Numeric.Histogram:binBounds from Chart-1.5.3

Average Error: 6.5 → 2.1

Time: 19.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r606069 = x;
        double r606070 = y;
        double r606071 = r606070 - r606069;
        double r606072 = z;
        double r606073 = r606071 * r606072;
        double r606074 = t;
        double r606075 = r606073 / r606074;
        double r606076 = r606069 + r606075;
        return r606076;
}

↓

double f(double x, double y, double z, double t) {
        double r606077 = x;
        double r606078 = y;
        double r606079 = r606078 - r606077;
        double r606080 = t;
        double r606081 = z;
        double r606082 = r606080 / r606081;
        double r606083 = r606079 / r606082;
        double r606084 = r606077 + r606083;
        return r606084;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.5
Target	2.1
Herbie	2.1

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

Derivation

1. Initial program 6.5

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

3. Applied associate-/l* 2.1

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

4. Final simplification 2.1

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

Reproduce

herbie shell --seed 2020045 
(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)))