Average Error: 2.5 → 2.3
Time: 5.2s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 5.8004430131694032 \cdot 10^{-254} \lor \neg \left(t \le 2.00454495394028621 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le 5.8004430131694032 \cdot 10^{-254} \lor \neg \left(t \le 2.00454495394028621 \cdot 10^{-60}\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r426571 = x;
        double r426572 = y;
        double r426573 = r426571 - r426572;
        double r426574 = z;
        double r426575 = r426574 - r426572;
        double r426576 = r426573 / r426575;
        double r426577 = t;
        double r426578 = r426576 * r426577;
        return r426578;
}
↓
double f(double x, double y, double z, double t) {
        double r426579 = t;
        double r426580 = 5.800443013169403e-254;
        bool r426581 = r426579 <= r426580;
        double r426582 = 2.0045449539402862e-60;
        bool r426583 = r426579 <= r426582;
        double r426584 = !r426583;
        bool r426585 = r426581 || r426584;
        double r426586 = x;
        double r426587 = y;
        double r426588 = r426586 - r426587;
        double r426589 = z;
        double r426590 = r426589 - r426587;
        double r426591 = r426588 / r426590;
        double r426592 = r426591 * r426579;
        double r426593 = r426588 * r426579;
        double r426594 = r426593 / r426590;
        double r426595 = r426585 ? r426592 : r426594;
        return r426595;
}

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

Original2.5
Target2.5
Herbie2.3
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 5.800443013169403e-254 or 2.0045449539402862e-60 < t

    1. Initial program 2.4

      \[\frac{x - y}{z - y} \cdot t\]

    if 5.800443013169403e-254 < t < 2.0045449539402862e-60

    1. Initial program 2.5

      \[\frac{x - y}{z - y} \cdot t\]
    2. Using strategy rm

    3. Applied associate-*l/1.6

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 5.8004430131694032 \cdot 10^{-254} \lor \neg \left(t \le 2.00454495394028621 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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