Average Error: 6.3 → 1.5
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2117257699034317484720128 \lor \neg \left(t \le 4.298768646380980053593446645561660090143 \cdot 10^{-219}\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2117257699034317484720128 \lor \neg \left(t \le 4.298768646380980053593446645561660090143 \cdot 10^{-219}\right):\\
\;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r267038 = x;
        double r267039 = y;
        double r267040 = z;
        double r267041 = r267040 - r267038;
        double r267042 = r267039 * r267041;
        double r267043 = t;
        double r267044 = r267042 / r267043;
        double r267045 = r267038 + r267044;
        return r267045;
}
↓
double f(double x, double y, double z, double t) {
        double r267046 = t;
        double r267047 = -2.1172576990343175e+24;
        bool r267048 = r267046 <= r267047;
        double r267049 = 4.29876864638098e-219;
        bool r267050 = r267046 <= r267049;
        double r267051 = !r267050;
        bool r267052 = r267048 || r267051;
        double r267053 = y;
        double r267054 = r267053 / r267046;
        double r267055 = z;
        double r267056 = x;
        double r267057 = r267055 - r267056;
        double r267058 = r267054 * r267057;
        double r267059 = r267058 + r267056;
        double r267060 = r267053 * r267057;
        double r267061 = r267060 / r267046;
        double r267062 = r267061 + r267056;
        double r267063 = r267052 ? r267059 : r267062;
        return r267063;
}

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

Original6.3
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 < -2.1172576990343175e+24 or 4.29876864638098e-219 < t

    1. Initial program 7.8

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

    2. Simplified1.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef1.4

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

    if -2.1172576990343175e+24 < t < 4.29876864638098e-219

    1. Initial program 1.9

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

    2. Simplified3.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef3.9

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

    6. Applied associate-*l/1.9

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2117257699034317484720128 \lor \neg \left(t \le 4.298768646380980053593446645561660090143 \cdot 10^{-219}\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(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)))