Average Error: 5.5 → 4.3
Time: 1.2m
Precision: 64
Internal precision: 384
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
⬇
\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t \le -9.470409034523649 \cdot 10^{+89}:\\ \;\;\;\;\left(b \cdot c - 4.0 \cdot \left(x \cdot i + a \cdot t\right)\right) + \left(18.0 \cdot \left(z \cdot \left(y \cdot \left(t \cdot x\right)\right)\right) - 27.0 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4.0 \cdot \left(x \cdot i + a \cdot t\right)\right) + \left(\left(t \cdot 18.0\right) \cdot \left(z \cdot \left(y \cdot x\right)\right) - 27.0 \cdot \left(k \cdot j\right)\right)\\ \end{array}\]

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

Derivation

  1. Split input into 2 regimes.

  2. if (* (* (* (* x 18.0) y) z) t) < -9.470409034523649e+89

    1. Initial program 22.1

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

    2. Applied simplify 18.8

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

    3. Applied taylor 12.5

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

    4. Taylor expanded around inf 12.5

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

    if -9.470409034523649e+89 < (* (* (* (* x 18.0) y) z) t)

    1. Initial program 3.4

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

    2. Applied simplify 4.0

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

    3. Applied taylor 3.2

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

    4. Taylor expanded around inf 3.2

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

    6. Applied associate-*r* 3.3

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

Runtime

Time bar (total: 1.2m) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(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)))