Average Error: 7.5 → 7.4
Time: 42.8s
Precision: 64
Internal precision: 128
\[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]
⬇
\[\begin{array}{l} \mathbf{if}\;t \le -3.8447453506502606 \cdot 10^{-190}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;t \le 3.3156380580081446 \cdot 10^{+107}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}} - 4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{if}\;t \le 7.696604323863346 \cdot 10^{+213}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}} - 4.5 \cdot \frac{t \cdot z}{a}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original7.5
Comparison5.5
Herbie7.4
\[ \begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \lt 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9.0 \cdot t\right)}{a \cdot 2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \]

Derivation

  1. Split input into 2 regimes.

  2. if t < -3.8447453506502606e-190 or 3.3156380580081446e+107 < t < 7.696604323863346e+213

    1. Initial program 9.2

      \[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]

    2. Applied taylor 9.2

      \[\leadsto 0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t \cdot z}{a}\]

    3. Taylor expanded around 0 9.2

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
    4. Using strategy rm

    5. Applied associate-/l* 8.0

      \[\leadsto 0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}}\]

    if -3.8447453506502606e-190 < t < 3.3156380580081446e+107 or 7.696604323863346e+213 < t

    1. Initial program 5.9

      \[\frac{x \cdot y - \left(z \cdot 9.0\right) \cdot t}{a \cdot 2.0}\]

    2. Applied taylor 5.9

      \[\leadsto 0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t \cdot z}{a}\]

    3. Taylor expanded around 0 5.9

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
    4. Using strategy rm

    5. Applied associate-/l* 6.8

      \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} - 4.5 \cdot \frac{t \cdot z}{a}\]
  3. Recombined 2 regimes into one program.
  4. Removed slow pow expressions

Runtime

Time bar (total: 42.8s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1434845648 3023931597 1833908445 1892332934 2207144950 1865795020)'
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"

  :target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))