Average Error: 2.3 → 2.3
Time: 5.3s
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 r693631 = x;
        double r693632 = y;
        double r693633 = r693631 - r693632;
        double r693634 = z;
        double r693635 = r693634 - r693632;
        double r693636 = r693633 / r693635;
        double r693637 = t;
        double r693638 = r693636 * r693637;
        return r693638;
}
↓
double f(double x, double y, double z, double t) {
        double r693639 = x;
        double r693640 = z;
        double r693641 = y;
        double r693642 = r693640 - r693641;
        double r693643 = r693639 / r693642;
        double r693644 = r693641 / r693642;
        double r693645 = r693643 - r693644;
        double r693646 = t;
        double r693647 = r693645 * r693646;
        return r693647;
}

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 +o rules:numerics
(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))