Average Error: 2.1 → 2.1
Time: 3.8s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(z - t\right) \cdot \frac{x}{y} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(z - t\right) \cdot \frac{x}{y} + t
double f(double x, double y, double z, double t) {
        double r506684 = x;
        double r506685 = y;
        double r506686 = r506684 / r506685;
        double r506687 = z;
        double r506688 = t;
        double r506689 = r506687 - r506688;
        double r506690 = r506686 * r506689;
        double r506691 = r506690 + r506688;
        return r506691;
}
↓
double f(double x, double y, double z, double t) {
        double r506692 = z;
        double r506693 = t;
        double r506694 = r506692 - r506693;
        double r506695 = x;
        double r506696 = y;
        double r506697 = r506695 / r506696;
        double r506698 = r506694 * r506697;
        double r506699 = r506698 + r506693;
        return r506699;
}

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
Target2.3
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  3. Applied *-commutative2.1

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

  4. Final simplification2.1

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-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))