Average Error: 3.4 → 0.8
Time: 33.8s
Precision: 64
Internal precision: 128
\[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]
⬇
\[\begin{array}{l} \mathbf{if}\;z \le -2.2705645183745452 \cdot 10^{-110}:\\ \;\;\;\;\left(x \cdot 2.0 - 9.0 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + \left(a \cdot 27.0\right) \cdot b\\ \mathbf{if}\;z \le 3.312219404886358 \cdot 10^{+35}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(9.0 \cdot \left(z \cdot y\right)\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - 9.0 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + \left(a \cdot 27.0\right) \cdot b\\ \end{array}\]

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

Target

Original3.4
Comparison2.4
Herbie0.8
\[ \begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + a \cdot \left(27.0 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - 9.0 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27.0\right) \cdot b\\ \end{array} \]

Derivation

  1. Split input into 2 regimes.

  2. if z < -2.2705645183745452e-110 or 3.312219404886358e+35 < z

    1. Initial program 6.3

      \[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]

    2. Applied taylor 1.1

      \[\leadsto \left(x \cdot 2.0 - 9.0 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + \left(a \cdot 27.0\right) \cdot b\]

    3. Taylor expanded around inf 1.1

      \[\leadsto \left(x \cdot 2.0 - \color{blue}{9.0 \cdot \left(z \cdot \left(y \cdot t\right)\right)}\right) + \left(a \cdot 27.0\right) \cdot b\]

    if -2.2705645183745452e-110 < z < 3.312219404886358e+35

    1. Initial program 0.6

      \[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]

    2. Applied taylor 0.5

      \[\leadsto \left(x \cdot 2.0 - \left(9.0 \cdot \left(z \cdot y\right)\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]

    3. Taylor expanded around 0 0.5

      \[\leadsto \left(x \cdot 2.0 - \color{blue}{\left(9.0 \cdot \left(z \cdot y\right)\right)} \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]
  3. Recombined 2 regimes into one program.
  4. Removed slow pow expressions

Runtime

Time bar (total: 33.8s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1949458275 2014334845 2071894301 1864689860 3065213165 1681962525)'
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"

  :target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))