Average Error: 2.3 → 2.3
Time: 3.6s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\left(\frac{x}{z - y} - \frac{y}{z - y}\right) \cdot t\]
\frac{x - y}{z - y} \cdot t
↓
\left(\frac{x}{z - y} - \frac{y}{z - y}\right) \cdot t
double f(double x, double y, double z, double t) {
        double r337725 = x;
        double r337726 = y;
        double r337727 = r337725 - r337726;
        double r337728 = z;
        double r337729 = r337728 - r337726;
        double r337730 = r337727 / r337729;
        double r337731 = t;
        double r337732 = r337730 * r337731;
        return r337732;
}
↓
double f(double x, double y, double z, double t) {
        double r337733 = x;
        double r337734 = z;
        double r337735 = y;
        double r337736 = r337734 - r337735;
        double r337737 = r337733 / r337736;
        double r337738 = r337735 / r337736;
        double r337739 = r337737 - r337738;
        double r337740 = t;
        double r337741 = r337739 * r337740;
        return r337741;
}

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

Original2.3
Target2.3
Herbie2.3
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.3

    \[\frac{x - y}{z - y} \cdot t\]
  2. Using strategy rm

  3. Applied div-sub2.3

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

  4. Final simplification2.3

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

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))