Average Error: 1.3 → 1.4
Time: 18.9s
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 r25498967 = x;
        double r25498968 = y;
        double r25498969 = z;
        double r25498970 = t;
        double r25498971 = r25498969 - r25498970;
        double r25498972 = a;
        double r25498973 = r25498972 - r25498970;
        double r25498974 = r25498971 / r25498973;
        double r25498975 = r25498968 * r25498974;
        double r25498976 = r25498967 + r25498975;
        return r25498976;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25498977 = t;
        double r25498978 = -4.347512852047913;
        bool r25498979 = r25498977 <= r25498978;
        double r25498980 = x;
        double r25498981 = y;
        double r25498982 = a;
        double r25498983 = z;
        double r25498984 = r25498983 - r25498977;
        double r25498985 = r25498982 / r25498984;
        double r25498986 = r25498977 / r25498984;
        double r25498987 = r25498985 - r25498986;
        double r25498988 = r25498981 / r25498987;
        double r25498989 = r25498980 + r25498988;
        double r25498990 = 2.7589848075703794e-216;
        bool r25498991 = r25498977 <= r25498990;
        double r25498992 = r25498984 * r25498981;
        double r25498993 = r25498982 - r25498977;
        double r25498994 = r25498992 / r25498993;
        double r25498995 = r25498980 + r25498994;
        double r25498996 = r25498984 / r25498993;
        double r25498997 = r25498981 * r25498996;
        double r25498998 = r25498997 + r25498980;
        double r25498999 = r25498991 ? r25498995 : r25498998;
        double r25499000 = r25498979 ? r25498989 : r25498999;
        return r25499000;
}

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 
(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)))))