Average Error: 6.6 → 2.5
Time: 4.4s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2409170190487766637167962488832:\\ \;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\ \mathbf{elif}\;t \le 1.625406329571911990929648461559105916592 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{1}{t} \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2409170190487766637167962488832:\\
\;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\

\mathbf{elif}\;t \le 1.625406329571911990929648461559105916592 \cdot 10^{-217}:\\
\;\;\;\;x + \frac{1}{t} \cdot \left(\left(y - x\right) \cdot z\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r580711 = x;
        double r580712 = y;
        double r580713 = r580712 - r580711;
        double r580714 = z;
        double r580715 = r580713 * r580714;
        double r580716 = t;
        double r580717 = r580715 / r580716;
        double r580718 = r580711 + r580717;
        return r580718;
}
↓
double f(double x, double y, double z, double t) {
        double r580719 = t;
        double r580720 = -2.4091701904877666e+30;
        bool r580721 = r580719 <= r580720;
        double r580722 = x;
        double r580723 = y;
        double r580724 = r580723 - r580722;
        double r580725 = r580724 / r580719;
        double r580726 = 1.0;
        double r580727 = z;
        double r580728 = r580726 / r580727;
        double r580729 = r580725 / r580728;
        double r580730 = r580722 + r580729;
        double r580731 = 1.625406329571912e-217;
        bool r580732 = r580719 <= r580731;
        double r580733 = r580726 / r580719;
        double r580734 = r580724 * r580727;
        double r580735 = r580733 * r580734;
        double r580736 = r580722 + r580735;
        double r580737 = cbrt(r580719);
        double r580738 = r580737 * r580737;
        double r580739 = r580724 / r580738;
        double r580740 = r580727 / r580737;
        double r580741 = r580739 * r580740;
        double r580742 = r580722 + r580741;
        double r580743 = r580732 ? r580736 : r580742;
        double r580744 = r580721 ? r580730 : r580743;
        return r580744;
}

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

Original6.6
Target2.0
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -2.4091701904877666e+30

    1. Initial program 10.3

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

    3. Applied associate-/l*1.4

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
    4. Using strategy rm

    5. Applied div-inv1.4

      \[\leadsto x + \frac{y - x}{\color{blue}{t \cdot \frac{1}{z}}}\]

    6. Applied associate-/r*1.2

      \[\leadsto x + \color{blue}{\frac{\frac{y - x}{t}}{\frac{1}{z}}}\]

    if -2.4091701904877666e+30 < t < 1.625406329571912e-217

    1. Initial program 1.9

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

    3. Applied associate-/l*3.2

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
    4. Using strategy rm

    5. Applied div-inv3.3

      \[\leadsto x + \frac{y - x}{\color{blue}{t \cdot \frac{1}{z}}}\]

    6. Applied *-un-lft-identity3.3

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

    7. Applied times-frac2.0

      \[\leadsto x + \color{blue}{\frac{1}{t} \cdot \frac{y - x}{\frac{1}{z}}}\]

    8. Simplified1.9

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

    if 1.625406329571912e-217 < t

    1. Initial program 6.8

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

    3. Applied add-cube-cbrt7.2

      \[\leadsto x + \frac{\left(y - x\right) \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\]

    4. Applied times-frac3.7

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2409170190487766637167962488832:\\ \;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\ \mathbf{elif}\;t \le 1.625406329571911990929648461559105916592 \cdot 10^{-217}:\\ \;\;\;\;x + \frac{1}{t} \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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