Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Average Error: 2.4 → 1.2

Time: 18.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.462318185401108278911963335029297785762 \cdot 10^{117} \lor \neg \left(\frac{x - y}{z - y} \le -7.398316728801853286900513540804094569714 \cdot 10^{-92}\right) \land \frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r289735 = x;
        double r289736 = y;
        double r289737 = r289735 - r289736;
        double r289738 = z;
        double r289739 = r289738 - r289736;
        double r289740 = r289737 / r289739;
        double r289741 = t;
        double r289742 = r289740 * r289741;
        return r289742;
}

↓

double f(double x, double y, double z, double t) {
        double r289743 = x;
        double r289744 = y;
        double r289745 = r289743 - r289744;
        double r289746 = z;
        double r289747 = r289746 - r289744;
        double r289748 = r289745 / r289747;
        double r289749 = -1.4623181854011083e+117;
        bool r289750 = r289748 <= r289749;
        double r289751 = -7.398316728801853e-92;
        bool r289752 = r289748 <= r289751;
        double r289753 = !r289752;
        double r289754 = -0.0;
        bool r289755 = r289748 <= r289754;
        bool r289756 = r289753 && r289755;
        bool r289757 = r289750 || r289756;
        double r289758 = t;
        double r289759 = r289745 * r289758;
        double r289760 = r289759 / r289747;
        double r289761 = r289748 * r289758;
        double r289762 = r289757 ? r289760 : r289761;
        return r289762;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.4
Target	2.4
Herbie	1.2

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

Derivation

1. Split input into 2 regimes

2. if (/ (- x y) (- z y)) < -1.4623181854011083e+117 or -7.398316728801853e-92 < (/ (- x y) (- z y)) < -0.0

   1. Initial program 6.9

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

   3. Applied associate-*l/ 3.0

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

   if -1.4623181854011083e+117 < (/ (- x y) (- z y)) < -7.398316728801853e-92 or -0.0 < (/ (- x y) (- z y))

   1. Initial program 1.4

      \[\frac{x - y}{z - y} \cdot t\]
3. Recombined 2 regimes into one program.

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \le -1.462318185401108278911963335029297785762 \cdot 10^{117} \lor \neg \left(\frac{x - y}{z - y} \le -7.398316728801853286900513540804094569714 \cdot 10^{-92}\right) \land \frac{x - y}{z - y} \le -0.0:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 +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))