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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -2.429342480740140650041385945281389977987 \cdot 10^{-176} \lor \neg \left(t \le 3.038275486400102813641711171286818002615 \cdot 10^{-154}\right):\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;t \le -2.429342480740140650041385945281389977987 \cdot 10^{-176} \lor \neg \left(t \le 3.038275486400102813641711171286818002615 \cdot 10^{-154}\right):\\
\;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\

\end{array}

double f(double x, double y, double z, double t) {
        double r359251 = x;
        double r359252 = y;
        double r359253 = r359251 / r359252;
        double r359254 = z;
        double r359255 = t;
        double r359256 = r359254 - r359255;
        double r359257 = r359253 * r359256;
        double r359258 = r359257 + r359255;
        return r359258;
}

↓

double f(double x, double y, double z, double t) {
        double r359259 = t;
        double r359260 = -2.4293424807401407e-176;
        bool r359261 = r359259 <= r359260;
        double r359262 = 3.038275486400103e-154;
        bool r359263 = r359259 <= r359262;
        double r359264 = !r359263;
        bool r359265 = r359261 || r359264;
        double r359266 = z;
        double r359267 = r359266 - r359259;
        double r359268 = x;
        double r359269 = y;
        double r359270 = r359268 / r359269;
        double r359271 = r359267 * r359270;
        double r359272 = r359259 + r359271;
        double r359273 = r359269 / r359267;
        double r359274 = r359268 / r359273;
        double r359275 = r359274 + r359259;
        double r359276 = r359265 ? r359272 : r359275;
        return r359276;
}

Original	2.1
Target	2.4
Herbie	1.8

Derivation

Split input into 2 regimes
if t < -2.4293424807401407e-176 or 3.038275486400103e-154 < t
1. Initial program 0.9
  \[\frac{x}{y} \cdot \left(z - t\right) + t\]
if -2.4293424807401407e-176 < t < 3.038275486400103e-154
1. Initial program 5.6
  \[\frac{x}{y} \cdot \left(z - t\right) + t\]
2. Using strategy rm
3. Applied *-un-lft-identity5.6
  \[\leadsto \frac{x}{\color{blue}{1 \cdot y}} \cdot \left(z - t\right) + t\]
4. Applied *-un-lft-identity5.6
  \[\leadsto \frac{\color{blue}{1 \cdot x}}{1 \cdot y} \cdot \left(z - t\right) + t\]
5. Applied times-frac5.6
  \[\leadsto \color{blue}{\left(\frac{1}{1} \cdot \frac{x}{y}\right)} \cdot \left(z - t\right) + t\]
6. Applied associate-*l*5.6
  \[\leadsto \color{blue}{\frac{1}{1} \cdot \left(\frac{x}{y} \cdot \left(z - t\right)\right)} + t\]
7. Simplified4.6
  \[\leadsto \frac{1}{1} \cdot \color{blue}{\frac{x}{\frac{y}{z - t}}} + t\]
Recombined 2 regimes into one program.
Final simplification1.8
\[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.429342480740140650041385945281389977987 \cdot 10^{-176} \lor \neg \left(t \le 3.038275486400102813641711171286818002615 \cdot 10^{-154}\right):\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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

Error

Try it out

Target

Derivation

`if t < -2.4293424807401407e-176 or 3.038275486400103e-154 < t`

`if -2.4293424807401407e-176 < t < 3.038275486400103e-154`

Reproduce

In
Out