Average Error: 6.2 → 1.0
Time: 4.6s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.21688783645265377 \cdot 10^{-84}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.21688783645265377 \cdot 10^{-84}\right):\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r464438 = x;
        double r464439 = y;
        double r464440 = r464439 - r464438;
        double r464441 = z;
        double r464442 = r464440 * r464441;
        double r464443 = t;
        double r464444 = r464442 / r464443;
        double r464445 = r464438 + r464444;
        return r464445;
}
↓
double f(double x, double y, double z, double t) {
        double r464446 = x;
        double r464447 = y;
        double r464448 = r464447 - r464446;
        double r464449 = z;
        double r464450 = r464448 * r464449;
        double r464451 = t;
        double r464452 = r464450 / r464451;
        double r464453 = r464446 + r464452;
        double r464454 = -inf.0;
        bool r464455 = r464453 <= r464454;
        double r464456 = 4.216887836452654e-84;
        bool r464457 = r464453 <= r464456;
        double r464458 = !r464457;
        bool r464459 = r464455 || r464458;
        double r464460 = r464451 / r464449;
        double r464461 = r464448 / r464460;
        double r464462 = r464446 + r464461;
        double r464463 = r464459 ? r464462 : r464453;
        return r464463;
}

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

Original6.2
Target2.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -inf.0 or 4.216887836452654e-84 < (+ x (/ (* (- y x) z) t))

    1. Initial program 12.8

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

    3. Applied associate-/l*1.4

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 4.216887836452654e-84

    1. Initial program 0.7

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.21688783645265377 \cdot 10^{-84}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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)))