Average Error: 16.0 → 7.8
Time: 21.7s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -1.9079071000270957 \cdot 10^{-242}:\\ \;\;\;\;\left(y + x\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 9.635345176449361 \cdot 10^{-222}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\frac{y}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -1.9079071000270957 \cdot 10^{-242}:\\
\;\;\;\;\left(y + x\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\

\mathbf{elif}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 9.635345176449361 \cdot 10^{-222}:\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r28828068 = x;
        double r28828069 = y;
        double r28828070 = r28828068 + r28828069;
        double r28828071 = z;
        double r28828072 = t;
        double r28828073 = r28828071 - r28828072;
        double r28828074 = r28828073 * r28828069;
        double r28828075 = a;
        double r28828076 = r28828075 - r28828072;
        double r28828077 = r28828074 / r28828076;
        double r28828078 = r28828070 - r28828077;
        return r28828078;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28828079 = y;
        double r28828080 = x;
        double r28828081 = r28828079 + r28828080;
        double r28828082 = z;
        double r28828083 = t;
        double r28828084 = r28828082 - r28828083;
        double r28828085 = r28828084 * r28828079;
        double r28828086 = a;
        double r28828087 = r28828086 - r28828083;
        double r28828088 = r28828085 / r28828087;
        double r28828089 = r28828081 - r28828088;
        double r28828090 = -1.9079071000270957e-242;
        bool r28828091 = r28828089 <= r28828090;
        double r28828092 = cbrt(r28828087);
        double r28828093 = r28828092 * r28828092;
        double r28828094 = r28828084 / r28828093;
        double r28828095 = r28828079 / r28828092;
        double r28828096 = r28828094 * r28828095;
        double r28828097 = r28828081 - r28828096;
        double r28828098 = 9.635345176449361e-222;
        bool r28828099 = r28828089 <= r28828098;
        double r28828100 = r28828082 * r28828079;
        double r28828101 = r28828100 / r28828083;
        double r28828102 = r28828101 + r28828080;
        double r28828103 = cbrt(r28828084);
        double r28828104 = r28828103 / r28828092;
        double r28828105 = r28828095 * r28828104;
        double r28828106 = r28828103 * r28828103;
        double r28828107 = r28828106 / r28828092;
        double r28828108 = r28828105 * r28828107;
        double r28828109 = r28828081 - r28828108;
        double r28828110 = r28828099 ? r28828102 : r28828109;
        double r28828111 = r28828091 ? r28828097 : r28828110;
        return r28828111;
}

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

Original16.0
Target8.1
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-07}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (+ x y) (/ (* (- z t) y) (- a t))) < -1.9079071000270957e-242

    1. Initial program 12.3

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

    3. Applied add-cube-cbrt12.5

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

    4. Applied times-frac7.1

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

    if -1.9079071000270957e-242 < (- (+ x y) (/ (* (- z t) y) (- a t))) < 9.635345176449361e-222

    1. Initial program 53.7

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

    2. Taylor expanded around inf 19.3

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

    if 9.635345176449361e-222 < (- (+ x y) (/ (* (- z t) y) (- a t)))

    1. Initial program 12.4

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

    3. Applied add-cube-cbrt12.6

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

    4. Applied times-frac7.0

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

    6. Applied add-cube-cbrt7.0

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

    7. Applied times-frac7.0

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

    8. Applied associate-*l*6.3

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

  4. Final simplification7.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le -1.9079071000270957 \cdot 10^{-242}:\\ \;\;\;\;\left(y + x\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;\left(y + x\right) - \frac{\left(z - t\right) \cdot y}{a - t} \le 9.635345176449361 \cdot 10^{-222}:\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\frac{y}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(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 (- 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))))