Average Error: 2.4 → 1.4
Time: 4.0s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\ \;\;\;\;1 \cdot \frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;1 \cdot \left(\frac{t}{z - y} \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\
\;\;\;\;1 \cdot \frac{t}{\frac{z - y}{x - y}}\\

\mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\
\;\;\;\;1 \cdot \left(\frac{t}{z - y} \cdot \left(x - y\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r454957 = x;
        double r454958 = y;
        double r454959 = r454957 - r454958;
        double r454960 = z;
        double r454961 = r454960 - r454958;
        double r454962 = r454959 / r454961;
        double r454963 = t;
        double r454964 = r454962 * r454963;
        return r454964;
}
↓
double f(double x, double y, double z, double t) {
        double r454965 = x;
        double r454966 = y;
        double r454967 = r454965 - r454966;
        double r454968 = z;
        double r454969 = r454968 - r454966;
        double r454970 = r454967 / r454969;
        double r454971 = -1.4772699565267299e-242;
        bool r454972 = r454970 <= r454971;
        double r454973 = 1.0;
        double r454974 = t;
        double r454975 = r454969 / r454967;
        double r454976 = r454974 / r454975;
        double r454977 = r454973 * r454976;
        double r454978 = -0.0;
        bool r454979 = r454970 <= r454978;
        double r454980 = r454974 / r454969;
        double r454981 = r454980 * r454967;
        double r454982 = r454973 * r454981;
        double r454983 = r454970 * r454974;
        double r454984 = r454979 ? r454982 : r454983;
        double r454985 = r454972 ? r454977 : r454984;
        return r454985;
}

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

Original2.4
Target2.4
Herbie1.4
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (- x y) (- z y)) < -1.4772699565267299e-242

    1. Initial program 2.7

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

    3. Applied clear-num2.8

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

    5. Applied *-un-lft-identity2.8

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

    6. Applied *-un-lft-identity2.8

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

    7. Applied times-frac2.8

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

    8. Applied associate-*l*2.8

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

    9. Simplified2.5

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

    if -1.4772699565267299e-242 < (/ (- x y) (- z y)) < -0.0

    1. Initial program 13.3

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

    3. Applied clear-num14.8

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

    5. Applied *-un-lft-identity14.8

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

    6. Applied *-un-lft-identity14.8

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

    7. Applied times-frac14.8

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

    8. Applied associate-*l*14.8

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

    9. Simplified14.7

      \[\leadsto \frac{1}{1} \cdot \color{blue}{\frac{t}{\frac{z - y}{x - y}}}\]
    10. Using strategy rm

    11. Applied associate-/r/0.2

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

    if -0.0 < (/ (- x y) (- z y))

    1. Initial program 1.6

      \[\frac{x - y}{z - y} \cdot t\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.477269956526729882709689256541591977713 \cdot 10^{-242}:\\ \;\;\;\;1 \cdot \frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;1 \cdot \left(\frac{t}{z - y} \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 +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))