Average Error: 6.9 → 2.1
Time: 3.2s
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 r512093 = x;
        double r512094 = y;
        double r512095 = r512094 - r512093;
        double r512096 = z;
        double r512097 = r512095 * r512096;
        double r512098 = t;
        double r512099 = r512097 / r512098;
        double r512100 = r512093 + r512099;
        return r512100;
}
↓
double f(double x, double y, double z, double t) {
        double r512101 = x;
        double r512102 = y;
        double r512103 = r512102 - r512101;
        double r512104 = z;
        double r512105 = t;
        double r512106 = r512104 / r512105;
        double r512107 = r512103 * r512106;
        double r512108 = r512101 + r512107;
        return r512108;
}

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

Original6.9
Target2.0
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 6.9

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

  3. Applied *-un-lft-identity6.9

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

  4. Applied times-frac2.1

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

  5. Simplified2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2020083 
(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)))