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

Average Error: 2.1 → 2.1

Time: 6.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r500816 = x;
        double r500817 = y;
        double r500818 = r500816 / r500817;
        double r500819 = z;
        double r500820 = t;
        double r500821 = r500819 - r500820;
        double r500822 = r500818 * r500821;
        double r500823 = r500822 + r500820;
        return r500823;
}

↓

double f(double x, double y, double z, double t) {
        double r500824 = x;
        double r500825 = y;
        double r500826 = r500824 / r500825;
        double r500827 = z;
        double r500828 = t;
        double r500829 = r500827 - r500828;
        double r500830 = r500826 * r500829;
        double r500831 = r500830 + r500828;
        return r500831;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.3
Herbie	2.1

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

Derivation

1. Initial program 2.1

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

2. Final simplification 2.1

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

Reproduce

herbie shell --seed 2020001 +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))