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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -7.749546496277327553262645487066184764923 \cdot 10^{-262}:\\ \;\;\;\;\left(\sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right) \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} + x\\ \mathbf{elif}\;a \le 1.48761764606288953371074253554655075554 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right) \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} + x\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a \le -7.749546496277327553262645487066184764923 \cdot 10^{-262}:\\
\;\;\;\;\left(\sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right) \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} + x\\

\mathbf{elif}\;a \le 1.48761764606288953371074253554655075554 \cdot 10^{-89}:\\
\;\;\;\;x + \frac{y \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right) \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} + x\\

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r30125187 = x;
        double r30125188 = y;
        double r30125189 = r30125187 + r30125188;
        double r30125190 = z;
        double r30125191 = t;
        double r30125192 = r30125190 - r30125191;
        double r30125193 = r30125192 * r30125188;
        double r30125194 = a;
        double r30125195 = r30125194 - r30125191;
        double r30125196 = r30125193 / r30125195;
        double r30125197 = r30125189 - r30125196;
        return r30125197;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r30125198 = a;
        double r30125199 = -7.749546496277328e-262;
        bool r30125200 = r30125198 <= r30125199;
        double r30125201 = y;
        double r30125202 = 1.0;
        double r30125203 = t;
        double r30125204 = r30125198 - r30125203;
        double r30125205 = r30125204 / r30125201;
        double r30125206 = z;
        double r30125207 = r30125206 - r30125203;
        double r30125208 = r30125205 / r30125207;
        double r30125209 = r30125202 / r30125208;
        double r30125210 = r30125201 - r30125209;
        double r30125211 = cbrt(r30125210);
        double r30125212 = r30125211 * r30125211;
        double r30125213 = r30125212 * r30125211;
        double r30125214 = x;
        double r30125215 = r30125213 + r30125214;
        double r30125216 = 1.4876176460628895e-89;
        bool r30125217 = r30125198 <= r30125216;
        double r30125218 = r30125201 * r30125206;
        double r30125219 = r30125218 / r30125203;
        double r30125220 = r30125214 + r30125219;
        double r30125221 = r30125217 ? r30125220 : r30125215;
        double r30125222 = r30125200 ? r30125215 : r30125221;
        return r30125222;
}

Original	16.3
Target	8.5
Herbie	9.6

Derivation

Split input into 2 regimes
if a < -7.749546496277328e-262 or 1.4876176460628895e-89 < a
1. Initial program 15.5
  \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
2. Using strategy rm
3. Applied associate-/l*10.3
  \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\]
4. Using strategy rm
5. Applied associate--l+8.2
  \[\leadsto \color{blue}{x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)}\]
6. Using strategy rm
7. Applied clear-num8.5
  \[\leadsto x + \left(y - \color{blue}{\frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right)\]
8. Using strategy rm
9. Applied add-cube-cbrt9.0
  \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right) \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}}\]
if -7.749546496277328e-262 < a < 1.4876176460628895e-89
1. Initial program 19.5
  \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
2. Using strategy rm
3. Applied associate-/l*18.4
  \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\frac{a - t}{y}}}\]
4. Using strategy rm
5. Applied associate--l+12.7
  \[\leadsto \color{blue}{x + \left(y - \frac{z - t}{\frac{a - t}{y}}\right)}\]
6. Taylor expanded around inf 12.1
  \[\leadsto x + \color{blue}{\frac{z \cdot y}{t}}\]
Recombined 2 regimes into one program.
Final simplification9.6
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.749546496277327553262645487066184764923 \cdot 10^{-262}:\\ \;\;\;\;\left(\sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right) \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} + x\\ \mathbf{elif}\;a \le 1.48761764606288953371074253554655075554 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}}\right) \cdot \sqrt[3]{y - \frac{1}{\frac{\frac{a - t}{y}}{z - t}}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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

Error

Try it out

Target

Derivation

`if a < -7.749546496277328e-262 or 1.4876176460628895e-89 < a`

`if -7.749546496277328e-262 < a < 1.4876176460628895e-89`

Reproduce

In
Out