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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -3.272866911045129122978132119226252506887 \cdot 10^{-275} \lor \neg \left(a \le 7.950219722796376295483377232937300519992 \cdot 10^{-173}\right):\\ \;\;\;\;x + \left(y - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a \le -3.272866911045129122978132119226252506887 \cdot 10^{-275} \lor \neg \left(a \le 7.950219722796376295483377232937300519992 \cdot 10^{-173}\right):\\
\;\;\;\;x + \left(y - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r470620 = x;
        double r470621 = y;
        double r470622 = r470620 + r470621;
        double r470623 = z;
        double r470624 = t;
        double r470625 = r470623 - r470624;
        double r470626 = r470625 * r470621;
        double r470627 = a;
        double r470628 = r470627 - r470624;
        double r470629 = r470626 / r470628;
        double r470630 = r470622 - r470629;
        return r470630;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r470631 = a;
        double r470632 = -3.272866911045129e-275;
        bool r470633 = r470631 <= r470632;
        double r470634 = 7.950219722796376e-173;
        bool r470635 = r470631 <= r470634;
        double r470636 = !r470635;
        bool r470637 = r470633 || r470636;
        double r470638 = x;
        double r470639 = y;
        double r470640 = z;
        double r470641 = t;
        double r470642 = r470640 - r470641;
        double r470643 = cbrt(r470642);
        double r470644 = r470643 * r470643;
        double r470645 = r470631 - r470641;
        double r470646 = cbrt(r470645);
        double r470647 = r470644 / r470646;
        double r470648 = r470643 / r470646;
        double r470649 = r470639 / r470646;
        double r470650 = r470648 * r470649;
        double r470651 = r470647 * r470650;
        double r470652 = r470639 - r470651;
        double r470653 = r470638 + r470652;
        double r470654 = r470640 * r470639;
        double r470655 = r470654 / r470641;
        double r470656 = r470655 + r470638;
        double r470657 = r470637 ? r470653 : r470656;
        return r470657;
}

Original	16.6
Target	8.5
Herbie	7.4

Derivation

Split input into 2 regimes
if a < -3.272866911045129e-275 or 7.950219722796376e-173 < a
1. Initial program 16.1
  \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
2. Using strategy rm
3. Applied add-cube-cbrt16.3
  \[\leadsto \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}\]
4. Applied times-frac10.6
  \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}}\]
5. Using strategy rm
6. Applied add-cube-cbrt10.6
  \[\leadsto \left(x + y\right) - \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\]
7. Applied times-frac10.6
  \[\leadsto \left(x + y\right) - \color{blue}{\left(\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\right)} \cdot \frac{y}{\sqrt[3]{a - t}}\]
8. Applied associate-*l*10.2
  \[\leadsto \left(x + y\right) - \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)}\]
9. Using strategy rm
10. Applied associate--l+7.3
  \[\leadsto \color{blue}{x + \left(y - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)}\]
if -3.272866911045129e-275 < a < 7.950219722796376e-173
1. Initial program 19.9
  \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
2. Taylor expanded around inf 7.9
  \[\leadsto \color{blue}{\frac{z \cdot y}{t} + x}\]
Recombined 2 regimes into one program.
Final simplification7.4
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.272866911045129122978132119226252506887 \cdot 10^{-275} \lor \neg \left(a \le 7.950219722796376295483377232937300519992 \cdot 10^{-173}\right):\\ \;\;\;\;x + \left(y - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019308 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.47542934445772333e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y))))

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

Error

Try it out

Target

Derivation

`if a < -3.272866911045129e-275 or 7.950219722796376e-173 < a`

`if -3.272866911045129e-275 < a < 7.950219722796376e-173`

Reproduce

In
Out