Average Error: 2.3 → 2.3
Time: 14.2s
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 r398458 = x;
        double r398459 = y;
        double r398460 = r398458 - r398459;
        double r398461 = z;
        double r398462 = r398461 - r398459;
        double r398463 = r398460 / r398462;
        double r398464 = t;
        double r398465 = r398463 * r398464;
        return r398465;
}
↓
double f(double x, double y, double z, double t) {
        double r398466 = x;
        double r398467 = z;
        double r398468 = y;
        double r398469 = r398467 - r398468;
        double r398470 = r398466 / r398469;
        double r398471 = r398468 / r398469;
        double r398472 = r398470 - r398471;
        double r398473 = t;
        double r398474 = r398472 * r398473;
        return r398474;
}

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 2019208 +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))