Average Error: 2.4 → 2.5
Time: 18.2s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.964560534600160347403713372594171320397 \cdot 10^{-27} \lor \neg \left(y \le 6.516499639302412812533785208688468786947 \cdot 10^{-90}\right):\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.964560534600160347403713372594171320397 \cdot 10^{-27} \lor \neg \left(y \le 6.516499639302412812533785208688468786947 \cdot 10^{-90}\right):\\
\;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \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 r360585 = x;
        double r360586 = y;
        double r360587 = r360585 - r360586;
        double r360588 = z;
        double r360589 = r360588 - r360586;
        double r360590 = r360587 / r360589;
        double r360591 = t;
        double r360592 = r360590 * r360591;
        return r360592;
}
↓
double f(double x, double y, double z, double t) {
        double r360593 = y;
        double r360594 = -1.9645605346001603e-27;
        bool r360595 = r360593 <= r360594;
        double r360596 = 6.516499639302413e-90;
        bool r360597 = r360593 <= r360596;
        double r360598 = !r360597;
        bool r360599 = r360595 || r360598;
        double r360600 = x;
        double r360601 = r360600 - r360593;
        double r360602 = 1.0;
        double r360603 = z;
        double r360604 = r360603 - r360593;
        double r360605 = r360602 / r360604;
        double r360606 = r360601 * r360605;
        double r360607 = t;
        double r360608 = r360606 * r360607;
        double r360609 = r360601 * r360607;
        double r360610 = r360609 / r360604;
        double r360611 = r360599 ? r360608 : r360610;
        return r360611;
}

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

Derivation

  1. Split input into 2 regimes

  2. if y < -1.9645605346001603e-27 or 6.516499639302413e-90 < y

    1. Initial program 0.3

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

    3. Applied div-inv0.5

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

    if -1.9645605346001603e-27 < y < 6.516499639302413e-90

    1. Initial program 5.9

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

    3. Applied div-inv5.9

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

    5. Applied un-div-inv5.9

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

    6. Applied associate-*l/5.8

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.964560534600160347403713372594171320397 \cdot 10^{-27} \lor \neg \left(y \le 6.516499639302412812533785208688468786947 \cdot 10^{-90}\right):\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(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))