Average Error: 2.3 → 2.4
Time: 3.6s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 8.74690451588153372 \cdot 10^{-269}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;t \le 3.5231411634558426 \cdot 10^{-34}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le 8.74690451588153372 \cdot 10^{-269}:\\
\;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\

\mathbf{elif}\;t \le 3.5231411634558426 \cdot 10^{-34}:\\
\;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r440353 = x;
        double r440354 = y;
        double r440355 = r440353 - r440354;
        double r440356 = z;
        double r440357 = r440356 - r440354;
        double r440358 = r440355 / r440357;
        double r440359 = t;
        double r440360 = r440358 * r440359;
        return r440360;
}
↓
double f(double x, double y, double z, double t) {
        double r440361 = t;
        double r440362 = 8.746904515881534e-269;
        bool r440363 = r440361 <= r440362;
        double r440364 = x;
        double r440365 = y;
        double r440366 = r440364 - r440365;
        double r440367 = 1.0;
        double r440368 = z;
        double r440369 = r440368 - r440365;
        double r440370 = r440367 / r440369;
        double r440371 = r440366 * r440370;
        double r440372 = r440371 * r440361;
        double r440373 = 3.5231411634558426e-34;
        bool r440374 = r440361 <= r440373;
        double r440375 = r440366 * r440361;
        double r440376 = r440375 / r440369;
        double r440377 = r440361 / r440369;
        double r440378 = r440366 * r440377;
        double r440379 = r440374 ? r440376 : r440378;
        double r440380 = r440363 ? r440372 : r440379;
        return r440380;
}

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
Herbie2.4
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 3 regimes

  2. if t < 8.746904515881534e-269

    1. Initial program 2.6

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

    3. Applied div-inv2.7

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

    if 8.746904515881534e-269 < t < 3.5231411634558426e-34

    1. Initial program 1.8

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

    3. Applied associate-*l/1.5

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

    if 3.5231411634558426e-34 < t

    1. Initial program 1.9

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

    3. Applied div-inv2.1

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

    4. Applied associate-*l*2.5

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

    5. Simplified2.4

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 8.74690451588153372 \cdot 10^{-269}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;t \le 3.5231411634558426 \cdot 10^{-34}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +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))