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 r563264 = x;
        double r563265 = y;
        double r563266 = r563264 - r563265;
        double r563267 = z;
        double r563268 = r563267 - r563265;
        double r563269 = r563266 / r563268;
        double r563270 = t;
        double r563271 = r563269 * r563270;
        return r563271;
}
↓
double f(double x, double y, double z, double t) {
        double r563272 = x;
        double r563273 = y;
        double r563274 = r563272 - r563273;
        double r563275 = z;
        double r563276 = r563275 - r563273;
        double r563277 = r563274 / r563276;
        double r563278 = -1.4772699565267299e-242;
        bool r563279 = r563277 <= r563278;
        double r563280 = 1.0;
        double r563281 = t;
        double r563282 = r563276 / r563274;
        double r563283 = r563281 / r563282;
        double r563284 = r563280 * r563283;
        double r563285 = -0.0;
        bool r563286 = r563277 <= r563285;
        double r563287 = r563281 / r563276;
        double r563288 = r563287 * r563274;
        double r563289 = r563280 * r563288;
        double r563290 = r563277 * r563281;
        double r563291 = r563286 ? r563289 : r563290;
        double r563292 = r563279 ? r563284 : r563291;
        return r563292;
}

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

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

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

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

    7. Applied times-frac2.8

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

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

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

    9. Applied times-frac2.8

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

    10. Applied associate-*l*2.8

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

    11. Simplified2.5

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

    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

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

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

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

    7. Applied times-frac14.8

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

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

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

    9. Applied times-frac14.8

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

    10. Applied associate-*l*14.8

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

    11. Simplified14.7

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

    13. Applied associate-/r/0.2

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

    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 
(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))