Average Error: 1.5 → 1.7
Time: 15.9s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.993850181954760056083277772969421378107 \cdot 10^{-198}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.993850181954760056083277772969421378107 \cdot 10^{-198}:\\
\;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r382665 = x;
        double r382666 = y;
        double r382667 = z;
        double r382668 = t;
        double r382669 = r382667 - r382668;
        double r382670 = a;
        double r382671 = r382670 - r382668;
        double r382672 = r382669 / r382671;
        double r382673 = r382666 * r382672;
        double r382674 = r382665 + r382673;
        return r382674;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r382675 = x;
        double r382676 = -5.99385018195476e-198;
        bool r382677 = r382675 <= r382676;
        double r382678 = z;
        double r382679 = t;
        double r382680 = r382678 - r382679;
        double r382681 = y;
        double r382682 = a;
        double r382683 = r382682 - r382679;
        double r382684 = r382681 / r382683;
        double r382685 = r382680 * r382684;
        double r382686 = r382675 + r382685;
        double r382687 = r382680 / r382683;
        double r382688 = r382681 * r382687;
        double r382689 = r382675 + r382688;
        double r382690 = r382677 ? r382686 : r382689;
        return r382690;
}

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

Original1.5
Target0.4
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -5.99385018195476e-198

    1. Initial program 1.4

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

    3. Applied pow11.4

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

    4. Applied pow11.4

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

    5. Applied pow-prod-down1.4

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

    6. Simplified2.0

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

    if -5.99385018195476e-198 < x

    1. Initial program 1.6

      \[x + y \cdot \frac{z - t}{a - t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.993850181954760056083277772969421378107 \cdot 10^{-198}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :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)))))