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

Average Error: 2.2 → 2.2

Time: 20.1s

Precision: 64

Math

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

↓

\[\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\]

C

double f(double x, double y, double z, double t) {
        double r372164 = x;
        double r372165 = y;
        double r372166 = r372164 / r372165;
        double r372167 = z;
        double r372168 = t;
        double r372169 = r372167 - r372168;
        double r372170 = r372166 * r372169;
        double r372171 = r372170 + r372168;
        return r372171;
}

↓

double f(double x, double y, double z, double t) {
        double r372172 = x;
        double r372173 = y;
        double r372174 = r372172 / r372173;
        double r372175 = z;
        double r372176 = t;
        double r372177 = r372175 - r372176;
        double r372178 = fma(r372174, r372177, r372176);
        return r372178;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.5
Herbie	2.2

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

Derivation

1. Initial program 2.2

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

2. Simplified 2.2

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

3. Final simplification 2.2

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :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))