Average Error: 2.1 → 1.5
Time: 4.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.554277062255470137394898281085509956894 \cdot 10^{-90} \lor \neg \left(y \le 5.254045475746620239720312111798513775031 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.554277062255470137394898281085509956894 \cdot 10^{-90} \lor \neg \left(y \le 5.254045475746620239720312111798513775031 \cdot 10^{-51}\right):\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r437471 = x;
        double r437472 = y;
        double r437473 = r437471 / r437472;
        double r437474 = z;
        double r437475 = t;
        double r437476 = r437474 - r437475;
        double r437477 = r437473 * r437476;
        double r437478 = r437477 + r437475;
        return r437478;
}
↓
double f(double x, double y, double z, double t) {
        double r437479 = y;
        double r437480 = -3.55427706225547e-90;
        bool r437481 = r437479 <= r437480;
        double r437482 = 5.25404547574662e-51;
        bool r437483 = r437479 <= r437482;
        double r437484 = !r437483;
        bool r437485 = r437481 || r437484;
        double r437486 = x;
        double r437487 = z;
        double r437488 = t;
        double r437489 = r437487 - r437488;
        double r437490 = r437489 / r437479;
        double r437491 = r437486 * r437490;
        double r437492 = r437491 + r437488;
        double r437493 = r437486 * r437489;
        double r437494 = r437493 / r437479;
        double r437495 = r437494 + r437488;
        double r437496 = r437485 ? r437492 : r437495;
        return r437496;
}

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

Original2.1
Target2.2
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.55427706225547e-90 or 5.25404547574662e-51 < y

    1. Initial program 1.1

      \[\frac{x}{y} \cdot \left(z - t\right) + t\]
    2. Using strategy rm

    3. Applied div-inv1.1

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

    4. Applied associate-*l*1.4

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

    5. Simplified1.4

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

    if -3.55427706225547e-90 < y < 5.25404547574662e-51

    1. Initial program 5.0

      \[\frac{x}{y} \cdot \left(z - t\right) + t\]
    2. Using strategy rm

    3. Applied associate-*l/2.0

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.554277062255470137394898281085509956894 \cdot 10^{-90} \lor \neg \left(y \le 5.254045475746620239720312111798513775031 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))