Average Error: 3.3 → 1.9
Time: 2.8s
Precision: binary64
\[x \cdot \left(1 - y \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z \le -5.9823418309629038 \cdot 10^{165}:\\ \;\;\;\;x \cdot 1 + z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(y \cdot z\right) \cdot \left(-x\right)\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Split input into 2 regimes

  2. if (* y z) < -5.9823418309629038e165

    1. Initial program 20.9

      \[x \cdot \left(1 - y \cdot z\right)\]
    2. Using strategy rm

    3. Applied sub-neg20.9

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y \cdot z\right)\right)}\]

    4. Applied distribute-lft-in20.9

      \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-y \cdot z\right)}\]

    5. Simplified20.9

      \[\leadsto x \cdot 1 + \color{blue}{x \cdot \left(y \cdot \left(-z\right)\right)}\]
    6. Using strategy rm

    7. Applied associate-*r*2.6

      \[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot y\right) \cdot \left(-z\right)}\]

    if -5.9823418309629038e165 < (* y z)

    1. Initial program 1.8

      \[x \cdot \left(1 - y \cdot z\right)\]
    2. Using strategy rm

    3. Applied sub-neg1.8

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y \cdot z\right)\right)}\]

    4. Applied distribute-lft-in1.8

      \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-y \cdot z\right)}\]

    5. Simplified1.8

      \[\leadsto x \cdot 1 + \color{blue}{x \cdot \left(y \cdot \left(-z\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \le -5.9823418309629038 \cdot 10^{165}:\\ \;\;\;\;x \cdot 1 + z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + \left(y \cdot z\right) \cdot \left(-x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))