Average Error: 6.6 → 1.5
Time: 27.8s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5792166923042434167341056:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 8.712463262678465058615477551470014327641 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5792166923042434167341056:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;t \le 8.712463262678465058615477551470014327641 \cdot 10^{-81}:\\
\;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r23692161 = x;
        double r23692162 = y;
        double r23692163 = z;
        double r23692164 = r23692163 - r23692161;
        double r23692165 = r23692162 * r23692164;
        double r23692166 = t;
        double r23692167 = r23692165 / r23692166;
        double r23692168 = r23692161 + r23692167;
        return r23692168;
}
↓
double f(double x, double y, double z, double t) {
        double r23692169 = t;
        double r23692170 = -5.792166923042434e+24;
        bool r23692171 = r23692169 <= r23692170;
        double r23692172 = x;
        double r23692173 = y;
        double r23692174 = z;
        double r23692175 = r23692174 - r23692172;
        double r23692176 = r23692169 / r23692175;
        double r23692177 = r23692173 / r23692176;
        double r23692178 = r23692172 + r23692177;
        double r23692179 = 8.712463262678465e-81;
        bool r23692180 = r23692169 <= r23692179;
        double r23692181 = r23692175 * r23692173;
        double r23692182 = r23692181 / r23692169;
        double r23692183 = r23692172 + r23692182;
        double r23692184 = r23692180 ? r23692183 : r23692178;
        double r23692185 = r23692171 ? r23692178 : r23692184;
        return r23692185;
}

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
Target2.0
Herbie1.5
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -5.792166923042434e+24 or 8.712463262678465e-81 < t

    1. Initial program 9.1

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

    3. Applied associate-/l*1.4

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

    if -5.792166923042434e+24 < t < 8.712463262678465e-81

    1. Initial program 1.8

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5792166923042434167341056:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 8.712463262678465058615477551470014327641 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

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

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