Error

Target

Derivation

1. Split input into 2 regimes

2. if y < -2.5055034693753377e-107 or 4.4400627125562316e-139 < y

   1. Initial program 0.9

      \[\frac{x - y}{z - y} \cdot t\]

   if -2.5055034693753377e-107 < y < 4.4400627125562316e-139

   1. Initial program 5.3

      \[\frac{x - y}{z - y} \cdot t\]
   2. Using strategy rm

   3. Applied *-un-lft-identity5.3

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

   4. Applied add-cube-cbrt6.2

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{1 \cdot \left(z - y\right)} \cdot t\]

   5. Applied times-frac6.2

      \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{1} \cdot \frac{\sqrt[3]{x - y}}{z - y}\right)} \cdot t\]

   6. Applied associate-*l*4.9

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{1} \cdot \left(\frac{\sqrt[3]{x - y}}{z - y} \cdot t\right)}\]
   7. Using strategy rm

   8. Applied associate-*l/5.4

      \[\leadsto \frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{1} \cdot \color{blue}{\frac{\sqrt[3]{x - y} \cdot t}{z - y}}\]

   9. Applied associate-*r/6.8

      \[\leadsto \color{blue}{\frac{\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{1} \cdot \left(\sqrt[3]{x - y} \cdot t\right)}{z - y}}\]

   10. Applied simplify6.1

       \[\leadsto \frac{\color{blue}{\frac{x - y}{\frac{1}{t}}}}{z - y}\]
3. Recombined 2 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 50.2s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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