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

↓

\[x + \frac{y - x}{\frac{t}{z}}\]

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

↓

x + \frac{y - x}{\frac{t}{z}}

double f(double x, double y, double z, double t) {
        double r298444 = x;
        double r298445 = y;
        double r298446 = r298445 - r298444;
        double r298447 = z;
        double r298448 = r298446 * r298447;
        double r298449 = t;
        double r298450 = r298448 / r298449;
        double r298451 = r298444 + r298450;
        return r298451;
}

↓

double f(double x, double y, double z, double t) {
        double r298452 = x;
        double r298453 = y;
        double r298454 = r298453 - r298452;
        double r298455 = t;
        double r298456 = z;
        double r298457 = r298455 / r298456;
        double r298458 = r298454 / r298457;
        double r298459 = r298452 + r298458;
        return r298459;
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Target

Original	6.2
Target	1.9
Herbie	1.8

\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

Initial program 6.2
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
Using strategy rm
Applied associate-/l*1.8
\[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
Final simplification1.8
\[\leadsto x + \frac{y - x}{\frac{t}{z}}\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.0255111955330046e-135) (- x (* (/ z t) (- x y))) (if (< x 4.2750321637007147e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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

In
Out

Error

Try it out

Target

Derivation

Reproduce