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

Average Error: 2.1 → 2.1

Time: 17.0s

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 r20762508 = x;
        double r20762509 = y;
        double r20762510 = r20762508 / r20762509;
        double r20762511 = z;
        double r20762512 = t;
        double r20762513 = r20762511 - r20762512;
        double r20762514 = r20762510 * r20762513;
        double r20762515 = r20762514 + r20762512;
        return r20762515;
}

↓

double f(double x, double y, double z, double t) {
        double r20762516 = x;
        double r20762517 = y;
        double r20762518 = r20762516 / r20762517;
        double r20762519 = z;
        double r20762520 = t;
        double r20762521 = r20762519 - r20762520;
        double r20762522 = r20762518 * r20762521;
        double r20762523 = r20762522 + r20762520;
        return r20762523;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.4
Herbie	2.1

\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

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 2019162 +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))