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

Average Error: 2.0 → 2.0

Time: 13.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r356158 = x;
        double r356159 = y;
        double r356160 = r356158 / r356159;
        double r356161 = z;
        double r356162 = t;
        double r356163 = r356161 - r356162;
        double r356164 = r356160 * r356163;
        double r356165 = r356164 + r356162;
        return r356165;
}

↓

double f(double x, double y, double z, double t) {
        double r356166 = x;
        double r356167 = y;
        double r356168 = r356166 / r356167;
        double r356169 = z;
        double r356170 = t;
        double r356171 = r356169 - r356170;
        double r356172 = fma(r356168, r356171, r356170);
        return r356172;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.0
Target	2.5
Herbie	2.0

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

Derivation

1. Initial program 2.0

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

2. Simplified 2.0

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

3. Final simplification 2.0

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :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))