Average Error: 6.5 → 2.1
Time: 3.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.5028999843123688 \cdot 10^{-201} \lor \neg \left(x \le 5.86993056876950949 \cdot 10^{-45}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.5028999843123688 \cdot 10^{-201} \lor \neg \left(x \le 5.86993056876950949 \cdot 10^{-45}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r404594 = x;
        double r404595 = y;
        double r404596 = r404595 - r404594;
        double r404597 = z;
        double r404598 = r404596 * r404597;
        double r404599 = t;
        double r404600 = r404598 / r404599;
        double r404601 = r404594 + r404600;
        return r404601;
}
↓
double f(double x, double y, double z, double t) {
        double r404602 = x;
        double r404603 = -1.5028999843123688e-201;
        bool r404604 = r404602 <= r404603;
        double r404605 = 5.86993056876951e-45;
        bool r404606 = r404602 <= r404605;
        double r404607 = !r404606;
        bool r404608 = r404604 || r404607;
        double r404609 = y;
        double r404610 = r404609 - r404602;
        double r404611 = z;
        double r404612 = t;
        double r404613 = r404611 / r404612;
        double r404614 = r404610 * r404613;
        double r404615 = r404602 + r404614;
        double r404616 = 1.0;
        double r404617 = r404610 * r404611;
        double r404618 = r404612 / r404617;
        double r404619 = r404616 / r404618;
        double r404620 = r404602 + r404619;
        double r404621 = r404608 ? r404615 : r404620;
        return r404621;
}

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

Original6.5
Target1.8
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.5028999843123688e-201 or 5.86993056876951e-45 < x

    1. Initial program 7.4

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

    3. Applied *-un-lft-identity7.4

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

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

    if -1.5028999843123688e-201 < x < 5.86993056876951e-45

    1. Initial program 4.5

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

    3. Applied clear-num4.6

      \[\leadsto x + \color{blue}{\frac{1}{\frac{t}{\left(y - x\right) \cdot z}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.5028999843123688 \cdot 10^{-201} \lor \neg \left(x \le 5.86993056876950949 \cdot 10^{-45}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(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)))