Average Error: 6.0 → 1.3
Time: 20.7s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -1.538194312931815 \cdot 10^{+215}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 4.9051309220405685 \cdot 10^{+274}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -1.538194312931815 \cdot 10^{+215}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 4.9051309220405685 \cdot 10^{+274}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r21367451 = x;
        double r21367452 = y;
        double r21367453 = r21367452 - r21367451;
        double r21367454 = z;
        double r21367455 = r21367453 * r21367454;
        double r21367456 = t;
        double r21367457 = r21367455 / r21367456;
        double r21367458 = r21367451 + r21367457;
        return r21367458;
}
↓
double f(double x, double y, double z, double t) {
        double r21367459 = x;
        double r21367460 = y;
        double r21367461 = r21367460 - r21367459;
        double r21367462 = z;
        double r21367463 = r21367461 * r21367462;
        double r21367464 = t;
        double r21367465 = r21367463 / r21367464;
        double r21367466 = r21367459 + r21367465;
        double r21367467 = -1.538194312931815e+215;
        bool r21367468 = r21367466 <= r21367467;
        double r21367469 = r21367464 / r21367462;
        double r21367470 = r21367461 / r21367469;
        double r21367471 = r21367459 + r21367470;
        double r21367472 = 4.9051309220405685e+274;
        bool r21367473 = r21367466 <= r21367472;
        double r21367474 = r21367473 ? r21367466 : r21367471;
        double r21367475 = r21367468 ? r21367471 : r21367474;
        return r21367475;
}

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

Original6.0
Target2.0
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -1.538194312931815e+215 or 4.9051309220405685e+274 < (+ x (/ (* (- y x) z) t))

    1. Initial program 25.3

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

    3. Applied associate-/l*2.5

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

    if -1.538194312931815e+215 < (+ x (/ (* (- y x) z) t)) < 4.9051309220405685e+274

    1. Initial program 0.9

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -1.538194312931815 \cdot 10^{+215}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 4.9051309220405685 \cdot 10^{+274}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 +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)))