Average Error: 1.9 → 1.9
Time: 3.6s
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 r434694 = x;
        double r434695 = y;
        double r434696 = r434694 / r434695;
        double r434697 = z;
        double r434698 = t;
        double r434699 = r434697 - r434698;
        double r434700 = r434696 * r434699;
        double r434701 = r434700 + r434698;
        return r434701;
}
↓
double f(double x, double y, double z, double t) {
        double r434702 = x;
        double r434703 = y;
        double r434704 = r434702 / r434703;
        double r434705 = z;
        double r434706 = t;
        double r434707 = r434705 - r434706;
        double r434708 = r434704 * r434707;
        double r434709 = r434708 + r434706;
        return r434709;
}

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

Original1.9
Target2.2
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  2. Final simplification1.9

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

Reproduce

herbie shell --seed 2020100 
(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))