Error

Derivation

1. Split input into 2 regimes

2. if x < -2.637706857500326e-102 or 1.018854104406312e-31 < x

   1. Initial program 8.1

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
   2. Using strategy rm

   3. Applied sub-neg8.1

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

   4. Applied distribute-lft-in8.1

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

   5. Applied associate-+r+8.1

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

   6. Applied simplify8.6

      \[\leadsto \color{blue}{\left((\left(z \cdot y - a \cdot t\right) \cdot x + \left(c \cdot \left(t \cdot j\right)\right))_* - \left(z \cdot c - i \cdot a\right) \cdot b\right)} + j \cdot \left(-i \cdot y\right)\]
   7. Using strategy rm

   8. Applied fma-udef8.6

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

   if -2.637706857500326e-102 < x < 1.018854104406312e-31

   1. Initial program 15.5

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
   2. Using strategy rm

   3. Applied sub-neg15.5

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

   4. Applied distribute-lft-in15.5

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

   5. Applied associate-+r+15.5

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

   6. Applied simplify16.0

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

   7. Taylor expanded around inf 10.4

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

   8. Applied simplify9.9

      \[\leadsto \color{blue}{(t \cdot \left(c \cdot j - x \cdot a\right) + \left(y \cdot \left(z \cdot x\right)\right))_* - (\left(z \cdot c - a \cdot i\right) \cdot b + \left(i \cdot \left(j \cdot y\right)\right))_*}\]
   9. Using strategy rm

   10. Applied associate-*r*9.1

       \[\leadsto (t \cdot \left(c \cdot j - x \cdot a\right) + \left(y \cdot \left(z \cdot x\right)\right))_* - (\left(z \cdot c - a \cdot i\right) \cdot b + \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)})_*\]
3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' +o rules:numerics
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))