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

↓

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

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 r319125 = x;
        double r319126 = y;
        double r319127 = r319126 - r319125;
        double r319128 = z;
        double r319129 = r319127 * r319128;
        double r319130 = t;
        double r319131 = r319129 / r319130;
        double r319132 = r319125 + r319131;
        return r319132;
}

↓

double f(double x, double y, double z, double t) {
        double r319133 = x;
        double r319134 = y;
        double r319135 = r319134 - r319133;
        double r319136 = t;
        double r319137 = z;
        double r319138 = r319136 / r319137;
        double r319139 = r319135 / r319138;
        double r319140 = r319133 + r319139;
        return r319140;
}

Error

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

Target

Original	6.2
Target	2.0
Herbie	2.2

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

Derivation

Initial program 6.2
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
Using strategy rm
Applied associate-/l*2.2
\[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
Final simplification2.2
\[\leadsto x + \frac{y - x}{\frac{t}{z}}\]

Reproduce

herbie shell --seed 2020003 
(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