Average Error: 6.5 → 2.0
Time: 2.7s
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 r651052 = x;
        double r651053 = y;
        double r651054 = r651053 - r651052;
        double r651055 = z;
        double r651056 = r651054 * r651055;
        double r651057 = t;
        double r651058 = r651056 / r651057;
        double r651059 = r651052 + r651058;
        return r651059;
}
↓
double f(double x, double y, double z, double t) {
        double r651060 = x;
        double r651061 = y;
        double r651062 = r651061 - r651060;
        double r651063 = z;
        double r651064 = t;
        double r651065 = r651063 / r651064;
        double r651066 = r651062 * r651065;
        double r651067 = r651060 + r651066;
        return r651067;
}

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

Original6.5
Target2.0
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.5

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

  3. Applied *-un-lft-identity6.5

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

  4. Applied times-frac2.0

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

  5. Simplified2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :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)))