Average Error: 6.4 → 1.9
Time: 11.8s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
x + \left(y - x\right) \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r22192855 = x;
        double r22192856 = y;
        double r22192857 = r22192856 - r22192855;
        double r22192858 = z;
        double r22192859 = r22192857 * r22192858;
        double r22192860 = t;
        double r22192861 = r22192859 / r22192860;
        double r22192862 = r22192855 + r22192861;
        return r22192862;
}
↓
double f(double x, double y, double z, double t) {
        double r22192863 = x;
        double r22192864 = y;
        double r22192865 = r22192864 - r22192863;
        double r22192866 = z;
        double r22192867 = t;
        double r22192868 = r22192866 / r22192867;
        double r22192869 = r22192865 * r22192868;
        double r22192870 = r22192863 + r22192869;
        return r22192870;
}

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

Original6.4
Target1.9
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.4

    \[x + \frac{\left(y - x\right) \cdot z}{t}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity6.4

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

  4. Applied times-frac1.9

    \[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{z}{t}}\]

  5. Simplified1.9

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

  6. Final simplification1.9

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))