Average Error: 16.4 → 10.3
Time: 9.1s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.2963627054695715 \cdot 10^{105} \lor \neg \left(t \le 2.2171165764838755 \cdot 10^{119}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \left(\sqrt[3]{z - t} \cdot y\right)}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{a - t}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.2963627054695715 \cdot 10^{105} \lor \neg \left(t \le 2.2171165764838755 \cdot 10^{119}\right):\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r608230 = x;
        double r608231 = y;
        double r608232 = r608230 + r608231;
        double r608233 = z;
        double r608234 = t;
        double r608235 = r608233 - r608234;
        double r608236 = r608235 * r608231;
        double r608237 = a;
        double r608238 = r608237 - r608234;
        double r608239 = r608236 / r608238;
        double r608240 = r608232 - r608239;
        return r608240;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r608241 = t;
        double r608242 = -1.2963627054695715e+105;
        bool r608243 = r608241 <= r608242;
        double r608244 = 2.2171165764838755e+119;
        bool r608245 = r608241 <= r608244;
        double r608246 = !r608245;
        bool r608247 = r608243 || r608246;
        double r608248 = z;
        double r608249 = y;
        double r608250 = r608248 * r608249;
        double r608251 = r608250 / r608241;
        double r608252 = x;
        double r608253 = r608251 + r608252;
        double r608254 = r608252 + r608249;
        double r608255 = r608248 - r608241;
        double r608256 = cbrt(r608255);
        double r608257 = r608256 * r608256;
        double r608258 = a;
        double r608259 = r608258 - r608241;
        double r608260 = cbrt(r608259);
        double r608261 = r608260 * r608260;
        double r608262 = cbrt(r608261);
        double r608263 = r608260 * r608262;
        double r608264 = r608257 / r608263;
        double r608265 = r608256 * r608249;
        double r608266 = r608264 * r608265;
        double r608267 = cbrt(r608260);
        double r608268 = r608267 * r608260;
        double r608269 = r608266 / r608268;
        double r608270 = r608254 - r608269;
        double r608271 = r608247 ? r608253 : r608270;
        return r608271;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.4
Target8.5
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.2963627054695715e+105 or 2.2171165764838755e+119 < t

    1. Initial program 30.3

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

    2. Taylor expanded around inf 17.2

      \[\leadsto \color{blue}{\frac{z \cdot y}{t} + x}\]

    if -1.2963627054695715e+105 < t < 2.2171165764838755e+119

    1. Initial program 9.2

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt9.3

      \[\leadsto \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}\]

    4. Applied times-frac6.2

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt6.2

      \[\leadsto \left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}} \cdot \frac{y}{\sqrt[3]{a - t}}\]

    7. Applied cbrt-prod6.3

      \[\leadsto \left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}\right)}} \cdot \frac{y}{\sqrt[3]{a - t}}\]

    8. Applied associate-*r*6.3

      \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \sqrt[3]{\sqrt[3]{a - t}}}} \cdot \frac{y}{\sqrt[3]{a - t}}\]
    9. Using strategy rm

    10. Applied add-cube-cbrt6.3

      \[\leadsto \left(x + y\right) - \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right) \cdot \sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{y}{\sqrt[3]{a - t}}\]

    11. Applied times-frac6.3

      \[\leadsto \left(x + y\right) - \color{blue}{\left(\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}}}\right)} \cdot \frac{y}{\sqrt[3]{a - t}}\]

    12. Applied associate-*l*5.4

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{\sqrt[3]{a - t}}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)}\]
    13. Using strategy rm

    14. Applied frac-times6.0

      \[\leadsto \left(x + y\right) - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \color{blue}{\frac{\sqrt[3]{z - t} \cdot y}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{a - t}}}\]

    15. Applied associate-*r/6.7

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \left(\sqrt[3]{z - t} \cdot y\right)}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{a - t}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.2963627054695715 \cdot 10^{105} \lor \neg \left(t \le 2.2171165764838755 \cdot 10^{119}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \left(\sqrt[3]{z - t} \cdot y\right)}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{a - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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-07) (- (+ y x) (* (* (- z t) (/ 1 (- 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 (- a t))) y))))

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