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

Average Error: 2.4 → 1.2

Time: 16.7s

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 r347716 = x;
        double r347717 = y;
        double r347718 = r347716 - r347717;
        double r347719 = z;
        double r347720 = r347719 - r347717;
        double r347721 = r347718 / r347720;
        double r347722 = t;
        double r347723 = r347721 * r347722;
        return r347723;
}

↓

double f(double x, double y, double z, double t) {
        double r347724 = x;
        double r347725 = y;
        double r347726 = r347724 - r347725;
        double r347727 = z;
        double r347728 = r347727 - r347725;
        double r347729 = r347726 / r347728;
        double r347730 = -1.4623181854011083e+117;
        bool r347731 = r347729 <= r347730;
        double r347732 = -7.398316728801853e-92;
        bool r347733 = r347729 <= r347732;
        double r347734 = !r347733;
        double r347735 = -0.0;
        bool r347736 = r347729 <= r347735;
        bool r347737 = r347734 && r347736;
        bool r347738 = r347731 || r347737;
        double r347739 = t;
        double r347740 = r347726 * r347739;
        double r347741 = r347740 / r347728;
        double r347742 = r347729 * r347739;
        double r347743 = r347738 ? r347741 : r347742;
        return r347743;
}

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 
(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))