Average Error: 2.0 → 2.0
Time: 4.9s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.64219457899372803 \cdot 10^{-224} \lor \neg \left(x \le 1.6257691218099716 \cdot 10^{-308}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.64219457899372803 \cdot 10^{-224} \lor \neg \left(x \le 1.6257691218099716 \cdot 10^{-308}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r547621 = x;
        double r547622 = y;
        double r547623 = r547622 - r547621;
        double r547624 = z;
        double r547625 = t;
        double r547626 = r547624 / r547625;
        double r547627 = r547623 * r547626;
        double r547628 = r547621 + r547627;
        return r547628;
}
↓
double f(double x, double y, double z, double t) {
        double r547629 = x;
        double r547630 = -8.642194578993728e-224;
        bool r547631 = r547629 <= r547630;
        double r547632 = 1.6257691218099716e-308;
        bool r547633 = r547629 <= r547632;
        double r547634 = !r547633;
        bool r547635 = r547631 || r547634;
        double r547636 = y;
        double r547637 = r547636 - r547629;
        double r547638 = z;
        double r547639 = t;
        double r547640 = r547638 / r547639;
        double r547641 = r547637 * r547640;
        double r547642 = r547629 + r547641;
        double r547643 = r547637 * r547638;
        double r547644 = r547643 / r547639;
        double r547645 = r547629 + r547644;
        double r547646 = r547635 ? r547642 : r547645;
        return r547646;
}

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
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -8.642194578993728e-224 or 1.6257691218099716e-308 < x

    1. Initial program 1.7

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

    if -8.642194578993728e-224 < x < 1.6257691218099716e-308

    1. Initial program 6.0

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

    3. Applied associate-*r/5.5

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.64219457899372803 \cdot 10^{-224} \lor \neg \left(x \le 1.6257691218099716 \cdot 10^{-308}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ 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))))