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

↓

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

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

↓

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

double f(double x, double y, double z, double t) {
        double r451624 = x;
        double r451625 = y;
        double r451626 = r451625 - r451624;
        double r451627 = z;
        double r451628 = r451626 * r451627;
        double r451629 = t;
        double r451630 = r451628 / r451629;
        double r451631 = r451624 + r451630;
        return r451631;
}

↓

double f(double x, double y, double z, double t) {
        double r451632 = x;
        double r451633 = z;
        double r451634 = t;
        double r451635 = r451633 / r451634;
        double r451636 = y;
        double r451637 = r451632 - r451636;
        double r451638 = r451635 * r451637;
        double r451639 = r451632 - r451638;
        return r451639;
}

Error

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

Target

Original	6.3
Target	2.1
Herbie	2.0

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

Derivation

Initial program 6.3
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
Simplified2.0
\[\leadsto \color{blue}{x - \frac{z}{t} \cdot \left(x - y\right)}\]
Final simplification2.0
\[\leadsto x - \frac{z}{t} \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2019194 
(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)))

In
Out

Error

Try it out

Target

Derivation

Reproduce