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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -1.2142764963497153 \cdot 10^{+208}:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\ \mathbf{elif}\;y \le 2.2006569390389888 \cdot 10^{+95}:\\ \;\;\;\;t + \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;y \le -1.2142764963497153 \cdot 10^{+208}:\\
\;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\

\mathbf{elif}\;y \le 2.2006569390389888 \cdot 10^{+95}:\\
\;\;\;\;t + \frac{\left(z - t\right) \cdot x}{y}\\

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

\end{array}

double f(double x, double y, double z, double t) {
        double r19090547 = x;
        double r19090548 = y;
        double r19090549 = r19090547 / r19090548;
        double r19090550 = z;
        double r19090551 = t;
        double r19090552 = r19090550 - r19090551;
        double r19090553 = r19090549 * r19090552;
        double r19090554 = r19090553 + r19090551;
        return r19090554;
}

↓

double f(double x, double y, double z, double t) {
        double r19090555 = y;
        double r19090556 = -1.2142764963497153e+208;
        bool r19090557 = r19090555 <= r19090556;
        double r19090558 = z;
        double r19090559 = t;
        double r19090560 = r19090558 - r19090559;
        double r19090561 = x;
        double r19090562 = r19090555 / r19090561;
        double r19090563 = r19090560 / r19090562;
        double r19090564 = r19090563 + r19090559;
        double r19090565 = 2.2006569390389888e+95;
        bool r19090566 = r19090555 <= r19090565;
        double r19090567 = r19090560 * r19090561;
        double r19090568 = r19090567 / r19090555;
        double r19090569 = r19090559 + r19090568;
        double r19090570 = r19090555 / r19090560;
        double r19090571 = r19090561 / r19090570;
        double r19090572 = r19090559 + r19090571;
        double r19090573 = r19090566 ? r19090569 : r19090572;
        double r19090574 = r19090557 ? r19090564 : r19090573;
        return r19090574;
}

Original	2.2
Target	2.4
Herbie	2.8

Derivation

Split input into 3 regimes
if y < -1.2142764963497153e+208
1. Initial program 1.8
  \[\frac{x}{y} \cdot \left(z - t\right) + t\]
2. Taylor expanded around 0 12.3
  \[\leadsto \color{blue}{\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right)} + t\]
3. Simplified1.8
  \[\leadsto \color{blue}{\frac{z - t}{\frac{y}{x}}} + t\]
if -1.2142764963497153e+208 < y < 2.2006569390389888e+95
1. Initial program 2.6
  \[\frac{x}{y} \cdot \left(z - t\right) + t\]
2. Using strategy rm
3. Applied associate-*l/3.4
  \[\leadsto \color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t\]
if 2.2006569390389888e+95 < y
1. Initial program 1.1
  \[\frac{x}{y} \cdot \left(z - t\right) + t\]
2. Using strategy rm
3. Applied associate-*l/10.9
  \[\leadsto \color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t\]
4. Using strategy rm
5. Applied associate-/l*1.5
  \[\leadsto \color{blue}{\frac{x}{\frac{y}{z - t}}} + t\]
Recombined 3 regimes into one program.
Final simplification2.8
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.2142764963497153 \cdot 10^{+208}:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\ \mathbf{elif}\;y \le 2.2006569390389888 \cdot 10^{+95}:\\ \;\;\;\;t + \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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 y < -1.2142764963497153e+208`

`if -1.2142764963497153e+208 < y < 2.2006569390389888e+95`

`if 2.2006569390389888e+95 < y`

Reproduce

In
Out