Average Error: 7.3 → 4.2
Time: 21.6s
Precision: 64
Internal precision: 128
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
⬇
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -1.9065966854774704 \cdot 10^{+60}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -8.963050224559816 \cdot 10^{-300}:\\ \;\;\;\;\left(\left(x - z\right) \cdot y\right) \cdot t\\ \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t \le -0.0:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - z\right) \cdot y\right) \cdot t\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original7.3
Comparison3.0
Herbie4.2
\[ \begin{array}{l} \mathbf{if}\;t \lt -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{if}\;t \lt 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array} \]

Derivation

  1. Split input into 2 regimes.

  2. if (* (- (* x y) (* z y)) t) < -1.9065966854774704e+60 or -8.963050224559816e-300 < (* (- (* x y) (* z y)) t) < -0.0

    1. Initial program 11.6

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    2. Applied simplify 2.5

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

    if -1.9065966854774704e+60 < (* (- (* x y) (* z y)) t) < -8.963050224559816e-300 or -0.0 < (* (- (* x y) (* z y)) t)

    1. Initial program 5.1

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    2. Applied simplify 8.8

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

    4. Applied associate-*r* 5.1

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

Runtime

Time bar (total: 21.6s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(308109862 3157295724 2075424664 3252260029 2236378824 3677209114)'
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"

  :target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

  (* (- (* x y) (* z y)) t))