Average Error: 2.2 → 2.2
Time: 3.5s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + t
double f(double x, double y, double z, double t) {
        double r593947 = x;
        double r593948 = y;
        double r593949 = r593947 / r593948;
        double r593950 = z;
        double r593951 = t;
        double r593952 = r593950 - r593951;
        double r593953 = r593949 * r593952;
        double r593954 = r593953 + r593951;
        return r593954;
}
↓
double f(double x, double y, double z, double t) {
        double r593955 = x;
        double r593956 = y;
        double r593957 = r593955 / r593956;
        double r593958 = z;
        double r593959 = r593957 * r593958;
        double r593960 = t;
        double r593961 = -r593960;
        double r593962 = r593957 * r593961;
        double r593963 = r593959 + r593962;
        double r593964 = r593963 + r593960;
        return r593964;
}

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

Original2.2
Target2.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.2

    \[\frac{x}{y} \cdot \left(z - t\right) + t\]
  2. Using strategy rm

  3. Applied sub-neg2.2

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

  4. Applied distribute-lft-in2.2

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

  5. Final simplification2.2

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

Reproduce

herbie shell --seed 2019353 
(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))