Average Error: 2.0 → 2.0
Time: 22.6s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\frac{x}{y} \cdot \left(z - t\right) + t
double f(double x, double y, double z, double t) {
        double r482768 = x;
        double r482769 = y;
        double r482770 = r482768 / r482769;
        double r482771 = z;
        double r482772 = t;
        double r482773 = r482771 - r482772;
        double r482774 = r482770 * r482773;
        double r482775 = r482774 + r482772;
        return r482775;
}
↓
double f(double x, double y, double z, double t) {
        double r482776 = x;
        double r482777 = y;
        double r482778 = r482776 / r482777;
        double r482779 = z;
        double r482780 = t;
        double r482781 = r482779 - r482780;
        double r482782 = r482778 * r482781;
        double r482783 = r482782 + r482780;
        return r482783;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target2.3
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  2. Final simplification2.0

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

Reproduce

herbie shell --seed 2020047 
(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))