Average Error: 2.0 → 2.3
Time: 17.7s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -2.080547098596797432317128420294030987216 \cdot 10^{-53}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \le 6.621919932312076046507554334385359162004 \cdot 10^{-309}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \le -2.080547098596797432317128420294030987216 \cdot 10^{-53}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;\frac{z}{t} \le 6.621919932312076046507554334385359162004 \cdot 10^{-309}:\\
\;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r25904367 = x;
        double r25904368 = y;
        double r25904369 = r25904368 - r25904367;
        double r25904370 = z;
        double r25904371 = t;
        double r25904372 = r25904370 / r25904371;
        double r25904373 = r25904369 * r25904372;
        double r25904374 = r25904367 + r25904373;
        return r25904374;
}
↓
double f(double x, double y, double z, double t) {
        double r25904375 = z;
        double r25904376 = t;
        double r25904377 = r25904375 / r25904376;
        double r25904378 = -2.0805470985967974e-53;
        bool r25904379 = r25904377 <= r25904378;
        double r25904380 = x;
        double r25904381 = y;
        double r25904382 = r25904381 - r25904380;
        double r25904383 = r25904382 * r25904377;
        double r25904384 = r25904380 + r25904383;
        double r25904385 = 6.621919932312076e-309;
        bool r25904386 = r25904377 <= r25904385;
        double r25904387 = r25904382 * r25904375;
        double r25904388 = r25904387 / r25904376;
        double r25904389 = r25904388 + r25904380;
        double r25904390 = r25904386 ? r25904389 : r25904384;
        double r25904391 = r25904379 ? r25904384 : r25904390;
        return r25904391;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target2.2
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ z t) < -2.0805470985967974e-53 or 6.621919932312076e-309 < (/ z t)

    1. Initial program 2.1

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

    if -2.0805470985967974e-53 < (/ z t) < 6.621919932312076e-309

    1. Initial program 1.8

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

    3. Applied associate-*r/2.5

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -2.080547098596797432317128420294030987216 \cdot 10^{-53}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \le 6.621919932312076046507554334385359162004 \cdot 10^{-309}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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