Average Error: 6.7 → 1.1
Time: 4.4s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -5.854653779005750876146040097723722068281 \cdot 10^{293}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.605413368066265688760018008293374023297 \cdot 10^{299}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -5.854653779005750876146040097723722068281 \cdot 10^{293}:\\
\;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.605413368066265688760018008293374023297 \cdot 10^{299}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r269066 = x;
        double r269067 = y;
        double r269068 = z;
        double r269069 = r269068 - r269066;
        double r269070 = r269067 * r269069;
        double r269071 = t;
        double r269072 = r269070 / r269071;
        double r269073 = r269066 + r269072;
        return r269073;
}
↓
double f(double x, double y, double z, double t) {
        double r269074 = x;
        double r269075 = y;
        double r269076 = z;
        double r269077 = r269076 - r269074;
        double r269078 = r269075 * r269077;
        double r269079 = t;
        double r269080 = r269078 / r269079;
        double r269081 = r269074 + r269080;
        double r269082 = -5.854653779005751e+293;
        bool r269083 = r269081 <= r269082;
        double r269084 = r269075 / r269079;
        double r269085 = 1.0;
        double r269086 = r269085 / r269077;
        double r269087 = r269084 / r269086;
        double r269088 = r269074 + r269087;
        double r269089 = 1.6054133680662657e+299;
        bool r269090 = r269081 <= r269089;
        double r269091 = r269079 / r269077;
        double r269092 = r269075 / r269091;
        double r269093 = r269074 + r269092;
        double r269094 = r269090 ? r269081 : r269093;
        double r269095 = r269083 ? r269088 : r269094;
        return r269095;
}

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

Original6.7
Target2.0
Herbie1.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -5.854653779005751e+293

    1. Initial program 49.2

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

    3. Applied associate-/l*4.7

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

    5. Applied div-inv4.7

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

    6. Applied associate-/r*1.0

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

    if -5.854653779005751e+293 < (+ x (/ (* y (- z x)) t)) < 1.6054133680662657e+299

    1. Initial program 0.8

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

    if 1.6054133680662657e+299 < (+ x (/ (* y (- z x)) t))

    1. Initial program 52.8

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

    3. Applied associate-/l*4.5

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -5.854653779005750876146040097723722068281 \cdot 10^{293}:\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.605413368066265688760018008293374023297 \cdot 10^{299}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 
(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)))