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

↓

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

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 r495712 = x;
        double r495713 = y;
        double r495714 = r495713 - r495712;
        double r495715 = z;
        double r495716 = r495714 * r495715;
        double r495717 = t;
        double r495718 = r495716 / r495717;
        double r495719 = r495712 + r495718;
        return r495719;
}

↓

double f(double x, double y, double z, double t) {
        double r495720 = x;
        double r495721 = y;
        double r495722 = r495721 - r495720;
        double r495723 = t;
        double r495724 = z;
        double r495725 = r495723 / r495724;
        double r495726 = r495722 / r495725;
        double r495727 = r495720 + r495726;
        return r495727;
}

Error

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

Target

Original	6.5
Target	1.9
Herbie	1.8

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

Derivation

Initial program 6.5
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
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 2020025 
(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)))

In
Out

Error

Try it out

Target

Derivation

Reproduce