Average Error: 9.8 → 0.2
Time: 21.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} = -\infty:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \le 4.883366253508727 \cdot 10^{+293}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} = -\infty:\\
\;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\

\mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \le 4.883366253508727 \cdot 10^{+293}:\\
\;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\

\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 r21712673 = x;
        double r21712674 = y;
        double r21712675 = z;
        double r21712676 = t;
        double r21712677 = r21712675 - r21712676;
        double r21712678 = r21712674 * r21712677;
        double r21712679 = a;
        double r21712680 = r21712679 - r21712676;
        double r21712681 = r21712678 / r21712680;
        double r21712682 = r21712673 + r21712681;
        return r21712682;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r21712683 = z;
        double r21712684 = t;
        double r21712685 = r21712683 - r21712684;
        double r21712686 = y;
        double r21712687 = r21712685 * r21712686;
        double r21712688 = a;
        double r21712689 = r21712688 - r21712684;
        double r21712690 = r21712687 / r21712689;
        double r21712691 = -inf.0;
        bool r21712692 = r21712690 <= r21712691;
        double r21712693 = x;
        double r21712694 = r21712686 / r21712689;
        double r21712695 = r21712694 * r21712685;
        double r21712696 = r21712693 + r21712695;
        double r21712697 = 4.883366253508727e+293;
        bool r21712698 = r21712690 <= r21712697;
        double r21712699 = r21712690 + r21712693;
        double r21712700 = r21712685 / r21712689;
        double r21712701 = r21712686 * r21712700;
        double r21712702 = r21712701 + r21712693;
        double r21712703 = r21712698 ? r21712699 : r21712702;
        double r21712704 = r21712692 ? r21712696 : r21712703;
        return r21712704;
}

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

Original9.8
Target1.2
Herbie0.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* y (- z t)) (- a t)) < -inf.0

    1. Initial program 60.2

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

    2. Simplified0.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef0.1

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

    if -inf.0 < (/ (* y (- z t)) (- a t)) < 4.883366253508727e+293

    1. Initial program 0.2

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

    2. Simplified3.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef3.2

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

    6. Applied associate-*l/0.2

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

    if 4.883366253508727e+293 < (/ (* y (- z t)) (- a t))

    1. Initial program 58.0

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

    2. Simplified0.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef0.7

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

    6. Applied div-inv0.7

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

    7. Applied associate-*l*0.6

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

    8. Simplified0.5

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} = -\infty:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \le 4.883366253508727 \cdot 10^{+293}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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