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

⬇

\[\begin{array}{l} \mathbf{if}\;x \le -1.3209176906660093 \cdot 10^{-170}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}} + x\\ \mathbf{if}\;x \le 2.0581640871701446 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \end{array}\]

Original	6.4
Comparison	2.0
Herbie	2.1

Derivation

Split input into 3 regimes.
if x < -1.3209176906660093e-170
1. Initial program 6.7
  \[x + \frac{y \cdot \left(z - x\right)}{t}\]
2. Applied taylor 6.7
  \[\leadsto x + \left(\frac{y \cdot z}{t} - \frac{y \cdot x}{t}\right)\]
3. Taylor expanded around 0 6.7
  
  \[\leadsto x + \color{blue}{\left(\frac{y \cdot z}{t} - \frac{y \cdot x}{t}\right)}\]
4. Applied simplify 0.7
  \[\leadsto \color{blue}{\frac{z - x}{\frac{t}{y}} + x}\]
if -1.3209176906660093e-170 < x < 2.0581640871701446e-95
1. Initial program 5.2
  \[x + \frac{y \cdot \left(z - x\right)}{t}\]
if 2.0581640871701446e-95 < x
1. Initial program 7.3
  \[x + \frac{y \cdot \left(z - x\right)}{t}\]
2. Applied taylor 7.3
  \[\leadsto x + \frac{y \cdot z - y \cdot x}{t}\]
3. Taylor expanded around 0 7.3
  
  \[\leadsto x + \frac{\color{blue}{y \cdot z - y \cdot x}}{t}\]
4. Applied simplify 0.3
  \[\leadsto \color{blue}{\frac{y}{t} \cdot \left(z - x\right) + x}\]
Recombined 3 regimes into one program.
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie --seed '#(3177963436 888103403 3093071472 2189699733 2284055197 1183748214)'
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

  :target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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

Error

Target

Derivation

`if x < -1.3209176906660093e-170`

`if -1.3209176906660093e-170 < x < 2.0581640871701446e-95`

`if 2.0581640871701446e-95 < x`

Runtime