Average Error: 2.2 → 2.2
Time: 4.6s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[t \cdot \frac{x - y}{z - y}\]
\frac{x - y}{z - y} \cdot t
↓
t \cdot \frac{x - y}{z - y}
double f(double x, double y, double z, double t) {
        double r444826 = x;
        double r444827 = y;
        double r444828 = r444826 - r444827;
        double r444829 = z;
        double r444830 = r444829 - r444827;
        double r444831 = r444828 / r444830;
        double r444832 = t;
        double r444833 = r444831 * r444832;
        return r444833;
}
↓
double f(double x, double y, double z, double t) {
        double r444834 = t;
        double r444835 = x;
        double r444836 = y;
        double r444837 = r444835 - r444836;
        double r444838 = z;
        double r444839 = r444838 - r444836;
        double r444840 = r444837 / r444839;
        double r444841 = r444834 * r444840;
        return r444841;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

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Target

Original2.2
Target2.2
Herbie2.2
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.2

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

  3. Applied *-un-lft-identity2.2

    \[\leadsto \frac{x - y}{\color{blue}{1 \cdot \left(z - y\right)}} \cdot t\]

  4. Applied *-un-lft-identity2.2

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x - y\right)}}{1 \cdot \left(z - y\right)} \cdot t\]

  5. Applied times-frac2.2

    \[\leadsto \color{blue}{\left(\frac{1}{1} \cdot \frac{x - y}{z - y}\right)} \cdot t\]

  6. Simplified2.2

    \[\leadsto \left(\color{blue}{1} \cdot \frac{x - y}{z - y}\right) \cdot t\]

  7. Final simplification2.2

    \[\leadsto t \cdot \frac{x - y}{z - y}\]

Reproduce

herbie shell --seed 2020062 +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))