Average Error: 16.7 → 10.1
Time: 7.4s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.35463550198866496 \cdot 10^{129} \lor \neg \left(t \le 1.3792081327255185 \cdot 10^{60}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{y}}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.35463550198866496 \cdot 10^{129} \lor \neg \left(t \le 1.3792081327255185 \cdot 10^{60}\right):\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r564106 = x;
        double r564107 = y;
        double r564108 = r564106 + r564107;
        double r564109 = z;
        double r564110 = t;
        double r564111 = r564109 - r564110;
        double r564112 = r564111 * r564107;
        double r564113 = a;
        double r564114 = r564113 - r564110;
        double r564115 = r564112 / r564114;
        double r564116 = r564108 - r564115;
        return r564116;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r564117 = t;
        double r564118 = -1.354635501988665e+129;
        bool r564119 = r564117 <= r564118;
        double r564120 = 1.3792081327255185e+60;
        bool r564121 = r564117 <= r564120;
        double r564122 = !r564121;
        bool r564123 = r564119 || r564122;
        double r564124 = z;
        double r564125 = y;
        double r564126 = r564124 * r564125;
        double r564127 = r564126 / r564117;
        double r564128 = x;
        double r564129 = r564127 + r564128;
        double r564130 = r564128 + r564125;
        double r564131 = cbrt(r564125);
        double r564132 = r564131 * r564131;
        double r564133 = a;
        double r564134 = r564133 - r564117;
        double r564135 = cbrt(r564134);
        double r564136 = r564135 * r564135;
        double r564137 = r564132 / r564136;
        double r564138 = r564124 - r564117;
        double r564139 = r564135 / r564131;
        double r564140 = r564138 / r564139;
        double r564141 = r564137 * r564140;
        double r564142 = r564130 - r564141;
        double r564143 = r564123 ? r564129 : r564142;
        return r564143;
}

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

Original16.7
Target8.6
Herbie10.1
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.354635501988665e+129 or 1.3792081327255185e+60 < t

    1. Initial program 30.0

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

    2. Taylor expanded around inf 17.9

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

    if -1.354635501988665e+129 < t < 1.3792081327255185e+60

    1. Initial program 8.6

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

    3. Applied associate-/l*6.8

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

    5. Applied add-cube-cbrt7.0

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

    6. Applied add-cube-cbrt7.0

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

    7. Applied times-frac7.0

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

    8. Applied *-un-lft-identity7.0

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

    9. Applied times-frac5.4

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

    10. Simplified5.4

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

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.35463550198866496 \cdot 10^{129} \lor \neg \left(t \le 1.3792081327255185 \cdot 10^{60}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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))))