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

Average Error: 2.1 → 2.3

Time: 19.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -4.905109613219859138336922312734014035451 \cdot 10^{-187}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;y \le -3.04519208312675320688845013544054791934 \cdot 10^{-279}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \le 4.499203940774102248093033787994564421277 \cdot 10^{-229}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;y \le 426736291374772731009997923845482855006200:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r22976860 = x;
        double r22976861 = y;
        double r22976862 = r22976860 - r22976861;
        double r22976863 = z;
        double r22976864 = r22976863 - r22976861;
        double r22976865 = r22976862 / r22976864;
        double r22976866 = t;
        double r22976867 = r22976865 * r22976866;
        return r22976867;
}

↓

double f(double x, double y, double z, double t) {
        double r22976868 = y;
        double r22976869 = -4.905109613219859e-187;
        bool r22976870 = r22976868 <= r22976869;
        double r22976871 = x;
        double r22976872 = r22976871 - r22976868;
        double r22976873 = 1.0;
        double r22976874 = z;
        double r22976875 = r22976874 - r22976868;
        double r22976876 = r22976873 / r22976875;
        double r22976877 = r22976872 * r22976876;
        double r22976878 = t;
        double r22976879 = r22976877 * r22976878;
        double r22976880 = -3.0451920831267532e-279;
        bool r22976881 = r22976868 <= r22976880;
        double r22976882 = r22976878 / r22976875;
        double r22976883 = r22976882 * r22976872;
        double r22976884 = 4.499203940774102e-229;
        bool r22976885 = r22976868 <= r22976884;
        double r22976886 = 4.267362913747727e+41;
        bool r22976887 = r22976868 <= r22976886;
        double r22976888 = r22976872 * r22976878;
        double r22976889 = r22976888 / r22976875;
        double r22976890 = r22976887 ? r22976889 : r22976879;
        double r22976891 = r22976885 ? r22976879 : r22976890;
        double r22976892 = r22976881 ? r22976883 : r22976891;
        double r22976893 = r22976870 ? r22976879 : r22976892;
        return r22976893;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.2
Herbie	2.3

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

Derivation

1. Split input into 3 regimes

2. if y < -4.905109613219859e-187 or -3.0451920831267532e-279 < y < 4.499203940774102e-229 or 4.267362913747727e+41 < y

   1. Initial program 1.3

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

   3. Applied div-inv 1.4

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

   if -4.905109613219859e-187 < y < -3.0451920831267532e-279

   1. Initial program 7.5

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

   3. Applied div-inv 7.6

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

   4. Applied associate-*l* 5.6

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

   5. Simplified 5.5

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

   if 4.499203940774102e-229 < y < 4.267362913747727e+41

   1. Initial program 3.0

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

   3. Applied associate-*l/ 4.2

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

4. Final simplification 2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.905109613219859138336922312734014035451 \cdot 10^{-187}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;y \le -3.04519208312675320688845013544054791934 \cdot 10^{-279}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \le 4.499203940774102248093033787994564421277 \cdot 10^{-229}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;y \le 426736291374772731009997923845482855006200:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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