Average Error: 6.6 → 1.0
Time: 13.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.37373105471283827 \cdot 10^{305}:\\ \;\;\;\;\frac{y}{\frac{t}{z - x}} + x\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 3.35127994072859967 \cdot 10^{271}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.37373105471283827 \cdot 10^{305}:\\
\;\;\;\;\frac{y}{\frac{t}{z - x}} + x\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 3.35127994072859967 \cdot 10^{271}:\\
\;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r474682 = x;
        double r474683 = y;
        double r474684 = z;
        double r474685 = r474684 - r474682;
        double r474686 = r474683 * r474685;
        double r474687 = t;
        double r474688 = r474686 / r474687;
        double r474689 = r474682 + r474688;
        return r474689;
}
↓
double f(double x, double y, double z, double t) {
        double r474690 = x;
        double r474691 = y;
        double r474692 = z;
        double r474693 = r474692 - r474690;
        double r474694 = r474691 * r474693;
        double r474695 = t;
        double r474696 = r474694 / r474695;
        double r474697 = r474690 + r474696;
        double r474698 = -3.3737310547128383e+305;
        bool r474699 = r474697 <= r474698;
        double r474700 = r474695 / r474693;
        double r474701 = r474691 / r474700;
        double r474702 = r474701 + r474690;
        double r474703 = 3.3512799407285997e+271;
        bool r474704 = r474697 <= r474703;
        double r474705 = 1.0;
        double r474706 = r474695 / r474694;
        double r474707 = r474705 / r474706;
        double r474708 = r474690 + r474707;
        double r474709 = r474691 / r474695;
        double r474710 = r474709 * r474693;
        double r474711 = r474690 + r474710;
        double r474712 = r474704 ? r474708 : r474711;
        double r474713 = r474699 ? r474702 : r474712;
        return r474713;
}

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
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -3.3737310547128383e+305

    1. Initial program 60.1

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

    3. Applied associate-/l*1.0

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

    5. Applied pow11.0

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

    if -3.3737310547128383e+305 < (+ x (/ (* y (- z x)) t)) < 3.3512799407285997e+271

    1. Initial program 0.8

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

    3. Applied clear-num0.8

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

    if 3.3512799407285997e+271 < (+ x (/ (* y (- z x)) t))

    1. Initial program 35.4

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

    3. Applied associate-/l*9.2

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

    5. Applied associate-/r/2.4

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.37373105471283827 \cdot 10^{305}:\\ \;\;\;\;\frac{y}{\frac{t}{z - x}} + x\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 3.35127994072859967 \cdot 10^{271}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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