Average Error: 2.0 → 2.0
Time: 12.6s
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 r602235 = x;
        double r602236 = y;
        double r602237 = r602235 - r602236;
        double r602238 = z;
        double r602239 = r602238 - r602236;
        double r602240 = r602237 / r602239;
        double r602241 = t;
        double r602242 = r602240 * r602241;
        return r602242;
}
↓
double f(double x, double y, double z, double t) {
        double r602243 = x;
        double r602244 = z;
        double r602245 = y;
        double r602246 = r602244 - r602245;
        double r602247 = r602243 / r602246;
        double r602248 = r602245 / r602246;
        double r602249 = r602247 - r602248;
        double r602250 = t;
        double r602251 = r602249 * r602250;
        return r602251;
}

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))