Average Error: 6.7 → 0.8
Time: 15.6s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.316175210633082378413674058419539304944 \cdot 10^{278}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\
\;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.316175210633082378413674058419539304944 \cdot 10^{278}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r26287752 = x;
        double r26287753 = y;
        double r26287754 = r26287753 - r26287752;
        double r26287755 = z;
        double r26287756 = r26287754 * r26287755;
        double r26287757 = t;
        double r26287758 = r26287756 / r26287757;
        double r26287759 = r26287752 + r26287758;
        return r26287759;
}
↓
double f(double x, double y, double z, double t) {
        double r26287760 = x;
        double r26287761 = y;
        double r26287762 = r26287761 - r26287760;
        double r26287763 = z;
        double r26287764 = r26287762 * r26287763;
        double r26287765 = t;
        double r26287766 = r26287764 / r26287765;
        double r26287767 = r26287760 + r26287766;
        double r26287768 = -inf.0;
        bool r26287769 = r26287767 <= r26287768;
        double r26287770 = r26287762 / r26287765;
        double r26287771 = fma(r26287770, r26287763, r26287760);
        double r26287772 = 1.3161752106330824e+278;
        bool r26287773 = r26287767 <= r26287772;
        double r26287774 = r26287763 / r26287765;
        double r26287775 = r26287762 * r26287774;
        double r26287776 = r26287760 + r26287775;
        double r26287777 = r26287773 ? r26287767 : r26287776;
        double r26287778 = r26287769 ? r26287771 : r26287777;
        return r26287778;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.7
Target2.1
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 64.0

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

    2. Simplified0.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)}\]

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 1.3161752106330824e+278

    1. Initial program 0.8

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

    if 1.3161752106330824e+278 < (+ x (/ (* (- y x) z) t))

    1. Initial program 41.6

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

    3. Applied *-un-lft-identity41.6

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

    4. Applied times-frac1.1

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

    5. Simplified1.1

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - x}{t}, z, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.316175210633082378413674058419539304944 \cdot 10^{278}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"

  :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)))