Average Error: 16.2 → 9.8
Time: 29.4s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.865242998422085 \cdot 10^{154} \lor \neg \left(t \le 1.0244000647700889 \cdot 10^{201}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{z - t}{\frac{a - t}{\sqrt[3]{y}}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.865242998422085 \cdot 10^{154} \lor \neg \left(t \le 1.0244000647700889 \cdot 10^{201}\right):\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r474119 = x;
        double r474120 = y;
        double r474121 = r474119 + r474120;
        double r474122 = z;
        double r474123 = t;
        double r474124 = r474122 - r474123;
        double r474125 = r474124 * r474120;
        double r474126 = a;
        double r474127 = r474126 - r474123;
        double r474128 = r474125 / r474127;
        double r474129 = r474121 - r474128;
        return r474129;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r474130 = t;
        double r474131 = -9.865242998422085e+154;
        bool r474132 = r474130 <= r474131;
        double r474133 = 1.024400064770089e+201;
        bool r474134 = r474130 <= r474133;
        double r474135 = !r474134;
        bool r474136 = r474132 || r474135;
        double r474137 = z;
        double r474138 = y;
        double r474139 = r474137 * r474138;
        double r474140 = r474139 / r474130;
        double r474141 = x;
        double r474142 = r474140 + r474141;
        double r474143 = r474141 + r474138;
        double r474144 = cbrt(r474138);
        double r474145 = r474144 * r474144;
        double r474146 = r474137 - r474130;
        double r474147 = a;
        double r474148 = r474147 - r474130;
        double r474149 = r474148 / r474144;
        double r474150 = r474146 / r474149;
        double r474151 = r474145 * r474150;
        double r474152 = r474143 - r474151;
        double r474153 = r474136 ? r474142 : r474152;
        return r474153;
}

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

Original16.2
Target8.2
Herbie9.8
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -9.865242998422085e+154 or 1.024400064770089e+201 < t

    1. Initial program 31.6

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

    2. Taylor expanded around inf 16.5

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

    if -9.865242998422085e+154 < t < 1.024400064770089e+201

    1. Initial program 11.7

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

    3. Applied associate-/l*8.5

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

    5. Applied add-cube-cbrt8.7

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

    6. Applied *-un-lft-identity8.7

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

    7. Applied times-frac8.7

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

    8. Applied *-un-lft-identity8.7

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

    9. Applied times-frac7.8

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

    10. Simplified7.8

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

  4. Final simplification9.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.865242998422085 \cdot 10^{154} \lor \neg \left(t \le 1.0244000647700889 \cdot 10^{201}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{z - t}{\frac{a - t}{\sqrt[3]{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(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))))