Average Error: 2.1 → 1.1
Time: 15.6s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.655305076828330502431501672868973302443 \cdot 10^{-267}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 7.879231442577274431601425924431402017359 \cdot 10^{-214}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 2.868698711831718745718105448536592624265 \cdot 10^{98}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -1.655305076828330502431501672868973302443 \cdot 10^{-267}:\\
\;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\

\mathbf{elif}\;\frac{x - y}{z - y} \le 7.879231442577274431601425924431402017359 \cdot 10^{-214}:\\
\;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\

\mathbf{elif}\;\frac{x - y}{z - y} \le 2.868698711831718745718105448536592624265 \cdot 10^{98}:\\
\;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r21190492 = x;
        double r21190493 = y;
        double r21190494 = r21190492 - r21190493;
        double r21190495 = z;
        double r21190496 = r21190495 - r21190493;
        double r21190497 = r21190494 / r21190496;
        double r21190498 = t;
        double r21190499 = r21190497 * r21190498;
        return r21190499;
}
↓
double f(double x, double y, double z, double t) {
        double r21190500 = x;
        double r21190501 = y;
        double r21190502 = r21190500 - r21190501;
        double r21190503 = z;
        double r21190504 = r21190503 - r21190501;
        double r21190505 = r21190502 / r21190504;
        double r21190506 = -1.6553050768283305e-267;
        bool r21190507 = r21190505 <= r21190506;
        double r21190508 = 1.0;
        double r21190509 = r21190508 / r21190504;
        double r21190510 = r21190502 * r21190509;
        double r21190511 = t;
        double r21190512 = r21190510 * r21190511;
        double r21190513 = 7.879231442577274e-214;
        bool r21190514 = r21190505 <= r21190513;
        double r21190515 = r21190504 / r21190511;
        double r21190516 = r21190502 / r21190515;
        double r21190517 = 2.868698711831719e+98;
        bool r21190518 = r21190505 <= r21190517;
        double r21190519 = r21190518 ? r21190512 : r21190516;
        double r21190520 = r21190514 ? r21190516 : r21190519;
        double r21190521 = r21190507 ? r21190512 : r21190520;
        return r21190521;
}

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

Original2.1
Target2.2
Herbie1.1
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < -1.6553050768283305e-267 or 7.879231442577274e-214 < (/ (- x y) (- z y)) < 2.868698711831719e+98

    1. Initial program 0.8

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

    3. Applied div-inv0.9

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

    if -1.6553050768283305e-267 < (/ (- x y) (- z y)) < 7.879231442577274e-214 or 2.868698711831719e+98 < (/ (- x y) (- z y))

    1. Initial program 9.3

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

    3. Applied div-inv9.4

      \[\leadsto \color{blue}{\left(\left(x - y\right) \cdot \frac{1}{z - y}\right)} \cdot t\]
    4. Using strategy rm

    5. Applied pow19.4

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

    6. Applied pow19.4

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

    7. Applied pow19.4

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

    8. Applied pow-prod-down9.4

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

    9. Applied pow-prod-down9.4

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

    10. Simplified2.5

      \[\leadsto {\color{blue}{\left(\frac{x - y}{\frac{z - y}{t}}\right)}}^{1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.655305076828330502431501672868973302443 \cdot 10^{-267}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 7.879231442577274431601425924431402017359 \cdot 10^{-214}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le 2.868698711831718745718105448536592624265 \cdot 10^{98}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"

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

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