Average Error: 2.0 → 2.0
Time: 13.3s
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 r383445 = x;
        double r383446 = y;
        double r383447 = r383445 - r383446;
        double r383448 = z;
        double r383449 = r383448 - r383446;
        double r383450 = r383447 / r383449;
        double r383451 = t;
        double r383452 = r383450 * r383451;
        return r383452;
}
↓
double f(double x, double y, double z, double t) {
        double r383453 = x;
        double r383454 = z;
        double r383455 = y;
        double r383456 = r383454 - r383455;
        double r383457 = r383453 / r383456;
        double r383458 = r383455 / r383456;
        double r383459 = r383457 - r383458;
        double r383460 = t;
        double r383461 = r383459 * r383460;
        return r383461;
}

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

Original2.0
Target2.1
Herbie2.0
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.0

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

  3. Applied div-sub2.0

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

  4. Final simplification2.0

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

Reproduce

herbie shell --seed 2019303 +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))