Average Error: 6.5 → 0.8
Time: 20.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.812525037796768018373255724443839618269 \cdot 10^{293}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.812525037796768018373255724443839618269 \cdot 10^{293}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r366646 = x;
        double r366647 = y;
        double r366648 = r366647 - r366646;
        double r366649 = z;
        double r366650 = r366648 * r366649;
        double r366651 = t;
        double r366652 = r366650 / r366651;
        double r366653 = r366646 + r366652;
        return r366653;
}
↓
double f(double x, double y, double z, double t) {
        double r366654 = x;
        double r366655 = y;
        double r366656 = r366655 - r366654;
        double r366657 = z;
        double r366658 = r366656 * r366657;
        double r366659 = t;
        double r366660 = r366658 / r366659;
        double r366661 = r366654 + r366660;
        double r366662 = -inf.0;
        bool r366663 = r366661 <= r366662;
        double r366664 = r366659 / r366657;
        double r366665 = r366656 / r366664;
        double r366666 = r366654 + r366665;
        double r366667 = 1.812525037796768e+293;
        bool r366668 = r366661 <= r366667;
        double r366669 = r366657 / r366659;
        double r366670 = r366669 * r366656;
        double r366671 = r366654 + r366670;
        double r366672 = r366668 ? r366661 : r366671;
        double r366673 = r366663 ? r366666 : r366672;
        return r366673;
}

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
Target1.9
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. Using strategy rm

    3. Applied associate-/l*0.2

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 1.812525037796768e+293

    1. Initial program 0.8

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

    if 1.812525037796768e+293 < (+ x (/ (* (- y x) z) t))

    1. Initial program 50.1

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

    3. Applied associate-/l*2.0

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

    4. Taylor expanded around 0 50.1

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

    5. Simplified2.2

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.812525037796768018373255724443839618269 \cdot 10^{293}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot \left(y - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.0255111955330046e-135) (- x (* (/ z t) (- x y))) (if (< x 4.2750321637007147e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))