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

Average Error: 2.0 → 2.0

Time: 19.7s

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 r20251086 = x;
        double r20251087 = y;
        double r20251088 = r20251086 / r20251087;
        double r20251089 = z;
        double r20251090 = t;
        double r20251091 = r20251089 - r20251090;
        double r20251092 = r20251088 * r20251091;
        double r20251093 = r20251092 + r20251090;
        return r20251093;
}

↓

double f(double x, double y, double z, double t) {
        double r20251094 = x;
        double r20251095 = y;
        double r20251096 = r20251094 / r20251095;
        double r20251097 = z;
        double r20251098 = t;
        double r20251099 = r20251097 - r20251098;
        double r20251100 = r20251096 * r20251099;
        double r20251101 = r20251100 + r20251098;
        return r20251101;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.0
Target	2.1
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. Final simplification 2.0

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

Reproduce

herbie shell --seed 2019169 
(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))