \cdot 10^{-216} \lor \neg \left(x \le 6.675834613747172 \cdot 10^{-109}\right):\\ \;\;\;\;\left(c \cdot b - \left(j \cdot \left(k \cdot 27.0\right) + i \cdot \left(4.0 \cdot x\right)\right)\right) + \left(\left(\left(y \cdot 18.0\right) \cdot z\right) \cdot x - a \cdot 4.0\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(\left(x \cdot 18.0\right) \cdot y\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - i \cdot \left(4.0 \cdot x\right)\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018346 
(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)))