Average Error: 6.4 → 1.6
Time: 3.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -7.42763758103976 \cdot 10^{67} \lor \neg \left(z \le 2.3482764413141227 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le -7.42763758103976 \cdot 10^{67} \lor \neg \left(z \le 2.3482764413141227 \cdot 10^{-34}\right):\\
\;\;\;\;x + \frac{y - x}{t} \cdot z\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r500578 = x;
        double r500579 = y;
        double r500580 = r500579 - r500578;
        double r500581 = z;
        double r500582 = r500580 * r500581;
        double r500583 = t;
        double r500584 = r500582 / r500583;
        double r500585 = r500578 + r500584;
        return r500585;
}
↓
double f(double x, double y, double z, double t) {
        double r500586 = z;
        double r500587 = -7.42763758103976e+67;
        bool r500588 = r500586 <= r500587;
        double r500589 = 2.3482764413141227e-34;
        bool r500590 = r500586 <= r500589;
        double r500591 = !r500590;
        bool r500592 = r500588 || r500591;
        double r500593 = x;
        double r500594 = y;
        double r500595 = r500594 - r500593;
        double r500596 = t;
        double r500597 = r500595 / r500596;
        double r500598 = r500597 * r500586;
        double r500599 = r500593 + r500598;
        double r500600 = r500595 * r500586;
        double r500601 = 1.0;
        double r500602 = r500601 / r500596;
        double r500603 = r500600 * r500602;
        double r500604 = r500593 + r500603;
        double r500605 = r500592 ? r500599 : r500604;
        return r500605;
}

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

Original6.4
Target2.1
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.42763758103976e+67 or 2.3482764413141227e-34 < z

    1. Initial program 15.9

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

    3. Applied associate-/l*3.6

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

    5. Applied associate-/r/2.0

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

    if -7.42763758103976e+67 < z < 2.3482764413141227e-34

    1. Initial program 1.4

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

    3. Applied div-inv1.4

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.42763758103976 \cdot 10^{67} \lor \neg \left(z \le 2.3482764413141227 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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)))