Average Error: 2.3 → 1.6
Time: 16.4s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -5.297791397205154729856129555711534946183 \cdot 10^{-210} \lor \neg \left(\frac{x - y}{z - y} \le -0.0\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{z - y} \le -5.297791397205154729856129555711534946183 \cdot 10^{-210} \lor \neg \left(\frac{x - y}{z - y} \le -0.0\right):\\
\;\;\;\;\frac{x - y}{z - y} \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r313254 = x;
        double r313255 = y;
        double r313256 = r313254 - r313255;
        double r313257 = z;
        double r313258 = r313257 - r313255;
        double r313259 = r313256 / r313258;
        double r313260 = t;
        double r313261 = r313259 * r313260;
        return r313261;
}
↓
double f(double x, double y, double z, double t) {
        double r313262 = x;
        double r313263 = y;
        double r313264 = r313262 - r313263;
        double r313265 = z;
        double r313266 = r313265 - r313263;
        double r313267 = r313264 / r313266;
        double r313268 = -5.297791397205155e-210;
        bool r313269 = r313267 <= r313268;
        double r313270 = -0.0;
        bool r313271 = r313267 <= r313270;
        double r313272 = !r313271;
        bool r313273 = r313269 || r313272;
        double r313274 = t;
        double r313275 = r313267 * r313274;
        double r313276 = r313266 / r313274;
        double r313277 = r313264 / r313276;
        double r313278 = r313273 ? r313275 : r313277;
        return r313278;
}

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

Original2.3
Target2.3
Herbie1.6
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- x y) (- z y)) < -5.297791397205155e-210 or -0.0 < (/ (- x y) (- z y))

    1. Initial program 1.6

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

    if -5.297791397205155e-210 < (/ (- x y) (- z y)) < -0.0

    1. Initial program 11.4

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

    3. Applied div-inv11.4

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

    4. Applied associate-*l*0.7

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

    5. Simplified0.7

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

    7. Applied clear-num0.7

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

    9. Applied pow10.7

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

    10. Applied pow10.7

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

    11. Applied pow-prod-down0.7

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

    12. Simplified0.6

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -5.297791397205154729856129555711534946183 \cdot 10^{-210} \lor \neg \left(\frac{x - y}{z - y} \le -0.0\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 +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))