Average Error: 5.3 → 1.7
Time: 1.5m
Precision: 64
Internal Precision: 576
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le -2.370751832202315 \cdot 10^{+280} \lor \neg \left(y \cdot z \le -1.1160499523160222 \cdot 10^{-51}\right) \land \left(y \cdot z \le 2.37312731091155 \cdot 10^{-153} \lor \neg \left(y \cdot z \le 9.178851352047611 \cdot 10^{+305}\right)\right):\\ \;\;\;\;\left(\left(\left(\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot x\right) \cdot y\right) - \left(4.0 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(4.0 \cdot x\right) \cdot i\right) - k \cdot \left(27.0 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right) \cdot 18.0 - \left(4.0 \cdot a\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - k \cdot \left(27.0 \cdot j\right)\\ \end{array}\]

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 (* z y) < -2.370751832202315e+280 or -1.1160499523160222e-51 < (* z y) < 2.37312731091155e-153 or 9.178851352047611e+305 < (* z y)

    1. Initial program 4.0

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

    3. Applied associate-*l*2.7

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

    if -2.370751832202315e+280 < (* z y) < -1.1160499523160222e-51 or 2.37312731091155e-153 < (* z y) < 9.178851352047611e+305

    1. Initial program 6.5

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

    2. Taylor expanded around inf 3.8

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

    4. Applied associate-*r*0.9

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \le -2.370751832202315 \cdot 10^{+280} \lor \neg \left(y \cdot z \le -1.1160499523160222 \cdot 10^{-51}\right) \land \left(y \cdot z \le 2.37312731091155 \cdot 10^{-153} \lor \neg \left(y \cdot z \le 9.178851352047611 \cdot 10^{+305}\right)\right):\\ \;\;\;\;\left(\left(\left(\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot x\right) \cdot y\right) - \left(4.0 \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(4.0 \cdot x\right) \cdot i\right) - k \cdot \left(27.0 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot \left(t \cdot x\right)\right) \cdot 18.0 - \left(4.0 \cdot a\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - k \cdot \left(27.0 \cdot j\right)\\ \end{array}\]

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed 2018215 
(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)))