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

Average Error: 2.2 → 2.3

Time: 5.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r438221 = x;
        double r438222 = y;
        double r438223 = r438221 - r438222;
        double r438224 = z;
        double r438225 = r438224 - r438222;
        double r438226 = r438223 / r438225;
        double r438227 = t;
        double r438228 = r438226 * r438227;
        return r438228;
}

↓

double f(double x, double y, double z, double t) {
        double r438229 = x;
        double r438230 = z;
        double r438231 = y;
        double r438232 = r438230 - r438231;
        double r438233 = r438229 / r438232;
        double r438234 = 1.0;
        double r438235 = r438232 / r438231;
        double r438236 = r438234 / r438235;
        double r438237 = r438233 - r438236;
        double r438238 = t;
        double r438239 = r438237 * r438238;
        return r438239;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.2
Herbie	2.3

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

Derivation

1. Initial program 2.2

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

3. Applied div-sub 2.2

   \[\leadsto \color{blue}{\left(\frac{x}{z - y} - \frac{y}{z - y}\right)} \cdot t\]
4. Using strategy rm

5. Applied clear-num 2.3

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

6. Final simplification 2.3

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

Reproduce

herbie shell --seed 2020062 +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))