Average Error: 1.3 → 1.4
Time: 27.2s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.347512852047913:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \mathbf{elif}\;t \le 2.7589848075703794 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.347512852047913:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\\

\mathbf{elif}\;t \le 2.7589848075703794 \cdot 10^{-216}:\\
\;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\

\mathbf{else}:\\
\;\;\;\;y \cdot \frac{z - t}{a - t} + x\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r25524801 = x;
        double r25524802 = y;
        double r25524803 = z;
        double r25524804 = t;
        double r25524805 = r25524803 - r25524804;
        double r25524806 = a;
        double r25524807 = r25524806 - r25524804;
        double r25524808 = r25524805 / r25524807;
        double r25524809 = r25524802 * r25524808;
        double r25524810 = r25524801 + r25524809;
        return r25524810;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25524811 = t;
        double r25524812 = -4.347512852047913;
        bool r25524813 = r25524811 <= r25524812;
        double r25524814 = x;
        double r25524815 = y;
        double r25524816 = a;
        double r25524817 = z;
        double r25524818 = r25524817 - r25524811;
        double r25524819 = r25524816 / r25524818;
        double r25524820 = r25524811 / r25524818;
        double r25524821 = r25524819 - r25524820;
        double r25524822 = r25524815 / r25524821;
        double r25524823 = r25524814 + r25524822;
        double r25524824 = 2.7589848075703794e-216;
        bool r25524825 = r25524811 <= r25524824;
        double r25524826 = r25524818 * r25524815;
        double r25524827 = r25524816 - r25524811;
        double r25524828 = r25524826 / r25524827;
        double r25524829 = r25524814 + r25524828;
        double r25524830 = r25524818 / r25524827;
        double r25524831 = r25524815 * r25524830;
        double r25524832 = r25524831 + r25524814;
        double r25524833 = r25524825 ? r25524829 : r25524832;
        double r25524834 = r25524813 ? r25524823 : r25524833;
        return r25524834;
}

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

Original1.3
Target0.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -4.347512852047913

    1. Initial program 0.1

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

    3. Applied associate-*r/16.2

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

    5. Applied associate-/l*0.1

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
    6. Using strategy rm

    7. Applied div-sub0.1

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

    if -4.347512852047913 < t < 2.7589848075703794e-216

    1. Initial program 3.2

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

    3. Applied associate-*r/3.4

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

    if 2.7589848075703794e-216 < t

    1. Initial program 0.7

      \[x + y \cdot \frac{z - t}{a - t}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.347512852047913:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \mathbf{elif}\;t \le 2.7589848075703794 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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