Average Error: 5.7 → 1.7
Time: 1.0m
Precision: 64
Internal Precision: 576
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.457016936050244 \cdot 10^{-14} \lor \neg \left(x \le 3.0500689133593523 \cdot 10^{-34}\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot x\right) \cdot \left(\left(t \cdot z\right) \cdot y\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(18.0 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4.0\right) + \left(b \cdot c - \left(4.0 \cdot x\right) \cdot i\right)\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]

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 < -4.457016936050244e-14 or 3.0500689133593523e-34 < x

    1. Initial program 11.7

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

    3. Applied associate-*l*8.8

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

    5. Applied associate-*l*1.8

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

    if -4.457016936050244e-14 < x < 3.0500689133593523e-34

    1. Initial program 1.5

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

    3. Applied associate--l+1.5

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

    4. Simplified1.6

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.457016936050244 \cdot 10^{-14} \lor \neg \left(x \le 3.0500689133593523 \cdot 10^{-34}\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot x\right) \cdot \left(\left(t \cdot z\right) \cdot y\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(18.0 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4.0\right) + \left(b \cdot c - \left(4.0 \cdot x\right) \cdot i\right)\right) - k \cdot \left(j \cdot 27.0\right)\\ \end{array}\]

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed 2018219 
(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)))