Average Error: 6.6 → 0.8
Time: 17.5s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 6.459980878239823112823689377523232903306 \cdot 10^{298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\
\;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 6.459980878239823112823689377523232903306 \cdot 10^{298}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r345707 = x;
        double r345708 = y;
        double r345709 = r345708 - r345707;
        double r345710 = z;
        double r345711 = r345709 * r345710;
        double r345712 = t;
        double r345713 = r345711 / r345712;
        double r345714 = r345707 + r345713;
        return r345714;
}
↓
double f(double x, double y, double z, double t) {
        double r345715 = x;
        double r345716 = y;
        double r345717 = r345716 - r345715;
        double r345718 = z;
        double r345719 = r345717 * r345718;
        double r345720 = t;
        double r345721 = r345719 / r345720;
        double r345722 = r345715 + r345721;
        double r345723 = -inf.0;
        bool r345724 = r345722 <= r345723;
        double r345725 = r345720 / r345717;
        double r345726 = r345718 / r345725;
        double r345727 = r345715 + r345726;
        double r345728 = 6.459980878239823e+298;
        bool r345729 = r345722 <= r345728;
        double r345730 = r345718 / r345720;
        double r345731 = r345717 * r345730;
        double r345732 = r345715 + r345731;
        double r345733 = r345729 ? r345722 : r345732;
        double r345734 = r345724 ? r345727 : r345733;
        return r345734;
}

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

Original6.6
Target2.1
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

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

    4. Taylor expanded around 0 64.0

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

    5. Simplified0.2

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 6.459980878239823e+298

    1. Initial program 0.8

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

    if 6.459980878239823e+298 < (+ x (/ (* (- y x) z) t))

    1. Initial program 52.3

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

    3. Applied *-un-lft-identity52.3

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 6.459980878239823112823689377523232903306 \cdot 10^{298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))