Average Error: 16.5 → 10.0
Time: 8.8s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.83393402370477073 \cdot 10^{176} \lor \neg \left(t \le 1.659061563989157 \cdot 10^{220}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}\right) \cdot \left(\left(\sqrt[3]{z - t} \cdot \sqrt[3]{\frac{1}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}\right) \cdot \frac{y}{\sqrt[3]{a - t}}\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.83393402370477073 \cdot 10^{176} \lor \neg \left(t \le 1.659061563989157 \cdot 10^{220}\right):\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r604164 = x;
        double r604165 = y;
        double r604166 = r604164 + r604165;
        double r604167 = z;
        double r604168 = t;
        double r604169 = r604167 - r604168;
        double r604170 = r604169 * r604165;
        double r604171 = a;
        double r604172 = r604171 - r604168;
        double r604173 = r604170 / r604172;
        double r604174 = r604166 - r604173;
        return r604174;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r604175 = t;
        double r604176 = -9.833934023704771e+176;
        bool r604177 = r604175 <= r604176;
        double r604178 = 1.659061563989157e+220;
        bool r604179 = r604175 <= r604178;
        double r604180 = !r604179;
        bool r604181 = r604177 || r604180;
        double r604182 = z;
        double r604183 = y;
        double r604184 = r604182 * r604183;
        double r604185 = r604184 / r604175;
        double r604186 = x;
        double r604187 = r604185 + r604186;
        double r604188 = r604186 + r604183;
        double r604189 = r604182 - r604175;
        double r604190 = a;
        double r604191 = r604190 - r604175;
        double r604192 = cbrt(r604191);
        double r604193 = r604192 * r604192;
        double r604194 = r604189 / r604193;
        double r604195 = cbrt(r604194);
        double r604196 = r604195 * r604195;
        double r604197 = cbrt(r604189);
        double r604198 = 1.0;
        double r604199 = r604198 / r604193;
        double r604200 = cbrt(r604199);
        double r604201 = r604197 * r604200;
        double r604202 = r604183 / r604192;
        double r604203 = r604201 * r604202;
        double r604204 = r604196 * r604203;
        double r604205 = r604188 - r604204;
        double r604206 = r604181 ? r604187 : r604205;
        return r604206;
}

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

Original16.5
Target8.4
Herbie10.0
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -9.833934023704771e+176 or 1.659061563989157e+220 < t

    1. Initial program 34.0

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

    2. Taylor expanded around inf 15.2

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

    if -9.833934023704771e+176 < t < 1.659061563989157e+220

    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-frac8.7

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

    6. Applied add-cube-cbrt8.7

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

    7. Applied associate-*l*8.7

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

    9. Applied div-inv8.7

      \[\leadsto \left(x + y\right) - \left(\sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}\right) \cdot \left(\sqrt[3]{\color{blue}{\left(z - t\right) \cdot \frac{1}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\]

    10. Applied cbrt-prod8.7

      \[\leadsto \left(x + y\right) - \left(\sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}\right) \cdot \left(\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{\frac{1}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}\right)} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.83393402370477073 \cdot 10^{176} \lor \neg \left(t \le 1.659061563989157 \cdot 10^{220}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}} \cdot \sqrt[3]{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}\right) \cdot \left(\left(\sqrt[3]{z - t} \cdot \sqrt[3]{\frac{1}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}\right) \cdot \frac{y}{\sqrt[3]{a - t}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(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))))